CN101901006A - Optimum control system and method of industrial process with dual-layer optimization - Google Patents

Abstract

An optimum control system of industrial process with dual-layer optimization comprises a field intelligent instrument connected with an industrial process object, a DCS system and an upper computer; the industrial process object, the field intelligent instrument, the DCS system and the upper computer are connected in turn; the upper computer comprises a signal collection module, an initializing module, a constraint conversion module and a dual-layer optimization module. The invention further provides an optimum control method of industrial process with dual-layer optimization, which converts the optimum control problem with boundary fixing constraint through a dual-layer plan strategy into a dual-layer optimization problem, to carry out iterative optimization. The invention can precisely work out the optimum control problem of industrial process with boundary fixing feature, with stable and effective solution and good precision. It is an optimum control system and method with wide application.

Description

Double-layer optimized industrial process optimal control system and method

Technical Field

The invention relates to the field of industrial process control, in particular to an optimal control system for an industrial process with double-layer optimization.

Background

With the increasing demand of the industrial process for the online optimal control, it has become more and more important to improve the solving performance of the optimal control algorithm and improve the calculation efficiency and accuracy of the online application thereof.

Industrial process optimal control problems often have state variable side-value fixed constraints such as limits on valves, reactor capacity, pressure, mole fraction, etc. Therefore, the edge value fixing problem is a leading edge and a hot spot of the industrial process optimal control research.

The penalty function method is a common strategy for processing the edge value fixing problem, and adds a penalty function item on the basis of an original objective function to form a new objective function, so that the edge value fixing constraint in a dynamic model is eliminated, but the effectiveness of the penalty function method is closely related to the value of a penalty factor, the selected value is ill-conditioned, the calculation effect is seriously influenced, and how to select a proper penalty factor has no rule and can be circulated, so that the gradual trial calculation is often needed, and the efficiency is lower.

Disclosure of Invention

In order to overcome the defects that the existing penalty function method can cause ill-condition phenomenon when processing the edge value fixing optimal control problem, the calculation is inaccurate, and the solving efficiency is low, the invention provides the double-layer optimization industrial process optimal control system and method which can accurately and quickly find the optimal solution of the edge value fixing problem, and have high stability and wide applicability.

The technical scheme adopted by the invention for solving the technical problems is as follows:

the utility model provides a double-deck industrial process optimal control system who optimizes, includes on-the-spot intelligent detection instrument, DCS system and the host computer of being connected with the industrial process object, on-the-spot intelligent detection instrument, DCS system and host computer link to each other in proper order, the host computer include:

the signal acquisition module is used for setting sampling time and acquiring dynamic information of the industrial process object uploaded by the on-site intelligent instrument;

the initialization module is used for setting initial parameters, discretizing decision variables z (t) and carrying out initial assignment, and comprises the following specific steps:

(3.1) time domain [0, t_f]The average division into N small segments: [0, t ]₁]，[t₁，t₂]，…，[t_N-1，t_N]Wherein, t_N＝t_f(ii) a Each time segment having a length t_f/N，t_fIndicating a termination time;

(3.2) discretizing the N-dimensional decision variables z (t) on the time segments in step (3.1), i.e. each decision variable is represented by N segment constants, and taking the initial decision variable z⁰Is an arbitrary constant;

(3.3) setting the optimized convergence precision of the inner and outer layers as zeta₁、ζ₂When the iteration error of the optimized target value is smaller than the convergence precision, stopping iteration, wherein the iteration times are k and l respectively; setting the initial search step length of the inner layer optimization as alpha 0 and gamma 0, and the initial decision variable of the iterative search as z1⁰；

The constraint transformation module is used for transforming the control variable boundary constraint and the state variable final value constraint in the boundary value fixed optimal control problem, and adopts the following steps to complete the following steps:

(3.1) processing the control variable boundary constraints by intermediate variables, i.e. for the boundary constraints having the formula (1)

u_min≤u(t)≤u_max (1)

m dimensional control variableAmount u (t), u_min、u_maxAll the variables are constants which respectively correspond to the lower bound and the upper bound of the control variable, subscripts min and max respectively represent the minimum value and the maximum value, and the following transformation is adopted:

u(t)＝0.5(u_max-u_min)×{sin[z(t)]+1}+u_min (2)

converting u (t) into a trigonometric function expression of an intermediate variable z (t) which is not constrained by a boundary, and solving the z (t) as a decision variable of an optimal control problem;

(3.2) converting the state variable final value constraint into a new objective function, i.e. for the final value constraint equation (3):

x_j(t_f)＝x_jf j＝1，2，..，c (3)

state variable x of_j(t) where c represents the number of state variables constrained by the final value, x_jfGiven a constant, x_j(t_f) Represents a state variable x_j(t) at terminal time t_fThe following objective function formula (4) is constructed:

<math><mrow><msub><mi>J</mi><mn>1</mn></msub><mo>=</mo><munderover><mi>&Sigma;</mi><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mi>c</mi></munderover><msup><mrow><mo>[</mo><msub><mi>x</mi><mi>j</mi></msub><mrow><mo>(</mo><msub><mi>t</mi><mi>f</mi></msub><mo>)</mo></mrow><mo>-</mo><msub><mi>x</mi><mi>jf</mi></msub><mo>]</mo></mrow><mn>2</mn></msup><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>4</mn><mo>)</mo></mrow></mrow></math>

J₁an inner layer objective function solved for the double-layer optimization module;

a double-layer optimization module for finding optimal controlObjective function J of problem making₂In the optimum case of the method,

and can satisfy the final value constraint equation (3) and the state equation (6):

$\frac{\mathrm{dx}\left(t\right)}{\mathrm{dt}}=f[x\left(t\right),z\left(t\right),t],x\left(0\right)=x_0---\left(6\right)$

is determined by the optimal decision variable z^*(t) wherein,

ψ denotes the components of the objective function under endpoint conditions and over a period of time, x denotes a given n-dimensional state variable, x₀The variable value of the state at the initial time (t is 0), f is a function variable, and the solution is carried out by adopting an inner-layer and outer-layer optimized structure:

(4.1) inner layer optimization, i.e. finding the objective function J₁The optimal decision variable z1(t), and z1(t) must satisfy equation of state (6) and inner-layer optimized equation of covariate (7):

<math><mrow><mfrac><mrow><mi>d&lambda;</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow><mi>dt</mi></mfrac><mo>=</mo><mo>-</mo><mi>&lambda;</mi><msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mi>T</mi></msup><mo>&CenterDot;</mo><mfrac><mrow><mo>&PartialD;</mo><mi>f</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>]</mo></mrow><mrow><mo>&PartialD;</mo><mi>x</mi></mrow></mfrac><mo>,</mo></mrow></math> <math><mrow><mi>&lambda;</mi><mrow><mo>(</mo><msub><mi>t</mi><mi>f</mi></msub><mo>)</mo></mrow><mo>=</mo><mfrac><msub><mrow><mo>&PartialD;</mo><mi>J</mi></mrow><mn>1</mn></msub><mrow><mo>&PartialD;</mo><mi>x</mi><mrow><mo>(</mo><msub><mi>t</mi><mi>f</mi></msub><mo>)</mo></mrow></mrow></mfrac><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>7</mn><mo>)</mo></mrow></mrow></math>

wherein, λ (T) represents m dimensional covariates, superscript T represents variable transposition, and equations (6) and (7) form an inner layer ordinary differential equation system; transmitting an optimal decision variable z1(t) obtained by optimizing the inner layer to the outer layer to serve as an initial solution of the outer layer optimization;

(4.2) outer optimization, i.e. searching the objective function J based on the inner optimization₂The optimal decision variable z2(t), and z2(t) must satisfy the state equation (6) and the outer optimized covariant equation (8):

<math><mrow><mfrac><mrow><mi>d&theta;</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow><mi>dt</mi></mfrac><mo>=</mo><mo>-</mo><mfrac><mrow><mo>&PartialD;</mo><mi>&psi;</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>]</mo></mrow><mrow><mo>&PartialD;</mo><mi>x</mi></mrow></mfrac><mo>-</mo><mi>&theta;</mi><msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mi>T</mi></msup><mo>&CenterDot;</mo><mfrac><mrow><mo>&PartialD;</mo><mi>f</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>]</mo></mrow><mrow><mo>&PartialD;</mo><mi>x</mi></mrow></mfrac><mo>,</mo></mrow></math>

wherein θ (t) represents an m-dimensional covariant,

psi denotes the objective function J at endpoint conditions and over time, respectively₂The formula (6) and the formula (8) form an outer layer ordinary differential equation system; the optimal decision variable z2(t) obtained by the outer optimization is the optimal solution z of the double-layer optimization^*(t), corresponding J₂The value is the optimal target value J of the double-layer optimization^*；

Then, the optimal result z obtained by double-layer optimization is saved^*(t) and J^*。

As a preferred solution: in the double-layer optimization module, the inner-layer optimization and the outer-layer optimization are carried out by adopting the following steps:

the inner layer optimization of the step (4.1) is realized according to the following algorithm steps, and the superscript k represents the iteration number:

4.1.1) choosing an initial point z1 of the iteration⁰And if k is equal to l is equal to 0, then z1⁰＝z⁰Else z1⁰Value z2 as skin input^l；

4.1.2) iteration point z1 of the k-th time^kSubstituting the k into the inner layer ordinary differential equation system, when k is 0, z1^k＝z1⁰Respectively performing forward integration and backward integration on the expressions (6) and (7), solving a state variable x and a covariate lambda, and calculating a target value J of the kth iteration by the expression (4)₁ ^k；

4.1.3) determining whether the convergence condition expression (9) is satisfiedImmediately, if true, the optimal solution z1 for the inner layer^*＝z1^kMixing z1^*Transmitting the initial solution to the outer layer as the initial solution of the outer layer iteration; otherwise, turning to step (4.1.4), equation (9) is expressed as follows: (ii) a

|J₁ ^k-J₁ ^j+1|≤ζ₁ (9)

4.1.4) the state variable x and the iteration point z1^kCalculation of gradient g by substituting formula (10)^k：

<math><mrow><msup><mi>g</mi><mi>k</mi></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><mi>&lambda;</mi><msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mi>T</mi></msup><mo>&CenterDot;</mo><mfrac><mrow><mo>&PartialD;</mo><mi>f</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mn>1</mn><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>]</mo></mrow><mrow><mo>&PartialD;</mo><mi>z</mi><mn>1</mn><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>10</mn><mo>)</mo></mrow></mrow></math>

Saving z1^kAnd g^kThen calculate the search direction d^k，d^k-1Indicating the search direction, β, of the previous iteration^kAre the intermediate parameters:

<math><mrow><msup><mi>d</mi><mi>k</mi></msup><mo>=</mo><mfenced open='{' close=''><mtable><mtr><mtd><mo>-</mo><msup><mi>g</mi><mi>k</mi></msup><mo>,</mo></mtd><mtd><mi>k</mi><mo>=</mo><mn>1</mn><mo>;</mo></mtd></mtr><mtr><mtd><mo>-</mo><msup><mi>g</mi><mi>k</mi></msup><mo>+</mo><msup><mi>&beta;</mi><mi>k</mi></msup><msup><mi>d</mi><mrow><mi>k</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>,</mo></mtd><mtd><mi>k</mi><mo>&GreaterEqual;</mo><mn>2</mn><mo>.</mo></mtd></mtr></mtable></mfenced></mrow></math> wherein, <math><mrow><msup><mi>&beta;</mi><mi>k</mi></msup><mo>=</mo><mfrac><mrow><msup><mrow><mo>(</mo><msup><mi>g</mi><mi>k</mi></msup><mo>)</mo></mrow><mi>T</mi></msup><mrow><mo>(</mo><msup><mi>g</mi><mi>k</mi></msup><mo>-</mo><msup><mi>g</mi><mrow><mi>k</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>)</mo></mrow></mrow><msup><mrow><mo>|</mo><mo>|</mo><msup><mi>g</mi><mrow><mi>k</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>|</mo><mo>|</mo></mrow><mn>2</mn></msup></mfrac><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>11</mn><mo>)</mo></mrow></mrow></math>

4.1.5) determining the optimal search step size α^k: if k is 0, then α is taken^kα 0, go to step 4.1.6);

otherwise, from the current iteration point z1^kStarting in the direction d^kOne-dimensional search is carried out to find the optimal step factor alpha^*And satisfies the following conditions:

<math><mrow><mi>H</mi><mn>1</mn><mrow><mo>(</mo><msup><mrow><mi>z</mi><mn>1</mn></mrow><mi>k</mi></msup><mo>+</mo><msup><mi>&alpha;</mi><mo>*</mo></msup><mo>&CenterDot;</mo><msup><mi>d</mi><mi>k</mi></msup><mo>)</mo></mrow><mo>=</mo><munder><mi>min</mi><mrow><mi>&alpha;</mi><mo>&GreaterEqual;</mo><mn>0</mn></mrow></munder><mi>H</mi><mn>1</mn><mrow><mo>(</mo><msup><mrow><mi>z</mi><mn>1</mn></mrow><mi>k</mi></msup><mo>+</mo><mi>&alpha;</mi><mo>&CenterDot;</mo><msup><mi>d</mi><mi>k</mi></msup><mo>)</mo></mrow><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>12</mn><mo>)</mo></mrow></mrow></math>

wherein H1 represents the Hamiltonian of the inner layer optimization problem, calculated by equation (13),

represents finding the step size α in α ∈ [0, + ∞) ] that minimizes H1^*Formula (13) is expressed as follows:

