CN101770209A - Method for performing scattering predictive control on multi-time-scale complex huge system - Google Patents

Abstract

The invention discloses a method for performing scattering predictive control on a multi-time-scale complex huge system. Aiming at a difference of the dynamical property of the interconnected subsystems of the multi-time-scale complex huge system, the state of each subsystem is sampled and calculated in different sampling periods. The method is characterized in that a predictive control method of a variable time domain is adopted to resolve the contradiction between the control performance optimization and the calculation complexity; an inequality constraints conversion method is adopted to convert a constraint optimization problem to a constraint-free optimization problem; the following actions of the subsystem are predicted by using a subsystem module; a predicting result of the subsystem is fed back and corrected by using a measured value; a loss relevant signal is estimated by using an original value substitution method; the calculation complexity is further decreased by using a reduction state space decomposition algorithm so as to promote the optimization timeliness. In this way, the distributed control of an industrial huge system is realized. A system for manufacturing iron proves the effectiveness of the method and shows that the method has the advantages of high convergence rate, high computing efficiency and excellent optimization performance.

Description

The dispersion forecast Control Algorithm of the big system of a kind of scale complex of many time

Technical field

The present invention relates to the global optimization and the control of system, relate in particular to the dispersion forecast Control Algorithm of the big system of a kind of scale complex of many time.

Background technology

By a large amount of dynamic cell system to be connected to each other the extensive interacted system that constitutes be common system configuration in the industrial processes such as chemical industry, oil, metallurgy, its optimal control plays an important role to increasing economic efficiency.But non-linear, the uncertain characteristic of its component units and complicated related [1] each other, and the difference of the dynamic perfromance of each subsystem on time scale, make control effect conventional, be difficult to reach expection towards the control device of single small-scale object.

As everyone knows, PREDICTIVE CONTROL based on model prediction, rolling optimization and feedback compensation is one of effective ways that solve the complex dynamic systems optimum control, and distributed control has significantly reduced computational complexity with parallel the carrying out of each subsystem that the design and the enforcement of optimal control policy decomposes interconnected big system.Therefore Distributed Predictive Control is the effective scheme that solves above-mentioned interconnected big system optimal control problem.The theoretical research of industrial complex large system in recent years [2]-[6] are confined to the Distributed Predictive Control of single time scale substantially, there is only a few research [7] to relate to the PREDICTIVE CONTROL of yardstick of many time, but it relates to the Multi-time Scale optimization problem in the single window, do not illustrate the concrete length and the move mode of rolling optimization window, and the counting yield of its optimized Algorithm is low, and the research of multirate system [8]-[11] are also inequality on notion and research emphasis with here " the big system of yardstick of many time ".Because often difference is bigger for the dynamic perfromance of each interconnection subsystem in the practical object,, will causes controlling poor effect, control performance deterioration, increase unnecessary consequences such as energy consumption as still taking same sampling computation period.And in actual applications, most industrial complex large systems do not adopt the mode of coordination optimization yet, but each subsystem is optimized isolatedly, and this way tends to cause the hysteresis of regulated quantity, thereby the production status of the high energy consumption of causing, low output becomes a technical bottleneck of limiting output.The dispersion forecast Control Algorithm of the big system of scale complex of many time is considered the difference between speed subsystem dynamic perfromance, takes into account the reduction of system function optimization and computational complexity, is a kind of complex large system optimal control method that the applications well prospect is arranged.

List of references:

[1] Ding Xiaodong. uncertain system optimum theory and applied research. the PhD dissertation .2002. of Donghua University

[2]Holger?Voos.Market-based?algorithms?for?optimal?decentralized?control?ofcomplex?dynamic?systems.Proceedings?of?the?38 ^*?Conference?on?Decision?&Control?Phoenix，Arizona?USA?December?1999

[3]Xiaoning?Du，Yugeng?Xi，Shaoyuan?Li.Distributed?Model?Predictive?Control?forLarge-scale?Systems.Proceedings?of?the?American?Control?Conference?Arlington，VAJune?25-27，2001.

[4]Camponogara?E，Jia?D，Krogh?B?H.Distributed?model?predictive?control.IEEEControl?Systems?Magazine，2002，22(1)：44-52.