H1＝λ(t)^T·f[x(t)，z1(t)，t] (13)

get

D is a coefficient integer value;

4.1.6) calculate the next iteration point

z1^k+1＝z1^k+α^k·d^k (14)

4.1.7) add 1 to the number of iterations, i.e. k ═ k +1, z1 in step 4.1.6)^k+1Saved as current point z1^kContinuing iteration, and turning to the step 4.1.2);

the outer optimization of said step (4.2) is carried out according to the following algorithm steps, the superscript l representing the current iteration number:

4.2.1) taking the current iteration point of the outer optimization as z2^l＝z1^*The initial value of l is 0;

4.2.2) mixing of z2^lSubstituting into an outer ordinary differential equation system, respectively performing forward integration and backward integration on the equations (6) and (8), solving a state variable x and a co-state variable theta, and calculating a target value J of the 1 st iteration by using the equation (5)₂ ^l；

4.2.3) judging whether the convergence condition formula (15) is satisfied, if so, judging the optimal solution z of the double-layer optimization^*＝z2^lOptimum objective function value J^*＝J₂ ^lSaving and delivering z^*And J^*To an output display module; otherwise, turning to the next step; formula (15) is expressed as follows:

|J₂ ^l-J₂ ^l+1|≤ζ₂ (15)

4.2.4) the state variable x and the iteration point z2^lCalculation of gradient h by substitution formula (16)^l：

<math><mrow><msup><mi>h</mi><mi>l</mi></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><mfrac><mrow><mo>&PartialD;</mo><mi>&psi;</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mn>2</mn><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>]</mo></mrow><mrow><mo>&PartialD;</mo><mi>z</mi><mn>2</mn><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac><mo>+</mo><mi>&theta;</mi><msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mi>T</mi></msup><mo>&CenterDot;</mo><mfrac><mrow><mo>&PartialD;</mo><mi>f</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mn>2</mn><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>]</mo></mrow><mrow><mo>&PartialD;</mo><mi>z</mi><mn>2</mn><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>16</mn><mo>)</mo></mrow></mrow></math>

Saving z2^lAnd h^lThen calculate the search direction e^l，e^l-1Representing the search direction, η, of a previous iteration^lAre the intermediate parameters:

<math><mrow><msup><mi>e</mi><mi>l</mi></msup><mo>=</mo><mfenced open='{' close=''><mtable><mtr><mtd><mo>-</mo><msup><mi>h</mi><mi>l</mi></msup><mo>,</mo></mtd><mtd><mi>l</mi><mo>=</mo><mn>1</mn><mo>;</mo></mtd></mtr><mtr><mtd><mo>-</mo><msup><mi>h</mi><mi>l</mi></msup><mo>+</mo><msup><mi>&eta;</mi><mi>l</mi></msup><msup><mi>e</mi><mrow><mi>l</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>,</mo></mtd><mtd><mi>l</mi><mo>&GreaterEqual;</mo><mn>2</mn><mo>.</mo></mtd></mtr></mtable></mfenced></mrow></math> wherein, <math><mrow><msup><mi>&eta;</mi><mi>l</mi></msup><mo>=</mo><mfrac><mrow><msup><mrow><mo>(</mo><msup><mi>h</mi><mi>l</mi></msup><mo>)</mo></mrow><mi>T</mi></msup><mrow><mo>(</mo><msup><mi>h</mi><mi>l</mi></msup><mo>-</mo><msup><mi>h</mi><mrow><mi>l</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>)</mo></mrow></mrow><msup><mrow><mo>|</mo><mo>|</mo><msup><mi>h</mi><mrow><mi>l</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>|</mo><mo>|</mo></mrow><mn>2</mn></msup></mfrac><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>17</mn><mo>)</mo></mrow></mrow></math>

4.2.5) determining the optimal search step size γ^l: if l is 0, then take γ^lGo to step 4.2.6, γ 0);

otherwise, from the current iteration point z2^lStarting in the direction h^lOne-dimensional search is carried out to find the optimal step factor gamma^*And satisfies the following conditions:

<math><mrow><mi>H</mi><mn>2</mn><mrow><mo>(</mo><msup><mrow><mi>z</mi><mn>2</mn></mrow><mi>l</mi></msup><mo>+</mo><msup><mi>&gamma;</mi><mo>*</mo></msup><mo>&CenterDot;</mo><msup><mi>e</mi><mi>l</mi></msup><mo>)</mo></mrow><mo>=</mo><mrow><munder><mi>min</mi><mrow><mi>&gamma;</mi><mo>&GreaterEqual;</mo><mn>0</mn></mrow></munder><mi>H</mi><mn>2</mn><mrow><mo>(</mo><msup><mrow><mi>z</mi><mn>2</mn></mrow><mi>l</mi></msup><mo>+</mo><msup><mrow><mi>&gamma;</mi><mo>&CenterDot;</mo><mi>e</mi></mrow><mi>l</mi></msup><mo>)</mo></mrow><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>18</mn><mo>)</mo></mrow></mrow></mrow></math>

wherein H2 represents the Hamiltonian of the skin optimization problem, calculated from equation (19),

represents finding the step size γ that minimizes H2 in γ ∈ [0, + ∞) ]^*；

H2＝ψ[x(t)，z2(t)，t]+θ(t)^T·f[x(t)，z2(t)，t] (19)

Get

B is a coefficient integer value;

4.2.6) calculate the next iteration point:

z2^l+1＝z2^l+γ^l·d^l (20)

4.2.7) add 1 to the number of iterations, i.e. l ═ l +1, z2 in step 4.2.6)^l+1Saved as current point z2^lContinue iteration, go to step 4.2.2).

Further, the host computer still includes: an output display module for outputting the optimal decision result z calculated by the double-layer optimization module^*(t) conversion into an optimal control trajectory u by equation (2)^*(t) then adding u^*(t) and an optimum target value J^*And transmitting the information to the DCS, and displaying the obtained optimization result information in the DCS.

A double-layer optimized optimal control method for an industrial process comprises the following steps:

1) specifying state variables and control variables for optimum control in a DCS system, and setting upper and lower boundaries u of the control variables according to conditions of an actual production environment and conditions of operation restrictions_max、u_minAnd sampling period of DCS, and corresponding variables in DCS databaseHistorical data of (2), control variable upper and lower boundary values u_max、u_minTransmitting to an upper computer;

2) and (3) converting an edge value fixed constraint in the optimal control problem:

(2.1) constraint with boundary using intermediate variable z (t)

u_min≤u(t)≤u_max (1)

The m-dimensional control variable u (t) of (a):

u(t)＝0.5(u_max-u_min)×{sin[z(t)]+1}+u_min (2)

converting u (t) into a trigonometric function expression of an intermediate variable z (t) which is not constrained by a boundary, and solving the z (t) as a decision variable of an optimal control problem;

(2.2) converting the final value constraint equation (3) of the state variable into a new objective function J₁Formula (4):

x_j(t_f)＝x_jf(j＝1，2，..，c) (3)

<math><mrow><msub><mi>J</mi><mn>1</mn></msub><mo>=</mo><munderover><mi>&Sigma;</mi><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mi>c</mi></munderover><msup><mrow><mo>[</mo><msub><mi>x</mi><mi>j</mi></msub><mrow><mo>(</mo><msub><mi>t</mi><mi>f</mi></msub><mo>)</mo></mrow><mo>-</mo><msub><mi>x</mi><mi>jf</mi></msub><mo>]</mo></mrow><mn>2</mn></msup><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>4</mn><mo>)</mo></mrow></mrow></math>

where c denotes the number of state variables which are subject to a final value constraint, x_jfGiven a constant, x_j(t_f) Represents a state variable x_j(t) at terminal time t_fValue of (A), J₁The method is also an inner layer objective function solved by the double-layer optimization module;

3) setting initial parameters, initializing data input by a DCS, and completing the steps as follows:

(3.1) time domain [0, t_f]The average division into N small segments: [0, t ]₁]，[t₁，t₂]，…，[t_N-1，t_N]Wherein t is_N＝t_f(ii) a Each time segment having a length t_f/N；

(3.2) discretizing the N-dimensional decision variables z (t) on (3.1) said time segments, i.e. each decision variable is represented by N segment constants, and taking the initial decision variable z⁰Is an arbitrary constant;

(3.3) setting the optimized convergence precision of the inner and outer layers as zeta₁、ζ₂The iteration times are k and l respectively; setting the initial search step length of the inner layer optimization as alpha 0 and gamma 0, and the initial decision variable of the iterative search as z1⁰；

4) Finding the optimal decision variable z which not only optimizes the objective function formula (5) of the optimal control problem, but also satisfies the final value constraint formula (3) and the state equation (6)^*(t) and mixing z^*(t) and corresponding optimal target value J^*And transmitting the data to an output display module, and solving by adopting an inner-layer and outer-layer optimized structure:

$\frac{\mathrm{dx}\left(t\right)}{\mathrm{dt}}=f[x\left(t\right),z\left(t\right),t],$ x(0)＝x₀ (6)

(4.1) inner layer optimization, i.e. finding the objective function J₁The optimal decision variable z1(t), and z1(t) must satisfy equation of state (6) and inner-layer optimized equation of covariate (7):

<math><mrow><mfrac><mrow><mi>d&lambda;</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow><mi>dt</mi></mfrac><mo>=</mo><mo>-</mo><mi>&lambda;</mi><msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mi>T</mi></msup><mo>&CenterDot;</mo><mfrac><mrow><mo>&PartialD;</mo><mi>f</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>]</mo></mrow><mrow><mo>&PartialD;</mo><mi>x</mi></mrow></mfrac><mo>,</mo></mrow></math> <math><mrow><mi>&lambda;</mi><mrow><mo>(</mo><msub><mi>t</mi><mi>f</mi></msub><mo>)</mo></mrow><mo>=</mo><mfrac><msub><mrow><mo>&PartialD;</mo><mi>J</mi></mrow><mn>1</mn></msub><mrow><mo>&PartialD;</mo><mi>x</mi><mrow><mo>(</mo><msub><mi>t</mi><mi>f</mi></msub><mo>)</mo></mrow></mrow></mfrac><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>7</mn><mo>)</mo></mrow></mrow></math>

wherein, λ (T) represents m dimensional covariates, superscript T represents variable transposition, and equations (6) and (7) form an inner layer ordinary differential equation system; transmitting an optimal decision variable z1(t) obtained by optimizing the inner layer to the outer layer to serve as an initial solution of the outer layer optimization;

(4.2) outer optimization, i.e. searching the objective function J based on the inner optimization₂The optimal decision variable z2(t), and z2(t) must satisfy equation of state (6) and the outerLayer-optimized collaborative equation (8):

<math><mrow><mfrac><mrow><mi>d&theta;</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow><mi>dt</mi></mfrac><mo>=</mo><mo>-</mo><mfrac><mrow><mo>&PartialD;</mo><mi>&psi;</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>]</mo></mrow><mrow><mo>&PartialD;</mo><mi>x</mi></mrow></mfrac><mo>-</mo><msup><mrow><mi>&theta;</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow><mi>T</mi></msup><mo>&CenterDot;</mo><mfrac><mrow><mo>&PartialD;</mo><mi>f</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>]</mo></mrow><mrow><mo>&PartialD;</mo><mi>x</mi></mrow></mfrac><mo>,</mo></mrow></math>

wherein θ (t) represents an m-dimensional covariant,

psi denotes the objective function J at endpoint conditions and over time, respectively₂The formula (6) and the formula (8) form an outer layer ordinary differential equation system; the optimal decision variable z2(t) obtained by the outer optimization is the optimal solution z of the double-layer optimization^*(t), corresponding J₂The value is the optimal target value J of the double-layer optimization^*；

Then, the optimal result z obtained by double-layer optimization is saved^*(t) and J^*。

As a preferred solution: the inner layer optimization of the step (4.1) is realized according to the following algorithm steps, and the superscript k represents the iteration number:

4.1.1) choosing an initial point z1 of the iteration⁰And if k is equal to l is equal to 0, then z1⁰＝z⁰Else z1⁰Value z2 as skin input^l；

4.1.2) iteration point z1 of the k-th time^kSubstituting the k into the inner layer ordinary differential equation system, when k is 0, z1^k＝z1⁰Respectively performing forward integration and backward integration on the expressions (6) and (7), solving a state variable x and a covariate lambda, and calculating a target value J of the kth iteration by the expression (4)₁ ^k；

4.1.3) determining whether the convergence condition expression (9) is satisfied, and if so, determining the optimal solution z1 of the inner layer^*＝z1^kMixing z1^*Transmitting the initial solution to the outer layer as the initial solution of the outer layer iteration; otherwise, turning to step (4.1.4), equation (9) is expressed as follows: (ii) a

|J₁ ^k-J₁ ^j+1|≤ζ₁ (9)

4.1.4) the state variable x and the iteration point z1^kCalculation of gradient g by substituting formula (10)^k：

<math><mrow><msup><mi>g</mi><mi>k</mi></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><mi>&lambda;</mi><msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mi>T</mi></msup><mo>&CenterDot;</mo><mfrac><mrow><mo>&PartialD;</mo><mi>f</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mn>1</mn><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>]</mo></mrow><mrow><mo>&PartialD;</mo><mi>z</mi><mn>1</mn><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>10</mn><mo>)</mo></mrow></mrow></math>

Saving z1^kAnd g^kThen calculate the search direction d^k，d^k-1Indicating the search direction, β, of the previous iteration^kAre the intermediate parameters:

<math><mrow><msup><mi>d</mi><mi>k</mi></msup><mo>=</mo><mfenced open='{' close=''><mtable><mtr><mtd><mo>-</mo><msup><mi>g</mi><mi>k</mi></msup><mo>,</mo></mtd><mtd><mi>k</mi><mo>=</mo><mn>1</mn><mo>;</mo></mtd></mtr><mtr><mtd><mo>-</mo><msup><mi>g</mi><mi>k</mi></msup><mo>+</mo><msup><mi>&beta;</mi><mi>k</mi></msup><msup><mi>d</mi><mrow><mi>k</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>,</mo></mtd><mtd><mi>k</mi><mo>&GreaterEqual;</mo><mn>2</mn><mo>.</mo></mtd></mtr></mtable></mfenced></mrow></math> wherein, <math><mrow><msup><mi>&beta;</mi><mi>k</mi></msup><mo>=</mo><mfrac><mrow><msup><mrow><mo>(</mo><msup><mi>g</mi><mi>k</mi></msup><mo>)</mo></mrow><mi>T</mi></msup><mrow><mo>(</mo><msup><mi>g</mi><mi>k</mi></msup><mo>-</mo><msup><mi>g</mi><mrow><mi>k</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>)</mo></mrow></mrow><msup><mrow><mo>|</mo><mo>|</mo><msup><mi>g</mi><mrow><mi>k</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>|</mo><mo>|</mo></mrow><mn>2</mn></msup></mfrac><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>11</mn><mo>)</mo></mrow></mrow></math>

4.1.5) determining the optimal search step size α^k: if k is 0, then α is taken^kα 0, go to step 4.1.6);

otherwise, from the current iteration point z1^kStarting in the direction d^kOne-dimensional search is carried out to find the optimal step factor alpha^*And satisfies the following conditions:

<math><mrow><mi>H</mi><mn>1</mn><mrow><mo>(</mo><msup><mrow><mi>z</mi><mn>1</mn></mrow><mi>k</mi></msup><mo>+</mo><msup><mi>&alpha;</mi><mo>*</mo></msup><mo>&CenterDot;</mo><msup><mi>d</mi><mi>k</mi></msup><mo>)</mo></mrow><mo>=</mo><munder><mi>min</mi><mrow><mi>&alpha;</mi><mo>&GreaterEqual;</mo><mn>0</mn></mrow></munder><mi>H</mi><mn>1</mn><mrow><mo>(</mo><msup><mrow><mi>z</mi><mn>1</mn></mrow><mi>k</mi></msup><mo>+</mo><mi>&alpha;</mi><mo>&CenterDot;</mo><msup><mi>d</mi><mi>k</mi></msup><mo>)</mo></mrow><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>12</mn><mo>)</mo></mrow></mrow></math>

wherein H1 represents the Hamiltonian of the inner layer optimization problem, calculated by equation (13),

represents finding the step size α in α ∈ [0, + ∞) ] that minimizes H1^*Formula (13) is expressed as follows:

H1＝λ(t)^T·f[x(t)，z1(t)，t] (13)

get

D is a coefficient integer value;

4.1.6) calculate the next iteration point

z1^k+1＝z1^k+α^k·d^k (14)

4.1.7) add 1 to the number of iterations, i.e. k ═ k +1, z1 in step 4.1.6)^k+1Saved as current point z1^kContinuing iteration, and turning to the step 4.1.2);

the outer optimization of said step (4.2) is carried out according to the following algorithm steps, the superscript l representing the current iteration number:

4.2.1) taking the current iteration point of the outer optimization as z2^l＝z1^*An initial value of0；

4.2.2) mixing of z2^lSubstituting into an outer ordinary differential equation system, respectively performing forward integration and backward integration on the equations (6) and (8), solving a state variable x and a co-state variable theta, and calculating a target value J of the 1 st iteration by using the equation (5)₂ ^l；

4.2.3) judging whether the convergence condition formula (15) is satisfied, if so, judging the optimal solution z of the double-layer optimization^*＝z2^lOptimum objective function value J^*＝J₂ ^lSaving and delivering z^*And J^*To an output display module; otherwise, turning to the next step; formula (15) is expressed as follows:

|J₂ ^l-J₂ ^l+1|≤ζ₂ (15)

4.2.4) the state variable x and the iteration point z2^lCalculation of gradient h by substitution formula (16)^l：

<math><mrow><msup><mi>h</mi><mi>l</mi></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><mfrac><mrow><mo>&PartialD;</mo><mi>&psi;</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mn>2</mn><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>.</mo><mi>t</mi><mo>]</mo></mrow><mrow><mo>&PartialD;</mo><mi>z</mi><mn>2</mn><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac><mo>+</mo><mi>&theta;</mi><msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mi>T</mi></msup><mo>&CenterDot;</mo><mfrac><mrow><mo>&PartialD;</mo><mi>f</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mn>2</mn><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>]</mo></mrow><mrow><mo>&PartialD;</mo><mi>z</mi><mn>2</mn><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>16</mn><mo>)</mo></mrow></mrow></math>

Saving z2^lAnd h^lThen calculate the search direction e^l，e^l-1Representing the search direction, η, of a previous iteration^lAre the intermediate parameters:

<math><mrow><msup><mi>e</mi><mi>l</mi></msup><mo>=</mo><mfenced open='{' close=''><mtable><mtr><mtd><mo>-</mo><msup><mi>h</mi><mi>l</mi></msup><mo>,</mo></mtd><mtd><mi>l</mi><mo>=</mo><mn>1</mn><mo>;</mo></mtd></mtr><mtr><mtd><mo>-</mo><msup><mi>h</mi><mi>l</mi></msup><mo>+</mo><msup><mi>&eta;</mi><mi>l</mi></msup><msup><mi>e</mi><mrow><mi>l</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>,</mo></mtd><mtd><mi>l</mi><mo>&GreaterEqual;</mo><mn>2</mn><mo>.</mo></mtd></mtr></mtable></mfenced></mrow></math> wherein, <math><mrow><msup><mi>&eta;</mi><mi>l</mi></msup><mo>=</mo><mfrac><mrow><msup><mrow><mo>(</mo><msup><mi>h</mi><mi>l</mi></msup><mo>)</mo></mrow><mi>T</mi></msup><mrow><mo>(</mo><msup><mi>h</mi><mi>l</mi></msup><mo>-</mo><msup><mi>h</mi><mrow><mi>l</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>)</mo></mrow></mrow><msup><mrow><mo>|</mo><mo>|</mo><msup><mi>h</mi><mrow><mi>l</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>|</mo><mo>|</mo></mrow><mn>2</mn></msup></mfrac><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>17</mn><mo>)</mo></mrow></mrow></math>

4.2.5) determining the optimal search step size γ^l: if l is 0, then take γ^lGo to step 4.2.6, γ 0);

otherwise, from the current iteration point z2^lStarting in the direction h^lOne-dimensional search is carried out to find the optimal step factor gamma^*And satisfies the following conditions:

<math><mrow><mi>H</mi><mn>2</mn><mrow><mo>(</mo><msup><mrow><mi>z</mi><mn>2</mn></mrow><mi>l</mi></msup><mo>+</mo><msup><mi>&gamma;</mi><mo>*</mo></msup><mo>&CenterDot;</mo><msup><mi>e</mi><mi>l</mi></msup><mo>)</mo></mrow><mo>=</mo><munder><mi>min</mi><mrow><mi>&gamma;</mi><mo>&GreaterEqual;</mo><mn>0</mn></mrow></munder><mi>H</mi><mn>2</mn><mrow><mo>(</mo><msup><mrow><mi>z</mi><mn>2</mn></mrow><mi>l</mi></msup><mo>+</mo><mi>&gamma;</mi><mo>&CenterDot;</mo><msup><mi>e</mi><mi>l</mi></msup><mo>)</mo></mrow><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>18</mn><mo>)</mo></mrow></mrow></math>

wherein H2 represents the Hamiltonian of the skin optimization problem, calculated from equation (19),

represents finding the step size γ that minimizes H2 in γ ∈ [0, + ∞) ]^*；

H2＝ψ[x(t)，z2(t)，t]+θ(t)^T·f[x(t)，z2(t)，t] (19)

Get

B is a coefficient integer value;

4.2.6) calculate the next iteration point:

z2^l+1＝z2^l+γ^l·d^l (20)

4.2.7) add 1 to the number of iterations, i.e. l ═ l +1, z2 in step 4.2.6)^l+1Saved as current point z2^lContinue iteration, go to step 4.2.2).

Further, in the step 1), the data of the industrial process object collected by the on-site intelligent instrument is transmitted to a real-time database of the DCS system, the latest data obtained from the database of the DCS system in each sampling period is output to the upper computer, and initialization processing is performed by an initialization module of the upper computer.

Still further, in the step (4.2.3), the obtained optimal decision variable z^*Converting the result into an optimal control curve u^*(t) and displaying u on the human-machine interface of the upper computer^*(t) and an optimum target value J^*(ii) a At the same time, the optimum control curve u^*(t) transmitting the information to a control station of the DCS system through the bus interface, and displaying the obtained optimization result information in the DCS system.

The invention has the following beneficial effects: the method can accurately find the optimal solution of the industrial process optimal control problem with the edge value fixed characteristic, and has high optimal solution efficiency and good stability, thereby having wide application prospect in various fields of industrial process optimal control.

Drawings

FIG. 1 is a hardware block diagram of an industrial process optimization control system provided by the present invention;

fig. 2 is a schematic structure diagram of the upper computer implementing the optimal control method of the present invention.

Detailed Description

The present invention will be described in detail below with reference to the accompanying drawings.

Example 1

Referring to fig. 1 and 2, the double-layer optimized industrial process optimal control system comprises a field intelligent instrument 2 connected with an industrial process object 1, a DCS system and an upper computer 6, wherein the DCS system is composed of a bus interface 3, a control station 4 and a database 5; on-spot intelligent instrument 2, DCS system, host computer 6 pass through field bus and link to each other in proper order, the host computer include:

the signal acquisition module is used for setting sampling time and acquiring dynamic information of the industrial process object uploaded by the on-site intelligent instrument;

the initialization module is used for setting initial parameters, discretizing decision variables z (t) and carrying out initial assignment, and comprises the following specific steps:

(3.1) time domain [0, t_f]The average division into N small segments: [0, t ]₁]，[t₁，t₂]，…，[t_N-1，t_N]Wherein, t_N＝t_f(ii) a Each time segment having a length t_f/N，t_fIndicating a termination time;

(3.2) discretizing the N-dimensional decision variables z (t) on the time segments in step (3.1), i.e. each decision variable is represented by N segment constants, and taking the initial decision variable z⁰Is an arbitrary constant;

(3.3) setting the optimized convergence precision of the inner and outer layers as zeta₁、ζ₂When the iteration error of the optimized target value is smaller than the convergence precision, stopping iteration, wherein the iteration times are k and l respectively; setting the initial search step length of the inner layer optimization as alpha 0 and gamma 0, and the initial decision variable of the iterative search as z1⁰；

The constraint transformation module is used for transforming the control variable boundary constraint and the state variable final value constraint in the boundary value fixed optimal control problem, and adopts the following steps to complete the following steps:

(2.1) processing the control variable boundary constraints through intermediate variables, i.e. for the boundary constraints having the formula (1)

u_min≤u(t)≤u_max (1)

m-dimensional control variable u (t), subscripts min and max respectively represent minimum and maximum values, u_min、u_maxAll are constants, respectively corresponding to the lower and upper bounds of the control variable, byThe following transformations:

u(t)＝0.5(u_max-u_min)×{sin[z(t)]+1}+u_min (2)

converting u (t) into a trigonometric function expression of an intermediate variable z (t) which is not constrained by a boundary, and solving the z (t) as a decision variable of an optimal control problem;

(2.2) converting the state variable final value constraint into a new objective function, i.e. for the final value constraint equation (3):

x_j(t_f)＝x_jf(j＝1，2，...，c) (3)

state variable x of_f(t) where c represents the number of state variables constrained by the final value, x_jfGiven a constant, x_j(t_f) Represents a state variable x_j(t) at terminal time t_fThe following objective function formula (4) is constructed:

<math><mrow><msub><mi>J</mi><mn>1</mn></msub><mo>=</mo><munderover><mi>&Sigma;</mi><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mi>c</mi></munderover><msup><mrow><mo>[</mo><msub><mi>x</mi><mi>j</mi></msub><mrow><mo>(</mo><msub><mi>t</mi><mi>f</mi></msub><mo>)</mo></mrow><mo>-</mo><msub><mi>x</mi><mi>jf</mi></msub><mo>]</mo></mrow><mn>2</mn></msup><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>4</mn><mo>)</mo></mrow></mrow></math>

J₁an inner layer objective function solved for the double-layer optimization module;

a double-layer optimization module for finding an objective function J which not only enables optimal control problems₂In the optimum case of the method,

and can satisfy the final value constraint equation (3) and the state equation (6):

$\frac{\mathrm{dx}\left(t\right)}{\mathrm{dt}}=f[x\left(t\right),z\left(t\right),t],$ x(0)＝x⁰ (6)

is determined by the optimal decision variable z^*(t) in the formulae (5) and (6)