[5]Aswin?N.Venkat，James?B.Rawlings?and?Stephen?J.Wright.Stability?andoptimality?of?distributed?model?predictive?control.Proceedings?of?the?44th?IEEEConference?on?Decision?and?Control，and?the?European?Control?Conference，2005

[6]Aswin?N.Venkat，James?B.Rawlings，and?Stephen?J.Wright.Distributed?modelpredictive?control?of?large-scale?systems.Assessment?and?Future?Directions，LNCIS358，pp.591-605，2007.

[7] Chen Shaomian, Zhao Jun, Qian Jixin. Multi-time Scale is disperseed predictive control algorithm. robotization journal .2007.9.Vol.33, No.9.

[8] Dong Qingxia, Wang Ping. the research of many speed sampling system and emulation. the journal .2006.2.Vol.25.No.1. of Tianjin University of Technology

[9] Zou Yuanyuan, Liu Xiaohua. many speed monodrome generalized predictable control system and stability analysis. University Of Qingdao's journal (engineering version) .2005.12.Vol.20, No.4.

[10] Guo Chenghe, Qian Wenhan. robot many speed of multisensor sampled-data control system research. the flexible college journal .1997.9.Vol.33 in Shanghai, No.9.

[11] Luo Jie, Liu Xiaohua. based on the network predictive control algorithm of many speed sampling system. the journal .2008.24 of Ludong University (2): 122-126.

Summary of the invention

The objective of the invention is to overcome the deficiencies in the prior art, the dispersion forecast Control Algorithm of the big system of a kind of scale complex of many time is provided.

The dispersion forecast Control Algorithm of the big system of scale complex of many time comprises the steps:

1) supposes that the big system S of scale complex of many time has been divided into N the different subsystem S of inter-related dynamic perfromance _i, i=1,2 ..., N, N＞1, subsystem S _iContinuous model be M _i, continuous model M _iVariable comprise state variable x _i, control variable u _i, associated variable z _i, wherein, associated variable z _iExpression subsystem S _j, j=1,2, ..., N, j ≠ i is to subsystem S _iCoupling, satisfy static equality constraint z _i(t)=h _i(x ₁(t) ..., x _I-1(t), x _I+1(t) ..., x _N(t)), in addition, subsystem S _iContinuous model M _iAlso comprise static inequality constrain and dynamic equality constraint, use the inequality constrain transformation approach subsystem S _iThe static inequality constrain of continuous model be converted into subsystem S _iThe dynamic equality constraint of continuous model;

2) according to subsystem S _iDynamic perfromance determine subsystem S _iSampling period T _i, and T _iSatisfy T _i=T _Min* a _i, $T_{\min }=\underset{i=\mathrm{1,2},...,N}{\min }\left\{T_i\right\},$ a _iBe natural number, with T _iBe the sampling period, utilize forward-difference method subsystem S _iContinuous model in dynamic equation constrained approximation discretize; To static equality constraint z _i(t)=h _i(x ₁(t) ..., x _I-1(t), x _I+1(t) ..., x _N(t)), with T _iFor becoming after the sampling period discretize $z_i\left({\mathrm{kT}}_i\right)=h_i({\tilde{x}}_1\left({\mathrm{kT}}_i\right),\·\·\·,{\tilde{x}}_{i-1}\left({\mathrm{kT}}_i\right),{\tilde{x}}_{i+1}\left({\mathrm{kT}}_i\right),\·\·\·,{\tilde{x}}_N\left({\mathrm{kT}}_i\right)),$ K=k ₀, k ₀+ 1 ..., k _f, k ₀And k _fBe natural number, and k ₀＜k _f, J=1,2 ..., N, j ≠ i represents with T _iFor the sampling period to subsystem S _jState variable x _j(t) carry out the value that virtual sampling obtains, obtain subsystem S _iDiscrete model M _i', if T _j≤ T _i, the problem that does not then exist sampled value to lack; If T _j＞T _i, then the time point that does not overlap in sampling will the situation of sampled value disappearance occur, and the sampled value of disappearance replaces with the last sampled value;

3) the rolling optimization method of employing PREDICTIVE CONTROL is at t=kT _iConstantly, to subsystem S _iAt following t=(k+1) T _iTo t=(k+P _i) T _iThe system action of time period predicts and optimizes, wherein P _iBe subsystem S _iAt t=kT _iConstantly carry out the prediction time domain of rolling optimization, L _t=P _iT _iBe t=kT _iThe time window length of moment rolling optimization is by t=kT _iParticipate in the subsystem S of optimization constantly _tIn the slowest subsystem S _s, T _s≤ T _l, S _l∈ S _tDetermine, i.e. L _t=T _sP, P are constant, the minimum prediction time domain that expression allows; Subsystem S _iThe rolling optimization frequency be