ψ denotes the components of the objective function under endpoint conditions and over a period of time, x denotes a given n-dimensional state variable, x₀The variable value of the state at the initial time (t is 0), f is a function variable, and the solution is carried out by adopting an inner-layer and outer-layer optimized structure:

(4.1) inner layer optimization with the aim of finding the objective function J₁The optimal decision variable z1(t), and z1(t) must satisfy the state equation (6)) and the inner-layer optimized collaborative equation (7):

<math><mrow><mfrac><mrow><mi>d&lambda;</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow><mi>dt</mi></mfrac><mo>=</mo><mo>-</mo><mi>&lambda;</mi><msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mi>T</mi></msup><mo>&CenterDot;</mo><mfrac><mrow><mo>&PartialD;</mo><mi>f</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>]</mo></mrow><mrow><mo>&PartialD;</mo><mi>x</mi></mrow></mfrac><mo>,</mo></mrow></math> <math><mrow><mi>&lambda;</mi><mrow><mo>(</mo><msub><mi>t</mi><mi>f</mi></msub><mo>)</mo></mrow><mo>=</mo><mfrac><msub><mrow><mo>&PartialD;</mo><mi>J</mi></mrow><mn>1</mn></msub><mrow><mo>&PartialD;</mo><mi>x</mi><mrow><mo>(</mo><msub><mi>t</mi><mi>f</mi></msub><mo>)</mo></mrow></mrow></mfrac><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>7</mn><mo>)</mo></mrow></mrow></math>

wherein lambda (T) represents an m-dimensional co-modal variable, superscript T represents a variable transpose, and equations (6) and (7) form an inner-layer ordinary differential equation system; transmitting an optimal decision variable z1(t) obtained by optimizing the inner layer to the outer layer to serve as an initial solution of the outer layer optimization;

(4.2) outer optimization, the purpose is to search the objective function J based on the inner optimization₂The optimal decision variable z2(t), and z2(t) must satisfy the state equation (6) and the outer optimized covariant equation (8):

<math><mrow><mfrac><mrow><mi>d&theta;</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow><mi>dt</mi></mfrac><mo>=</mo><mo>-</mo><mfrac><mrow><mo>&PartialD;</mo><mi>&psi;</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>]</mo></mrow><mrow><mo>&PartialD;</mo><mi>x</mi></mrow></mfrac><mo>-</mo><msup><mrow><mi>&theta;</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow><mi>T</mi></msup><mo>&CenterDot;</mo><mfrac><mrow><mo>&PartialD;</mo><mi>f</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>]</mo></mrow><mrow><mo>&PartialD;</mo><mi>x</mi></mrow></mfrac><mo>,</mo></mrow></math>

wherein θ (t) represents an m-dimensional covariant,

psi denotes the objective function J at endpoint conditions and over time, respectively₂The formula (6) and the formula (8) form an outer layer ordinary differential equation system; the optimal decision variable z2(t) obtained by the outer optimization is the optimal solution z of the double-layer optimization^*(t), corresponding J₂The value is the optimal target value J of the double-layer optimization^*；

Then, the optimal result z obtained by double-layer optimization is saved^*(t) and J^*。

And the optimal result z^*(t) and J^*Transmitting to an output display module;

an output display module for outputting the optimal decision result z calculated by the double-layer optimization module^*(t) conversion into an optimal control trajectory u by equation (2)^*(t) then adding u^*(t) and an optimum target value J^*And transmitting the information to the DCS, and displaying the obtained optimization result information in the DCS.

The double-layer optimization module of the upper computer performs inner-layer and outer-layer optimization by adopting the following steps. The inner layer optimization of the step (4.1) is realized according to the following algorithm steps, and the superscript k represents the iteration number:

4.1.1) choosing an initial point z1 of the iteration⁰And if k is equal to l is equal to 0, then z1⁰＝z⁰Else z1⁰Value z2 as skin input^l；

4.1.2) iteration point z1 of the k-th time^kSubstituting the k into the inner layer ordinary differential equation system, when k is 0, z1^k＝z1⁰Forward integration and backward integration are performed on equations (6) and (7), respectivelySolving the state variable x and the covariate lambda, and calculating the target value J of the kth iteration by the formula (4)₁ ^k；

4.1.3) determining whether the convergence condition expression (9) is satisfied, and if so, determining the optimal solution z1 of the inner layer^*＝z1^kMixing z1^*Transmitting the initial solution to the outer layer as the initial solution of the outer layer iteration; otherwise, turning to the step (4.1.4);

|J₁ ^k-J₁ ^k+1|≤ζ₁ (9)

4.1.4) the state variable x and the iteration point z1^kCalculation of gradient g by substituting formula (10)^k：

<math><mrow><msup><mi>g</mi><mi>k</mi></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><mi>&lambda;</mi><msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mi>T</mi></msup><mo>&CenterDot;</mo><mfrac><mrow><mo>&PartialD;</mo><mi>f</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mn>1</mn><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>]</mo></mrow><mrow><mo>&PartialD;</mo><mi>z</mi><mn>1</mn><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>10</mn><mo>)</mo></mrow></mrow></math>

Saving z1^kAnd g^kThen calculate the search direction d^k，d^k-1Indicating the search direction, β, of the previous iteration^kAre the intermediate parameters:

<math><mrow><msup><mi>d</mi><mi>k</mi></msup><mo>=</mo><mfenced open='{' close=''><mtable><mtr><mtd><mo>-</mo><msup><mi>g</mi><mi>k</mi></msup><mo>,</mo></mtd><mtd><mi>k</mi><mo>=</mo><mn>1</mn><mo>;</mo></mtd></mtr><mtr><mtd><mo>-</mo><msup><mi>g</mi><mi>k</mi></msup><mo>+</mo><msup><mi>&beta;</mi><mi>k</mi></msup><msup><mi>d</mi><mrow><mi>k</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>,</mo></mtd><mtd><mi>k</mi><mo>&GreaterEqual;</mo><mn>2</mn><mo>.</mo></mtd></mtr></mtable></mfenced></mrow></math> wherein, <math><mrow><msup><mi>&beta;</mi><mi>k</mi></msup><mo>=</mo><mfrac><mrow><msup><mrow><mo>(</mo><msup><mi>g</mi><mi>k</mi></msup><mo>)</mo></mrow><mi>T</mi></msup><mrow><mo>(</mo><msup><mi>g</mi><mi>k</mi></msup><mo>-</mo><msup><mi>g</mi><mrow><mi>k</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>)</mo></mrow></mrow><msup><mrow><mo>|</mo><mo>|</mo><msup><mi>g</mi><mrow><mi>k</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>|</mo><mo>|</mo></mrow><mn>2</mn></msup></mfrac><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>11</mn><mo>)</mo></mrow></mrow></math>

4.1.5) determining the optimal search step size α^k: if k is 0, then α is taken^kα 0, go to step 4.1.6);

otherwise, from the current iteration point z1^kStarting in the direction d^kOne-dimensional search is carried out to find the optimal step factor alpha^*And satisfies the following conditions:

<math><mrow><mi>H</mi><mn>1</mn><mrow><mo>(</mo><msup><mrow><mi>z</mi><mn>1</mn></mrow><mi>k</mi></msup><mo>+</mo><msup><mi>&alpha;</mi><mo>*</mo></msup><mo>&CenterDot;</mo><msup><mi>d</mi><mi>k</mi></msup><mo>)</mo></mrow><mo>=</mo><munder><mi>min</mi><mrow><mi>&alpha;</mi><mo>&GreaterEqual;</mo><mn>0</mn></mrow></munder><mi>H</mi><mn>1</mn><mrow><mo>(</mo><msup><mrow><mi>z</mi><mn>1</mn></mrow><mi>k</mi></msup><mo>+</mo><mi>&alpha;</mi><mo>&CenterDot;</mo><msup><mi>d</mi><mi>k</mi></msup><mo>)</mo></mrow><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>12</mn><mo>)</mo></mrow></mrow></math>

wherein H1 represents the Hamiltonian of the inner layer optimization problem, calculated from equation (13),

represents finding the step size α in α ∈ [0, + ∞) ] that minimizes H1^*；

H1＝λ(t)^T·f[x(t)，z1(t)，t] (13)

GetD is a coefficient integer value;

4.1.6) calculate the next iteration point

z1^k+1＝z1^k+α^k·d^k (14)

Add 1 to the number of iterations, i.e. k ═ k +1, z1 in step 4.1.6)^k+1Saved as current point z1^kContinuing iteration, and turning to the step 4.1.2);

the outer optimization of said step (4.2) is carried out according to the following algorithm steps (the superscript l denotes the current iteration number):

4.2.1) taking the current iteration point of the outer optimization as z2^l＝z1^*The initial value of l is 0;

4.2.2) mixing of z2^lSubstituting into an outer ordinary differential equation system, respectively performing forward integration and backward integration on the equations (6) and (8), solving a state variable x and a co-state variable theta, and calculating a target value J of the 1 st iteration by using the equation (5)₂ ^l；

4.2.3) judging whether the convergence condition formula (15) is satisfied, if so, judging the optimal solution z of the double-layer optimization^*＝z2^lOptimum objective function value J^*＝J₂ ^lSaving and delivering z^*And J^*To an output display module; otherwise, turning to the next step; formula (15) is expressed as follows:

|J₂ ^l-J₂ ^l+1|≤ζ₂ (15)

4.2.4) the state variable x and the iteration point z2^lCalculation of gradient h by substitution formula (16)^l：

<math><mrow><msup><mi>h</mi><mi>l</mi></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><mfrac><mrow><mo>&PartialD;</mo><mi>&psi;</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mn>2</mn><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>]</mo></mrow><mrow><mo>&PartialD;</mo><mi>z</mi><mn>2</mn><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac><mo>+</mo><mi>&theta;</mi><msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mi>T</mi></msup><mo>&CenterDot;</mo><mfrac><mrow><mo>&PartialD;</mo><mi>f</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mn>2</mn><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>]</mo></mrow><mrow><mo>&PartialD;</mo><mi>z</mi><mn>2</mn><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>16</mn><mo>)</mo></mrow></mrow></math>

Saving z2^lAnd h^lThen calculate the search direction e^l，e^l-1Representing the search direction, η, of a previous iteration^lAre the intermediate parameters:

<math><mrow><msup><mi>e</mi><mi>l</mi></msup><mo>=</mo><mfenced open='{' close=''><mtable><mtr><mtd><mo>-</mo><msup><mi>h</mi><mi>l</mi></msup><mo>,</mo></mtd><mtd><mi>l</mi><mo>=</mo><mn>1</mn><mo>;</mo></mtd></mtr><mtr><mtd><mo>-</mo><msup><mi>h</mi><mi>l</mi></msup><mo>+</mo><msup><mi>&eta;</mi><mi>l</mi></msup><msup><mi>e</mi><mrow><mi>l</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>,</mo></mtd><mtd><mi>l</mi><mo>&GreaterEqual;</mo><mn>2</mn><mo>.</mo></mtd></mtr></mtable></mfenced></mrow></math> wherein, <math><mrow><msup><mi>&eta;</mi><mi>l</mi></msup><mo>=</mo><mfrac><mrow><msup><mrow><mo>(</mo><msup><mi>h</mi><mi>l</mi></msup><mo>)</mo></mrow><mi>T</mi></msup><mrow><mo>(</mo><msup><mi>h</mi><mi>l</mi></msup><mo>-</mo><msup><mi>h</mi><mrow><mi>l</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>)</mo></mrow></mrow><msup><mrow><mo>|</mo><mo>|</mo><msup><mi>h</mi><mrow><mi>l</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>|</mo><mo>|</mo></mrow><mn>2</mn></msup></mfrac><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>17</mn><mo>)</mo></mrow></mrow></math>

4.2.5) determining the optimal search step size γ^l: if l is 0, then take γ^lGo to step 4.2.6, γ 0);

otherwise, from the current iteration point z2^lStarting in the direction h^lOne-dimensional search is carried out to find the optimal step factor gamma^*And satisfies the following conditions:

<math><mrow><mi>H</mi><mn>2</mn><mrow><mo>(</mo><msup><mrow><mi>z</mi><mn>2</mn></mrow><mi>l</mi></msup><mo>+</mo><msup><mi>&gamma;</mi><mo>*</mo></msup><mo>&CenterDot;</mo><msup><mi>e</mi><mi>l</mi></msup><mo>)</mo></mrow><mo>=</mo><munder><mi>min</mi><mrow><mi>&gamma;</mi><mo>&GreaterEqual;</mo><mn>0</mn></mrow></munder><mi>H</mi><mn>2</mn><mrow><mo>(</mo><msup><mrow><mi>z</mi><mn>2</mn></mrow><mi>l</mi></msup><mo>+</mo><mi>&gamma;</mi><mo>&CenterDot;</mo><msup><mi>e</mi><mi>l</mi></msup><mo>)</mo></mrow><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>18</mn><mo>)</mo></mrow></mrow></math>

wherein H2 represents the Hamiltonian of the skin optimization problem, calculated from equation (19),

represents finding the step size γ that minimizes H2 in γ ∈ [0, + ∞) ]^*；

H2＝ψ[x(t)，z2(t)，t]+θ(t)^T·f[x(t)，z2(t)，t] (19)

GetB is a coefficient integer value;

4.2.6) calculate the next iteration point:

z2^l+1＝z2^l+γ^l·d^l (20)

4.2.7) add 1 to the number of iterations, i.e. l ═ l +1, z2 in step 4.2.6)^l+1Saved as current point z2^lContinue iteration, go to step 4.2.2).

The system hardware structure diagram of this embodiment is shown in fig. 1, and the core of the optimal control system includes three functional modules, namely a constraint conversion module 8, an initialization module 9, and a double-layer optimization module 10 in an upper computer 6 with a human-computer interface, and further includes: the field intelligent instrument 2, the DCS system and the field bus. The DCS system consists of a bus interface 3, a control station 4 and a database 5; the industrial process object 1, the field intelligent instrument 2, the DCS system and the upper computer 6 are sequentially connected through a field bus to achieve uploading and issuing of information flow, and the upper computer and the bottom layer system timely exchange information to achieve online optimization of the system.

Example 2

Referring to fig. 1 and 2, a double-layer optimized optimal control method for an industrial process, the optimal control method is implemented according to the following steps:

1) specifying a state variable and a control variable in a DCS system, and setting upper and lower boundaries u of the control variable according to conditions of an actual production environment and conditions of operation restrictions_max、u_minAnd the sampling period of the DCS, and the historical data of corresponding variables in the DCS database 5, the upper and lower boundary values u of the control variables_max、u_minTransmitting to the upper computer 6; in an information acquisition module 7 of an upper computer, setting sampling time, acquiring data of an industrial process object input by an on-site intelligent instrument, storing the data into a real-time database 5 of a DCS, and outputting the latest data obtained by the database 5 of the DCS to a constraint conversion module 8 and an initialization module 9 of the upper computer for processing in each sampling period;

2) in the constraint conversion module 8 of the upper computer, firstly, the m-dimensional control variable u (t) with the boundary constraint shown in the formula (1) is converted into a formula (2) by using an intermediate variable z (t), and the u (t) is converted into a middle-size control variable without the boundary constraint

u_min≤u(t)≤u_max (1)

u(t)＝0.5(u_max-u_min)×{sin[z(t)]+1}+u_min (2)

A trigonometric function expression of the intermediate variable z (t), and solving the z (t) as a decision variable of the optimal control problem; then, the final value constraint equation (3) of the state variable is converted into a new objective function J₁：

x_j(t_f)＝x_jf(j＝1，2，...，c) (3)

<math><mrow><msub><mi>J</mi><mn>1</mn></msub><mo>=</mo><munderover><mi>&Sigma;</mi><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mi>c</mi></munderover><msup><mrow><mo>[</mo><msub><mi>x</mi><mi>j</mi></msub><mrow><mo>(</mo><msub><mi>t</mi><mi>f</mi></msub><mo>)</mo></mrow><mo>-</mo><msub><mi>x</mi><mi>jf</mi></msub><mo>]</mo></mrow><mn>2</mn></msup><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>4</mn><mo>)</mo></mrow></mrow></math>

Where c denotes the number of state variables which are subject to a final value constraint, x_jfGiven a constant, x_j(t_f) Represents a state variable x_j(t) at terminal time t_fValue of (A), J₁Which is also the inner objective function solved by the two-layer optimization module 10.

3) In an initialization module 9 of the upper computer, initial parameters are set, and data input by the DCS system are initialized, and the method is completed according to the following steps:

(3.1) time domain [0, t_f]The average division into N small segments: [0, t ]₁]，[t₁，t₂]，…，[t_N-1，t_N]Wherein t is_N＝t_f(ii) a Each time segment having a length t_f/N；

(3.2) discretizing the N-dimensional decision variables z (t) on (3.1) said time segments, i.e. each decision variable is represented by N segment constants, and taking the initial decision variable z⁰Is an arbitrary constant;

(3.3) setting the optimized convergence precision of the inner and outer layers as zeta₁、ζ₂The iteration times are k and l respectively (the initial values are 0); setting the initial search step length of the inner layer optimization as alpha 0 and gamma 0, and the initial decision variable of the iterative search as z1⁰；

4) In the double-layer optimization module 10 of the upper computer, an objective function J which can not only make the optimal control problem is searched₂The optimal decision variable z of the equation (5) is optimal and can satisfy the final constraint equation (3) and the state equation (6)^*(t) and mixing z^*(t) and correspondingIs optimum target value J^*To the output display module. Solving is carried out by adopting an inner-outer layer optimized structure:

$\frac{\mathrm{dx}\left(t\right)}{\mathrm{dt}}=f[x\left(t\right),z\left(t\right),t],$ x(0)＝x₀ (6)

(4.1) inner layer optimization with the aim of finding the objective function J₁The optimal decision variable z1(t), and z1(t) must satisfy equation of state (6) and inner-layer optimized equation of covariate (7):

<math><mrow><mfrac><mrow><mi>d&lambda;</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow><mi>dt</mi></mfrac><mo>=</mo><mo>-</mo><mi>&lambda;</mi><msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mi>T</mi></msup><mo>&CenterDot;</mo><mfrac><mrow><mo>&PartialD;</mo><mi>f</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>]</mo></mrow><mrow><mo>&PartialD;</mo><mi>x</mi></mrow></mfrac><mo>,</mo></mrow></math> <math><mrow><mi>&lambda;</mi><mrow><mo>(</mo><msub><mi>t</mi><mi>f</mi></msub><mo>)</mo></mrow><mo>=</mo><mfrac><msub><mrow><mo>&PartialD;</mo><mi>J</mi></mrow><mn>1</mn></msub><mrow><mo>&PartialD;</mo><mi>x</mi><mrow><mo>(</mo><msub><mi>t</mi><mi>f</mi></msub><mo>)</mo></mrow></mrow></mfrac><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>7</mn><mo>)</mo></mrow></mrow></math>

wherein λ (T) represents m dimensional covariates, superscript T represents transpose of the variables, equation (6)

And the formula (7) form an inner layer ordinary differential equation system; transmitting an optimal decision variable z1(t) obtained by optimizing the inner layer to the outer layer to serve as an initial solution of the outer layer optimization;

(4.2) outer optimization, the purpose is to search the objective function J based on the inner optimization₂The optimal decision variable z2(t), and z2(t) must satisfy the state equation (6)) and the outer optimized covariant equation (8):

<math><mrow><mfrac><mrow><mi>d&theta;</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow><mi>dt</mi></mfrac><mo>=</mo><mo>-</mo><mfrac><mrow><mo>&PartialD;</mo><mi>&psi;</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>]</mo></mrow><mrow><mo>&PartialD;</mo><mi>x</mi></mrow></mfrac><mo>-</mo><msup><mrow><mi>&theta;</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow><mi>T</mi></msup><mo>&CenterDot;</mo><mfrac><mrow><mo>&PartialD;</mo><mi>f</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>]</mo></mrow><mrow><mo>&PartialD;</mo><mi>x</mi></mrow></mfrac><mo>,</mo></mrow></math>

wherein θ (t) represents an m-dimensional covariant,

psi denotes the objective function J at endpoint conditions and over time, respectively₂The formula (6) and the formula (8) form an outer layer ordinary differential equation system; the optimal decision variable z2(t) obtained by the outer optimization is the optimal solution z of the double-layer optimization^*(t), corresponding J₂The value is the optimal target value J of the double-layer optimization^*；

Then, the optimal result z obtained by double-layer optimization is saved^*(t) and J^*。

The inner layer optimization of the step (4.1) is realized according to the following algorithm steps, and the superscript k represents the iteration number:

4.1.1) choosing an initial point z1 of the iteration⁰And if k is 0, then z1⁰＝z⁰Else z1⁰Value z2 as skin input^l；

4.1.2) iteration point z1 of the k-th time^kSubstituting the k into the inner layer ordinary differential equation system, when k is 0, z1^k＝z1⁰Respectively performing forward integration and backward integration on the expressions (6) and (7), solving a state variable x and a covariate lambda, and calculating a target value J of the kth iteration by the expression (4)₁ ^k；

4.1.3) determining whether the convergence condition expression (9) is satisfied, and if so, determining the optimal solution z1 of the inner layer^*＝z1^kMixing z1^*Transmitting the initial solution to the outer layer as the initial solution of the outer layer iteration; otherwise, turning to step (4.1.4), equation (9) is expressed as follows: (ii) a

|J₁ ^k-J₁ ^k+1|≤ζ₁ (9)

4.1.4) the state variable x and the iteration point z1^kCalculation of gradient g by substituting formula (10)^k：

<math><mrow><msup><mi>g</mi><mi>k</mi></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><mi>&lambda;</mi><msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mi>T</mi></msup><mo>&CenterDot;</mo><mfrac><mrow><mo>&PartialD;</mo><mi>f</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mn>1</mn><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>]</mo></mrow><mrow><mo>&PartialD;</mo><mi>z</mi><mn>1</mn><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>10</mn><mo>)</mo></mrow></mrow></math>

Saving z1^kAnd g^kThen calculate the search direction d^k，d^k-1Indicating the search direction, β, of the previous iteration^kAre the intermediate parameters:

<math><mrow><msup><mi>d</mi><mi>k</mi></msup><mo>=</mo><mfenced open='{' close=''><mtable><mtr><mtd><mo>-</mo><msup><mi>g</mi><mi>k</mi></msup><mo>,</mo></mtd><mtd><mi>k</mi><mo>=</mo><mn>1</mn><mo>;</mo></mtd></mtr><mtr><mtd><mo>-</mo><msup><mi>g</mi><mi>k</mi></msup><mo>+</mo><msup><mi>&beta;</mi><mi>k</mi></msup><msup><mi>d</mi><mrow><mi>k</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>,</mo></mtd><mtd><mi>k</mi><mo>&GreaterEqual;</mo><mn>2</mn><mo>.</mo></mtd></mtr></mtable></mfenced></mrow></math> wherein, <math><mrow><msup><mi>&beta;</mi><mi>k</mi></msup><mo>=</mo><mfrac><mrow><msup><mrow><mo>(</mo><msup><mi>g</mi><mi>k</mi></msup><mo>)</mo></mrow><mi>T</mi></msup><mrow><mo>(</mo><msup><mi>g</mi><mi>k</mi></msup><mo>-</mo><msup><mi>g</mi><mrow><mi>k</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>)</mo></mrow></mrow><msup><mrow><mo>|</mo><mo>|</mo><msup><mi>g</mi><mrow><mi>k</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>|</mo><mo>|</mo></mrow><mn>2</mn></msup></mfrac><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>11</mn><mo>)</mo></mrow></mrow></math>

4.1.5) determining the optimal search step size α^k: if k is 0, then α is taken^kα 0, go to step 4.1.6);

otherwise, from the current iteration point z1^kStarting in the direction d^kOne-dimensional search is carried out to find the optimal step factor alpha^*And satisfies the following conditions:

<math><mrow><mi>H</mi><mn>1</mn><mrow><mo>(</mo><msup><mrow><mi>z</mi><mn>1</mn></mrow><mi>k</mi></msup><mo>+</mo><msup><mi>&alpha;</mi><mo>*</mo></msup><mo>&CenterDot;</mo><msup><mi>d</mi><mi>k</mi></msup><mo>)</mo></mrow><mo>=</mo><munder><mi>min</mi><mrow><mi>&alpha;</mi><mo>&GreaterEqual;</mo><mn>0</mn></mrow></munder><mi>H</mi><mn>1</mn><mrow><mo>(</mo><msup><mrow><mi>z</mi><mn>1</mn></mrow><mi>k</mi></msup><mo>+</mo><mi>&alpha;</mi><mo>&CenterDot;</mo><msup><mi>d</mi><mi>k</mi></msup><mo>)</mo></mrow><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>12</mn><mo>)</mo></mrow></mrow></math>

wherein H1 represents the Hamiltonian of the inner layer optimization problem, calculated by equation (13),

represents finding the step size α in α ∈ [0, + ∞) ] that minimizes H1^*Formula (13) is expressed as follows:

H1＝λ(t)^T·f[x(t)，z1(t)，t] (13)

get

D is a coefficient integer value;

4.1.6) calculate the next iteration point

z1^k+1＝z1^k+α^k·d^k (14)

4.1.7) add 1 to the number of iterations, i.e. k ═ k +1, z1 in step 4.1.6)^k+1Saved as current point z1^kContinuing iteration, and turning to the step 4.1.2);

the outer optimization of said step (4.2) is carried out according to the following algorithm steps, the superscript l representing the current iteration number:

4.2.1) taking the current iteration point of the outer optimization as z2^l＝z1^*The initial value of l is 0;

4.2.2) mixing of z2^lSubstituting into an outer ordinary differential equation system, respectively performing forward integration and backward integration on the equations (6) and (8), solving a state variable x and a co-state variable theta, and calculating a target value J of the 1 st iteration by using the equation (5)₂ ^l；

4.2.3) judging whether the convergence condition formula (15) is satisfied, if so, judging the optimal solution z of the double-layer optimization^*＝z2^lOptimum objective function value J^*＝J₂ ^lSaving and delivering z^*And J^*To an output display module; otherwise, turning to the next step; formula (15) is expressed as follows:

|J₂ ^l-J₂ ^l+1|≤ζ₂ (15)

4.2.4) the state variable x and the iteration point z2^lCalculation of gradient h by substitution formula (16)^l：

<math><mrow><msup><mi>h</mi><mi>l</mi></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><mfrac><mrow><mo>&PartialD;</mo><mi>&psi;</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mn>2</mn><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>.</mo><mi>t</mi><mo>]</mo></mrow><mrow><mo>&PartialD;</mo><mi>z</mi><mn>2</mn><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac><mo>+</mo><mi>&theta;</mi><msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mi>T</mi></msup><mo>&CenterDot;</mo><mfrac><mrow><mo>&PartialD;</mo><mi>f</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mn>2</mn><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>]</mo></mrow><mrow><mo>&PartialD;</mo><mi>z</mi><mn>2</mn><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>16</mn><mo>)</mo></mrow></mrow></math>

Saving z2^lAnd h^lThen calculate the search direction e^l，e^l-1Representing the search direction, η, of a previous iteration^lAre the intermediate parameters:

<math><mrow><msup><mi>e</mi><mi>l</mi></msup><mo>=</mo><mfenced open='{' close=''><mtable><mtr><mtd><mo>-</mo><msup><mi>h</mi><mi>l</mi></msup><mo>,</mo></mtd><mtd><mi>l</mi><mo>=</mo><mn>1</mn><mo>;</mo></mtd></mtr><mtr><mtd><mo>-</mo><msup><mi>h</mi><mi>l</mi></msup><mo>+</mo><msup><mi>&eta;</mi><mi>l</mi></msup><msup><mi>e</mi><mrow><mi>l</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>,</mo></mtd><mtd><mi>l</mi><mo>&GreaterEqual;</mo><mn>2</mn><mo>.</mo></mtd></mtr></mtable></mfenced></mrow></math> wherein, <math><mrow><msup><mi>&eta;</mi><mi>l</mi></msup><mo>=</mo><mfrac><mrow><msup><mrow><mo>(</mo><msup><mi>h</mi><mi>l</mi></msup><mo>)</mo></mrow><mi>T</mi></msup><mrow><mo>(</mo><msup><mi>h</mi><mi>l</mi></msup><mo>-</mo><msup><mi>h</mi><mrow><mi>l</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>)</mo></mrow></mrow><msup><mrow><mo>|</mo><mo>|</mo><msup><mi>h</mi><mrow><mi>l</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>|</mo><mo>|</mo></mrow><mn>2</mn></msup></mfrac><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>17</mn><mo>)</mo></mrow></mrow></math>

4.2.5) determining the optimal search step size γ^l: if l is 0, then take γ^lGo to step 4.2.6, γ 0); otherwise, from the current iteration point z2^lStarting in the direction h^lOne-dimensional search is carried out to find the optimal step factor gamma^*And satisfies the following conditions:

<math><mrow><mi>H</mi><mn>2</mn><mrow><mo>(</mo><msup><mrow><mi>z</mi><mn>2</mn></mrow><mi>l</mi></msup><mo>+</mo><msup><mi>&gamma;</mi><mo>*</mo></msup><mo>&CenterDot;</mo><msup><mi>e</mi><mi>l</mi></msup><mo>)</mo></mrow><mo>=</mo><munder><mi>min</mi><mrow><mi>&gamma;</mi><mo>&GreaterEqual;</mo><mn>0</mn></mrow></munder><mi>H</mi><mn>2</mn><mrow><mo>(</mo><msup><mrow><mi>z</mi><mn>2</mn></mrow><mi>l</mi></msup><mo>+</mo><mi>&gamma;</mi><mo>&CenterDot;</mo><msup><mi>e</mi><mi>l</mi></msup><mo>)</mo></mrow><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>18</mn><mo>)</mo></mrow></mrow></math>

wherein H2 represents the Hamiltonian of the skin optimization problem, calculated from equation (19),represents finding the step size γ that minimizes H2 in γ ∈ [0, + ∞) ]^*；

H2＝ψ[x(t)，z2(t)，t]+θ(t)^T·f[x(t)，z2(t)，t] (19)

Get

B is a coefficient integer value;

4.2.6) calculate the next iteration point:

z2^l+1＝z2^l+γ^l·d^l (20)

4.2.7) add 1 to the number of iterations, i.e. l ═ l +1, z2 in step 4.2.6)^l+1Saved as current point z2^lContinue iteration, go to step 4.2.2).

5) In an output display module 11 of the upper computer, the optimal decision variable z obtained in the step (4.2.3)^*Converting the passing equation (2) into an optimal control curve u^*(t) and the optimum target value J^*The images are displayed on a human-computer interface of the upper computer; at the same time, the optimum control curve u^*(t) transmitting the information to a control station of the DCS system through the bus interface, and displaying the obtained optimization result information in the DCS system.

And (3) commissioning of the system:

A. setting the time interval of each data detection and acquisition by using a timer;

B. the field intelligent instrument 2 detects the data of the industrial process object 1 and transmits the data to a real-time database 5 of the DCS system to obtain the latest variable data;

C. in a constraint conversion module 8 of the upper computer 6, processing the control variable boundary constraint, and taking the processing result as the input of an initialization module 9 and a double-layer optimization module 10;

D. initializing relevant parameters and variables of each module according to actual production requirements and operation limiting conditions in an initialization module 9 of the upper computer 6, and taking a processing result as the input of a double-layer optimization module 10;

E. the double-layer optimization module 10 of the upper computer 6 performs double-layer iterative optimization according to the variable substitution relation of the constraint conversion module 8 and the new objective function information, and the optimized result is transmitted to the output display module 11;

F. and an output display module 11 of the upper computer 6 converts the optimal decision curve calculated by the double-layer optimization module 10 according to the variable substitution relation of the constraint conversion module 8, transmits the obtained optimal control result information to the DCS, displays the optimal control result information on a human-computer interface of the upper computer 6 and a control station 4 of the DCS, transmits the obtained optimal control result information to a field work station through the DCS and a field bus for display, and executes optimal operation by the field work station.

The above-described embodiments are intended to illustrate rather than to limit the invention, and any modifications and variations of the present invention are within the spirit of the invention and the scope of the appended claims.

Claims (7)

1. The utility model provides a double-deck industrial process optimal control system who optimizes, includes on-the-spot intelligent detection instrument, DCS system and the host computer of being connected with the industrial process object, on-the-spot intelligent detection instrument, DCS system and host computer link to each other its characterized in that in proper order: the host computer include:

the signal acquisition module is used for setting sampling time and acquiring dynamic information of the industrial process object uploaded by the on-site intelligent instrument;

the initialization module is used for setting initial parameters, discretizing decision variables z (t) and carrying out initial assignment, and comprises the following specific steps:

(3.1) time domain [0, t_f]The average division into N small segments: [0, t ]₁]，[t₁，t₂]，…，[t_N-1，t_N]Wherein, t_N＝t_f(ii) a Each time segment having a length t_fThe time of termination is represented by/N, tf;

(3.2) discretizing the N-dimensional decision variables z (t) on the time segments in step (3.1), i.e. each decision variable is represented by N segment constants, and taking the initial decision variable z⁰Is an arbitrary constant;

(3.3) setting the optimized convergence precision of the inner and outer layers as zeta₁、ζ₂When the iteration error of the optimized target value is smaller than the convergence precision, stopping iteration, wherein the iteration times are k and l respectively; setting the initial search step length of the inner layer optimization as alpha 0 and gamma 0, and the initial decision variable of the iterative search as z1⁰；

The constraint transformation module is used for transforming the control variable boundary constraint and the state variable final value constraint in the boundary value fixed optimal control problem, and adopts the following steps to complete the following steps:

(2.1) processing the control variable boundary constraints through intermediate variables, i.e. for the boundary constraints having the formula (1)

u_min≤u(t)≤u_max (1)

m-dimensional control variables u (t), u_min、u_maxAll the variables are constants which respectively correspond to the lower bound and the upper bound of the control variable, subscripts min and max respectively represent the minimum value and the maximum value, and the following transformation is adopted:

u(t)＝0.5(u_max-u_min)×{sin[z(t)]+1}+u_min (2)

converting u (t) into a trigonometric function expression of an intermediate variable z (t) which is not constrained by a boundary, and solving the z (t) as a decision variable of an optimal control problem;

(2.2) converting the state variable final value constraint into a new objective function, i.e. for the final value constraint equation (3):

x_j(t_f)＝x_jf j＝1，2，...，c (3)

state variable x of_j(t) where c represents the number of state variables constrained by the final value, x_jfGiven a constant, x_j(t_f) Represents a state variable x_j(t) at terminal time t_fThe following objective function formula (4) is constructed:

<math><mrow><msub><mi>J</mi><mn>1</mn></msub><mo>=</mo><munderover><mi>&Sigma;</mi><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mi>c</mi></munderover><msup><mrow><mo>[</mo><msub><mi>x</mi><mi>j</mi></msub><mrow><mo>(</mo><msub><mi>t</mi><mi>f</mi></msub><mo>)</mo></mrow><mo>-</mo><msub><mi>x</mi><mi>jf</mi></msub><mo>]</mo></mrow><mn>2</mn></msup><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>4</mn><mo>)</mo></mrow></mrow></math>

J₁an inner layer objective function solved for the double-layer optimization module;

a double-layer optimization module for finding an objective function J which not only enables optimal control problems₂In the optimum case of the method,

and can satisfy the final value constraint equation (3) and the state equation (6):

$\frac{\mathrm{dx}\left(t\right)}{\mathrm{dt}}=f[x\left(t\right),z\left(t\right),t],$ x(0)＝x₀ (6)

is determined by the optimal decision variable z^*(t) wherein,

ψ denotes the components of the objective function under endpoint conditions and over a period of time, x denotes a given n-dimensional state variable, x₀The variable value of the state at the initial time (t is 0), f is a function variable, and the solution is carried out by adopting an inner-layer and outer-layer optimized structure:

(4.1) inner layer optimization, i.e. finding the objective function J₁The optimal decision variable z1(t), and z1(t) must satisfy equation of state (6) and inner-layer optimized equation of covariate (7):

<math><mrow><mfrac><mrow><mi>d&lambda;</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow><mi>dt</mi></mfrac><mo>=</mo><mo>-</mo><mi>&lambda;</mi><msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mi>T</mi></msup><mo>&CenterDot;</mo><mfrac><mrow><mo>&PartialD;</mo><mi>f</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>]</mo></mrow><mrow><mo>&PartialD;</mo><mi>x</mi></mrow></mfrac><mo>,</mo></mrow></math> <math><mrow><mi>&lambda;</mi><mrow><mo>(</mo><msub><mi>t</mi><mi>f</mi></msub><mo>)</mo></mrow><mo>=</mo><mfrac><msub><mrow><mo>&PartialD;</mo><mi>J</mi></mrow><mn>1</mn></msub><mrow><mo>&PartialD;</mo><mi>x</mi><mrow><mo>(</mo><msub><mi>t</mi><mi>f</mi></msub><mo>)</mo></mrow></mrow></mfrac><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>7</mn><mo>)</mo></mrow></mrow></math>

wherein, λ (T) represents m dimensional covariates, superscript T represents variable transposition, and equations (6) and (7) form an inner layer ordinary differential equation system; transmitting an optimal decision variable z1(t) obtained by optimizing the inner layer to the outer layer to serve as an initial solution of the outer layer optimization;

(4.2) outer optimization, i.e. searching the objective function J based on the inner optimization₂The optimal decision variable z2(t), and z2(t) must satisfy the state equation (6) and the outer optimized covariant equation (8):

<math><mrow><mfrac><mrow><mi>d&theta;</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow><mi>dt</mi></mfrac><mo>=</mo><mo>-</mo><mfrac><mrow><mo>&PartialD;</mo><mi>&psi;</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>]</mo></mrow><mrow><mo>&PartialD;</mo><mi>x</mi></mrow></mfrac><mo>-</mo><mi>&theta;</mi><msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mi>T</mi></msup><mo>&CenterDot;</mo><mfrac><mrow><mo>&PartialD;</mo><mi>f</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>]</mo></mrow><mrow><mo>&PartialD;</mo><mi>x</mi></mrow></mfrac><mo>,</mo></mrow></math>

wherein θ (t) represents an m-dimensional covariant,

psi denotes the objective function J at endpoint conditions and over time, respectively₂The formula (6) and the formula (8) form an outer layer ordinary differential equation system; the optimal decision variable z2(t) obtained by the outer optimization is the optimal solution z of the double-layer optimization^*(t), corresponding J₂The value is the optimal target value J of the double-layer optimization^*；

Then, the optimal result z obtained by double-layer optimization is saved^*(t) and J^*。

2. The double-layer optimized industrial process optimal control system of claim 1, wherein: in the double-layer optimization module, the inner-layer optimization and the outer-layer optimization are carried out by adopting the following steps:

the inner layer optimization of the step (4.1) is realized according to the following algorithm steps, and the superscript k represents the iteration number:

4.1.1) choosing an initial point z1 of the iteration⁰And if k is equal to l is equal to 0, then z1⁰＝z⁰Else z1⁰Value z2 as skin input^l；

4.1.2) iteration point z1 of the k-th time^kSubstituting the k into the inner layer ordinary differential equation system, when k is 0, z1^k＝z1⁰Respectively performing forward integration and backward integration on the expressions (6) and (7), solving a state variable x and a covariate lambda, and calculating a target value J of the kth iteration by the expression (4)₁ ^k；

4.1.3) determining whether the convergence condition expression (9) is satisfied, and if so, determining the optimal solution z1 of the inner layer^*＝z1^kMixing z1^*Transmitting the initial solution to the outer layer as the initial solution of the outer layer iteration; otherwise, turning to step (4.1.4), equation (9) is expressed as follows: (ii) a

|J₁ ^k-J₁ ^k+1|≤ζ₁ (9)

4.1.4) the state variable x and the iteration point z1^kCalculation of gradient g by substituting formula (10)^k：

<math><mrow><msup><mi>g</mi><mi>k</mi></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><mi>&lambda;</mi><msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mi>T</mi></msup><mo>&CenterDot;</mo><mfrac><mrow><mo>&PartialD;</mo><mi>f</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mn>1</mn><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>]</mo></mrow><mrow><mo>&PartialD;</mo><mi>z</mi><mn>1</mn><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>10</mn><mo>)</mo></mrow></mrow></math>

Saving z1^kAnd g^kThen calculate the search direction d^k，d^k-1Indicating the search direction, β, of the previous iteration^kAre the intermediate parameters:

<math><mrow><msup><mi>d</mi><mi>k</mi></msup><mo>=</mo><mfenced open='{' close=''><mtable><mtr><mtd><mo>-</mo><msup><mi>g</mi><mi>k</mi></msup><mo>,</mo></mtd><mtd><mi>k</mi><mo>=</mo><mn>1</mn><mo>;</mo></mtd></mtr><mtr><mtd><mo>-</mo><msup><mi>g</mi><mi>k</mi></msup><mo>+</mo><msup><mi>&beta;</mi><mi>k</mi></msup><msup><mi>d</mi><mrow><mi>k</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>,</mo></mtd><mtd><mi>k</mi><mo>&GreaterEqual;</mo><mn>2</mn><mo>.</mo></mtd></mtr></mtable></mfenced></mrow></math> wherein, <math><mrow><msup><mi>&beta;</mi><mi>k</mi></msup><mo>=</mo><mfrac><mrow><msup><mrow><mo>(</mo><msup><mi>g</mi><mi>k</mi></msup><mo>)</mo></mrow><mi>T</mi></msup><mrow><mo>(</mo><msup><mi>g</mi><mi>k</mi></msup><mo>-</mo><msup><mi>g</mi><mrow><mi>k</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>)</mo></mrow></mrow><msup><mrow><mo>|</mo><mo>|</mo><msup><mi>g</mi><mrow><mi>k</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>|</mo><mo>|</mo></mrow><mn>2</mn></msup></mfrac><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>11</mn><mo>)</mo></mrow></mrow></math>

4.1.5) determining the optimal search step size α^k: if k is 0, then α is taken^kα 0, go to step 4.1.6); otherwise, from the current iteration point z1^kStarting in the direction d^kOne-dimensional search is carried out to find the optimal step factor alpha^*And satisfies the following conditions:

<math><mrow><mi>H</mi><mn>1</mn><mrow><mo>(</mo><msup><mrow><mi>z</mi><mn>1</mn></mrow><mi>k</mi></msup><mo>+</mo><msup><mi>&alpha;</mi><mo>*</mo></msup><mo>&CenterDot;</mo><msup><mi>d</mi><mi>k</mi></msup><mo>)</mo></mrow><mo>=</mo><munder><mi>min</mi><mrow><mi>&alpha;</mi><mo>&GreaterEqual;</mo><mn>0</mn></mrow></munder><mi>H</mi><mn>1</mn><mrow><mo>(</mo><msup><mrow><mi>z</mi><mn>1</mn></mrow><mi>k</mi></msup><mo>+</mo><mi>&alpha;</mi><mo>&CenterDot;</mo><msup><mi>d</mi><mi>k</mi></msup><mo>)</mo></mrow><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>12</mn><mo>)</mo></mrow></mrow></math>

wherein H1 represents the Hamiltonian of the inner layer optimization problem, calculated by equation (13),

represents finding the step size α in α ∈ [0, + ∞) ] that minimizes H1^*Formula (13) is expressed as follows:

H1＝λ(t)^T·f[x(t)，z1(t)，t] (13)

get

D is a coefficient integer value;

4.1.6) calculate the next iteration point

z1^k+1＝z1^k+α^k·d^k (14)

4.1.7) add 1 to the number of iterations, i.e. k ═ k +1, z1 in step 4.1.6)^k+1Saved as current point z1^kContinuing iteration, and turning to the step 4.1.2);

the outer optimization of said step (4.2) is carried out according to the following algorithm steps, the superscript l representing the current iteration number:

4.2.1) taking the current iteration point of the outer optimization as z2^l＝z1^*The initial value of l is 0;

4.2.2) mixing of z2^lSubstituting into an outer ordinary differential equation system, respectively performing forward integration and backward integration on the formulas (6) and (8), and solvingThe state variable x and the covariate theta are obtained, and the target value J of the first iteration is calculated by the formula (5)₂ ^l；

4.2.3) judging whether the convergence condition formula (15) is satisfied, if so, judging the optimal solution z of the double-layer optimization^*＝z2^lOptimum objective function value J^*＝J₂ ^lSaving and delivering z^*And J^*To an output display module; otherwise, turning to the next step; formula (15) is expressed as follows:

|J₂ ^l-J₂ ^l+1|≤ζ₂ (15)

4.2.4) the state variable x and the iteration point z2^lCalculation of gradient h by substitution formula (16)^l：

<math><mrow><msup><mi>h</mi><mi>l</mi></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><mfrac><mrow><mo>&PartialD;</mo><mi>&psi;</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mn>2</mn><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>.</mo><mi>t</mi><mo>]</mo></mrow><mrow><mo>&PartialD;</mo><mi>z</mi><mn>2</mn><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac><mo>+</mo><mi>&theta;</mi><msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mi>T</mi></msup><mo>&CenterDot;</mo><mfrac><mrow><mo>&PartialD;</mo><mi>f</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mn>2</mn><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>]</mo></mrow><mrow><mo>&PartialD;</mo><mi>z</mi><mn>2</mn><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>16</mn><mo>)</mo></mrow></mrow></math>

Saving z2^lAnd h^lThen calculate the search direction e^l，e^l-1Representing the search direction, η, of a previous iteration^lAre the intermediate parameters:

<math><mrow><msup><mi>e</mi><mi>l</mi></msup><mo>=</mo><mfenced open='{' close=''><mtable><mtr><mtd><mo>-</mo><msup><mi>h</mi><mi>l</mi></msup><mo>,</mo></mtd><mtd><mi>l</mi><mo>=</mo><mn>1</mn><mo>;</mo></mtd></mtr><mtr><mtd><mo>-</mo><msup><mi>h</mi><mi>l</mi></msup><mo>+</mo><msup><mi>&eta;</mi><mi>l</mi></msup><msup><mi>e</mi><mrow><mi>l</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>,</mo></mtd><mtd><mi>l</mi><mo>&GreaterEqual;</mo><mn>2</mn><mo>.</mo></mtd></mtr></mtable></mfenced></mrow></math> wherein, <math><mrow><msup><mi>&eta;</mi><mi>l</mi></msup><mo>=</mo><mfrac><mrow><msup><mrow><mo>(</mo><msup><mi>h</mi><mi>l</mi></msup><mo>)</mo></mrow><mi>T</mi></msup><mrow><mo>(</mo><msup><mi>h</mi><mi>l</mi></msup><mo>-</mo><msup><mi>h</mi><mrow><mi>l</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>)</mo></mrow></mrow><msup><mrow><mo>|</mo><mo>|</mo><msup><mi>h</mi><mrow><mi>l</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>|</mo><mo>|</mo></mrow><mn>2</mn></msup></mfrac><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>17</mn><mo>)</mo></mrow></mrow></math>

4.2.5) determining the optimal search step size γ^l: if l is 0, then take γ^lGo to step 4.2.6, γ 0); otherwise, from the current iteration point z2^lStarting in the direction h^lOne-dimensional search is carried out to find the optimal step factor gamma^*And satisfies the following conditions:

<math><mrow><mi>H</mi><mn>2</mn><mrow><mo>(</mo><msup><mrow><mi>z</mi><mn>2</mn></mrow><mi>l</mi></msup><mo>+</mo><msup><mi>&gamma;</mi><mo>*</mo></msup><mo>&CenterDot;</mo><msup><mi>e</mi><mi>l</mi></msup><mo>)</mo></mrow><mo>=</mo><mrow><munder><mi>min</mi><mrow><mi>&gamma;</mi><mo>&GreaterEqual;</mo><mn>0</mn></mrow></munder><mi>H</mi><mn>2</mn><mrow><mo>(</mo><msup><mrow><mi>z</mi><mn>2</mn></mrow><mi>l</mi></msup><mo>+</mo><msup><mrow><mi>&gamma;</mi><mo>&CenterDot;</mo><mi>e</mi></mrow><mi>l</mi></msup><mo>)</mo></mrow></mrow><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>18</mn><mo>)</mo></mrow></mrow></math>

wherein H2 represents the Hamiltonian of the skin optimization problem, calculated from equation (19),

represents finding the step size γ that minimizes H2 in γ ∈ [0, + ∞) ]^*；

H2＝ψ[x(t)，z2(t)，t]+θ(t)^T·f[x(t)，z2(t)，t](19) Get

B is a coefficient integer value;

4.2.6) calculate the next iteration point:

z2^l+1＝z2^l+γ^l·d^l (20)

4.2.7) add 1 to the number of iterations, i.e. l ═ l +1, z2 in step 4.2.6)^l+1Saved as current point z2^lContinue iteration, go to step 4.2.2).

3. The double-layer optimized industrial process optimal control system according to claim 1 or 2, wherein: the host computer still includes: an output display module for outputting the optimal decision result z calculated by the double-layer optimization module^*(t) conversion into an optimal control trajectory u by equation (2)^*(t) then adding u^*(t) and an optimum target value J^*And transmitting the information to the DCS, and displaying the obtained optimization result information in the DCS.

4. An optimal control method implemented by the double-layer optimized industrial process optimal control system according to claim 1, characterized in that: the optimal control method comprises the following steps:

1) specifying state variables and control variables for optimum control in a DCS system, and setting upper and lower boundaries u of the control variables according to conditions of an actual production environment and conditions of operation restrictions_max、u_minAnd the sampling period of the DCS, and the historical data of corresponding variables in the DCS database, the upper and lower boundary values u of the control variables_max、u_minTransmitting to an upper computer;

2) and (3) converting an edge value fixed constraint in the optimal control problem:

(2.1) constraint with boundary using intermediate variable z (t)

u_min≤u(t)≤u_max (1)

The m-dimensional control variable u (t) of (a):

u(t)＝0.5(u_max-u_min)×{sin[z(t)]+1}+u_min (2)

converting u (t) into a trigonometric function expression of an intermediate variable z (t) which is not constrained by a boundary, and solving the z (t) as a decision variable of an optimal control problem;

(2.2) converting the final value constraint equation (3) of the state variable into a new objective function J₁Formula (4):

x_j(t_f)＝x_jf(j＝1，2，...，c) (3)

<math><mrow><msub><mi>J</mi><mn>1</mn></msub><mo>=</mo><munderover><mi>&Sigma;</mi><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mi>c</mi></munderover><msup><mrow><mo>[</mo><msub><mi>x</mi><mi>j</mi></msub><mrow><mo>(</mo><msub><mi>t</mi><mi>f</mi></msub><mo>)</mo></mrow><mo>-</mo><msub><mi>x</mi><mi>jf</mi></msub><mo>]</mo></mrow><mn>2</mn></msup><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>4</mn><mo>)</mo></mrow></mrow></math>

where c denotes the number of state variables which are subject to a final value constraint, x_jfGiven a constant, x_j(t_f) Represents a state variable x_j(t) at terminal time t_fValue of (A), J₁The method is also an inner layer objective function solved by the double-layer optimization module;

3) setting initial parameters, initializing data input by a DCS, and completing the steps as follows:

(3.1) time domain [0, t_f]The average division into N small segments: [0, t ]₁]，[t₁，t₂]，…，[t_N-1，t_N]Wherein t is_N＝t_f(ii) a Each time segment having a length t_f/N；

(3.2) discretizing the N-dimensional decision variables z (t) on (3.1) said time segments, i.e. each decision variable is represented by N segment constants, and taking the initial decision variable z⁰Is an arbitrary constant;

(3.3) setting the optimized convergence precision of the inner and outer layers as zeta₁、ζ₂The iteration times are k and l respectively; setting the initial search step length of the inner layer optimization as alpha 0 and gamma 0, and the initial decision variable of the iterative search as z1⁰；

4) Finding the optimal decision variable z which not only optimizes the objective function formula (5) of the optimal control problem, but also satisfies the final value constraint formula (3) and the state equation (6)^*(t) and mixing z^*(t) and corresponding optimal target value J^*And transmitting the data to an output display module, and solving by adopting an inner-layer and outer-layer optimized structure:

$\frac{\mathrm{dx}\left(t\right)}{\mathrm{dt}}=f[x\left(t\right),z\left(t\right),t],$ x(0)＝x₀ (6)

(4.1) inner-layer optimization, i.e. finding the decision variable z1(t) that optimizes the objective function J1, and z1(t) must satisfy the state equation (6) and the inner-layer optimized synergistic equation (7):

<math><mrow><mfrac><mrow><mi>d&lambda;</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow><mi>dt</mi></mfrac><mo>=</mo><mo>-</mo><mi>&lambda;</mi><msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mi>T</mi></msup><mo>&CenterDot;</mo><mfrac><mrow><mo>&PartialD;</mo><mi>f</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>]</mo></mrow><mrow><mo>&PartialD;</mo><mi>x</mi></mrow></mfrac><mo>,</mo></mrow></math> <math><mrow><mi>&lambda;</mi><mrow><mo>(</mo><msub><mi>t</mi><mi>f</mi></msub><mo>)</mo></mrow><mo>=</mo><mfrac><msub><mrow><mo>&PartialD;</mo><mi>J</mi></mrow><mn>1</mn></msub><mrow><mo>&PartialD;</mo><mi>x</mi><mrow><mo>(</mo><msub><mi>t</mi><mi>f</mi></msub><mo>)</mo></mrow></mrow></mfrac><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>7</mn><mo>)</mo></mrow></mrow></math>

wherein, λ (T) represents m dimensional covariates, superscript T represents variable transposition, and equations (6) and (7) form an inner layer ordinary differential equation system; transmitting an optimal decision variable z1(t) obtained by optimizing the inner layer to the outer layer to serve as an initial solution of the outer layer optimization;

(4.2) outer optimization, i.e. searching the objective function J based on the inner optimization₂The optimal decision variable z2(t), and z2(t) must satisfy the state equation (6) and the outer optimized covariant equation (8):

<math><mrow><mfrac><mrow><mi>d&theta;</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow><mi>dt</mi></mfrac><mo>=</mo><mo>-</mo><mfrac><mrow><mo>&PartialD;</mo><mi>&psi;</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>]</mo></mrow><mrow><mo>&PartialD;</mo><mi>x</mi></mrow></mfrac><mo>-</mo><mi>&theta;</mi><msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mi>T</mi></msup><mo>&CenterDot;</mo><mfrac><mrow><mo>&PartialD;</mo><mi>f</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>]</mo></mrow><mrow><mo>&PartialD;</mo><mi>x</mi></mrow></mfrac><mo>,</mo></mrow></math>

wherein θ (t) represents an m-dimensional covariant,

psi denotes the objective function J at endpoint conditions and over time, respectively₂The formula (6) and the formula (8) form an outer layer ordinary differential equation system; the optimal decision variable z2(t) obtained by the outer optimization is the optimal solution z of the double-layer optimization^*(t), corresponding J₂The value is the optimal target value J of the double-layer optimization^*；

Then, the optimal result z obtained by double-layer optimization is saved^*(t) and J^*。

5. The optimum control method according to claim 4, wherein: the inner layer optimization of the step (4.1) is realized according to the following algorithm steps, and the superscript k represents the iteration number:

4.1.1) choosing an initial point z1 of the iteration⁰And if k is equal to l is equal to 0, then z1⁰＝z⁰Else z1⁰Value z2 as skin input^l；

4.1.2) iteration point z1 of the k-th time^kSubstituting the k into the inner layer ordinary differential equation system, when k is 0, z1^k＝z1⁰Respectively performing forward integration and backward integration on the expressions (6) and (7), solving a state variable x and a covariate lambda, and calculating a target value J of the kth iteration by the expression (4)₁ ^k；

4.1.3) determining whether the convergence condition expression (9) is satisfied, and if so, determining the optimal solution z1 of the inner layer^*＝z1^kMixing z1^*Transmitting the initial solution to the outer layer as the initial solution of the outer layer iteration; otherwise, turning to step (4.1.4), equation (9) is expressed as follows: (ii) a

|J₁ ^k-J₁ ^j+1|≤ζ₁ (9)

4.1.4) the state variable x and the iteration point z1^kCalculation of gradient g by substituting formula (10)^k：

<math><mrow><msup><mi>g</mi><mi>k</mi></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><mi>&lambda;</mi><msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mi>T</mi></msup><mo>&CenterDot;</mo><mfrac><mrow><mo>&PartialD;</mo><mi>f</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mn>1</mn><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>]</mo></mrow><mrow><mo>&PartialD;</mo><mi>z</mi><mn>1</mn><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>10</mn><mo>)</mo></mrow></mrow></math>

Saving z1^kAnd g^kThen calculate the search direction d^k，d^k-1Indicating the search direction, β, of the previous iteration^kAre the intermediate parameters:

<math><mrow><msup><mi>d</mi><mi>k</mi></msup><mo>=</mo><mfenced open='{' close=''><mtable><mtr><mtd><mo>-</mo><msup><mi>g</mi><mi>k</mi></msup><mo>,</mo></mtd><mtd><mi>k</mi><mo>=</mo><mn>1</mn><mo>;</mo></mtd></mtr><mtr><mtd><mo>-</mo><msup><mi>g</mi><mi>k</mi></msup><mo>+</mo><msup><mi>&beta;</mi><mi>k</mi></msup><msup><mi>d</mi><mrow><mi>k</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>,</mo></mtd><mtd><mi>k</mi><mo>&GreaterEqual;</mo><mn>2</mn><mo>.</mo></mtd></mtr></mtable></mfenced></mrow></math> wherein, <math><mrow><msup><mi>&beta;</mi><mi>k</mi></msup><mo>=</mo><mfrac><mrow><msup><mrow><mo>(</mo><msup><mi>g</mi><mi>k</mi></msup><mo>)</mo></mrow><mi>T</mi></msup><mrow><mo>(</mo><msup><mi>g</mi><mi>k</mi></msup><mo>-</mo><msup><mi>g</mi><mrow><mi>k</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>)</mo></mrow></mrow><msup><mrow><mo>|</mo><mo>|</mo><msup><mi>g</mi><mrow><mi>k</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>|</mo><mo>|</mo></mrow><mn>2</mn></msup></mfrac><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>11</mn><mo>)</mo></mrow></mrow></math>

4.1.5) determining the optimal search step size α^k: if k is 0, then α is taken^kα 0, go to step 4.1.6); otherwise, from the current iteration point z1^kStarting in the direction d^kOne-dimensional search is carried out to find the optimal step factor alpha^*And satisfies the following conditions:

<math><mrow><mi>H</mi><mn>1</mn><mrow><mo>(</mo><msup><mrow><mi>z</mi><mn>1</mn></mrow><mi>k</mi></msup><mo>+</mo><msup><mi>&alpha;</mi><mo>*</mo></msup><mo>&CenterDot;</mo><msup><mi>d</mi><mi>k</mi></msup><mo>)</mo></mrow><mo>=</mo><munder><mi>min</mi><mrow><mi>&alpha;</mi><mo>&GreaterEqual;</mo><mn>0</mn></mrow></munder><mi>H</mi><mn>1</mn><mrow><mo>(</mo><msup><mrow><mi>z</mi><mn>1</mn></mrow><mi>k</mi></msup><mo>+</mo><mi>&alpha;</mi><mo>&CenterDot;</mo><msup><mi>d</mi><mi>k</mi></msup><mo>)</mo></mrow><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>12</mn><mo>)</mo></mrow></mrow></math>

wherein H1 represents the Hamiltonian of the inner layer optimization problem, calculated by equation (13),

represents finding the step size α in α ∈ [0, + ∞) ] that minimizes H1^*Formula (13) is expressed as follows:

H1＝λ(t)^T·f[x(t)，z1(t)，t] (13)

get

D is a coefficient integer value;

4.1.6) calculate the next iteration point

z1^k+1＝z1^k+α^k·d^k (14)

4.1.7) add 1 to the number of iterations, i.e. k ═ k +1, z1 in step 4.1.6)^k+1Saved as current point z1^kContinuing iteration, and turning to the step 4.1.2);

the outer optimization of said step (4.2) is carried out according to the following algorithm steps, the superscript l representing the current iteration number:

4.2.1) taking the current iteration point of the outer optimization as z2^l＝z1^*The initial value of l is 0;

4.2.2) mixing of z2^lSubstituting into an outer ordinary differential equation system, respectively performing forward integration and backward integration on the equations (6) and (8), solving a state variable x and a co-state variable theta, and calculating a target value J of the 1 st iteration by using the equation (5)₂ ^l；

4.2.3) judging whether the convergence condition formula (15) is satisfied, if so, judging the optimal solution z of the double-layer optimization^*＝z2^lOptimum objective function value J^*＝J₂ ^lSaving and delivering z^*And J^*To an output display module; otherwise, turning to the next step; formula (15) is expressed as follows:

|J₂ ^l-J₂ ^l+1|≤ζ₂ (15)

4.2.4) the state variable x and the iteration point z2^lCalculation of gradient h by substitution formula (16)^l：

<math><mrow><msup><mi>h</mi><mi>l</mi></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><mfrac><mrow><mo>&PartialD;</mo><mi>&psi;</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mn>2</mn><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>.</mo><mi>t</mi><mo>]</mo></mrow><mrow><mo>&PartialD;</mo><mi>z</mi><mn>2</mn><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac><mo>+</mo><mi>&theta;</mi><msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mi>T</mi></msup><mo>&CenterDot;</mo><mfrac><mrow><mo>&PartialD;</mo><mi>f</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mn>2</mn><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>]</mo></mrow><mrow><mo>&PartialD;</mo><mi>z</mi><mn>2</mn><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>16</mn><mo>)</mo></mrow></mrow></math>

Saving z2^lAnd h^lThen calculate the search direction e¹，e^1-1Representing the search direction, η, of a previous iteration^lAre the intermediate parameters:

<math><mrow><msup><mi>e</mi><mi>l</mi></msup><mo>=</mo><mfenced open='{' close=''><mtable><mtr><mtd><mo>-</mo><msup><mi>h</mi><mi>l</mi></msup><mo>,</mo></mtd><mtd><mi>l</mi><mo>=</mo><mn>1</mn><mo>;</mo></mtd></mtr><mtr><mtd><mo>-</mo><msup><mi>h</mi><mi>l</mi></msup><mo>+</mo><msup><mi>&eta;</mi><mi>l</mi></msup><msup><mi>e</mi><mrow><mi>l</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>,</mo></mtd><mtd><mi>l</mi><mo>&GreaterEqual;</mo><mn>2</mn><mo>.</mo></mtd></mtr></mtable></mfenced></mrow></math> wherein, <math><mrow><msup><mi>&eta;</mi><mi>l</mi></msup><mo>=</mo><mfrac><mrow><msup><mrow><mo>(</mo><msup><mi>h</mi><mi>l</mi></msup><mo>)</mo></mrow><mi>T</mi></msup><mrow><mo>(</mo><msup><mi>h</mi><mi>l</mi></msup><mo>-</mo><msup><mi>h</mi><mrow><mi>l</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>)</mo></mrow></mrow><msup><mrow><mo>|</mo><mo>|</mo><msup><mi>h</mi><mrow><mi>l</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>|</mo><mo>|</mo></mrow><mn>2</mn></msup></mfrac><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>17</mn><mo>)</mo></mrow></mrow></math>

4.2.5) determining the optimal search step size γ^l: if l is 0, then take γ^lGo to step 4.2.6, γ 0); otherwise, from the current iteration point z2^lStarting in the direction h^lOne-dimensional search is carried out to find the optimal step factor gamma^*And satisfies the following conditions:

<math><mrow><mi>H</mi><mn>2</mn><mrow><mo>(</mo><msup><mrow><mi>z</mi><mn>2</mn></mrow><mi>l</mi></msup><mo>+</mo><msup><mi>&gamma;</mi><mo>*</mo></msup><mo>&CenterDot;</mo><msup><mi>e</mi><mi>l</mi></msup><mo>)</mo></mrow><mo>=</mo><mrow><munder><mi>min</mi><mrow><mi>&gamma;</mi><mo>&GreaterEqual;</mo><mn>0</mn></mrow></munder><mi>H</mi><mn>2</mn><mrow><mo>(</mo><msup><mrow><mi>z</mi><mn>2</mn></mrow><mi>l</mi></msup><mo>+</mo><msup><mrow><mi>&gamma;</mi><mo>&CenterDot;</mo><mi>e</mi></mrow><mi>l</mi></msup><mo>)</mo></mrow></mrow><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>18</mn><mo>)</mo></mrow></mrow></math>

wherein H2 represents the Hamiltonian of the skin optimization problem, calculated from equation (19),

represents finding the step size γ that minimizes H2 in γ ∈ [0, + ∞) ]^*；

H2＝ψ[x(t)，z2(t)，t]+θ(t)^T·f[x(t)，z2(t)，t] (19)

Get

B is a coefficient integer value;

4.2.6) calculate the next iteration point:

z2^l+1＝z2^l+γ^l·d^l (20)

4.2.7) add 1 to the number of iterations, i.e. l ═ l +1, z2 in step 4.2.6)^l+1Saved as current point z2^lContinue iteration, go to step 4.2.2).

6. The optimum control method according to claim 4 or 5, wherein: in the step 1), the data of the industrial process object acquired by the on-site intelligent instrument is transmitted to a real-time database of the DCS, the latest data obtained from the database of the DCS in each sampling period is output to the upper computer, and initialization processing is carried out by an initialization module of the upper computer.

7. The optimum control method according to claim 4 or 5, wherein: the optimal decision variable z obtained in the step (4.2.3)^*Converting the result into an optimal control curve u^*(t) and displaying u on the human-machine interface of the upper computer^*(t) and an optimum target value J^*(ii) a At the same time, the optimum control curve u^*(t) transmitting the information to a control station of the DCS system through the bus interface, and displaying the obtained optimization result information in the DCS system.

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