4) model prediction and the feedback compensation method of employing PREDICTIVE CONTROL are at t=kT _iConstantly, utilize subsystem S _iDiscrete model to subsystem S _iAt following t=(k+1) T _iTo t=(k+P _i) T _iThe system action of time period is predicted, utilizes measured value to carry out feedback compensation to predicting the outcome.Use yojan state space decomposition algorithm to find the solution subsystem S _iAt following t=(k+1) T _iTo t=(k+P _i) T _iThe optimal control problem J of time period _{I, k}, realize the decentralised control of the big system of scale complex of many time.

Described step 1) comprises:

If subsystem S _iContinuous model M _iAs follows:

$\left\{\begin{array}{c}{\stackrel{\·}{x}}_i\left(t\right)=f_i(x_i\left(t\right),u_i\left(t\right),z_i\left(t\right))\\ g_i(x_i\left(t\right),z_i\left(t\right),u_i\left(t\right))\≥0\\ x_i\left(t_0\right)=x_{i,0}\end{array}\right.,$ t ₀≤t≤t _f

Wherein, x _iBe subsystem S _iState variable, u _iBe subsystem S _iControl variable, z _iBe subsystem S _iAssociated variable, and satisfy equation: z _i(t)=h _i(x ₁(t) ..., x _N(t)), f _iBe subsystem S _iThe dynamic equality constraint that satisfies, g _iBe subsystem S _iThe static inequality constrain of satisfying, t ₀And t _fBe respectively the initial and termination time of system, x _{I, 0}Be x _iOriginal state, for subsystem S _iStatic inequality constrain g _i(x _i(t), z _i(t), u _i(t)) 〉=0, the new state variable x of definition _{S, i}(t), satisfy equation:

$\left\{\begin{array}{c}{\stackrel{\·}{x}}_{s,i}\left(t\right)=f_{s,i}(x_i\left(t\right),u_i\left(t\right),z_i\left(t\right))={\left[G_i\left(t\right)\right]}^2\mathrm{\σ}\left(G_i\left(t\right)\right)\\ x_{s,i}\left(t_0\right)=0\end{array}\right.$

Wherein σ () is a step function, satisfies:

$\mathrm{\&sigma;}(G_i\left(t\right)=\left\{\begin{array}{cc}0,& G_i\left(t\right)\&GreaterEqual;0\\ K_{s,i}& G_i\left(t\right)<0\end{array}\right.$

K wherein _{S, i}Be a constant, terminal condition is:

$x_{s,i}\left(t_f\right)={\&Integral;}_{t_0}^{t_f}{G}_i^2\left(t\right)\mathrm{\&sigma;}\left(G_i\left(t\right)\right)\mathrm{dt}=0$

Subsystem model M then _iCan be expressed as the form of following augmented state equation:

${\stackrel{\&CenterDot;}{x}}_i\left(t\right)=F_i(x_i\left(t\right),u_i\left(t\right),z_i\left(t\right))\stackrel{\mathrm{\&Delta;}}{=}\left[\begin{array}{c}{f}_i(x_i\left(t\right),u_i\left(t\right),z_i\left(t\right))\\ G_i^2\left(t\right)\mathrm{\&sigma;}\left(G_i\left(t\right)\right)\end{array}\right]$

And z _i(t)=h _i(x ₁(t) ..., x _NAnd x (t)) _i(t ₀)=x _{I, 0}, wherein $x_i^T\left(t\right)\stackrel{\mathrm{\&Delta;}}{=}[x_i\left(t\right),x_{s,i}\left(t\right)]$ Be subsystem S _iThe augmented state vector.

Described step 2) comprising:

According to subsystem S _iDynamic perfromance determine subsystem S _iSampling period T _i, and T _iSatisfy T _i=T _Min* a _i, $T_{\min }=\underset{i=\mathrm{1,2},...,N}{\min }\left\{T_i\right\},$ a _iBe natural number, with T _iBe the sampling period, utilize forward-difference method $\stackrel{\&CenterDot;}{\mathrm{\&chi;}}\left(t\right)\&ap;\frac{\mathrm{\&chi;}\left((k+1)T_i\right)-\mathrm{\&chi;}\left({\mathrm{kT}}_i\right)}{T_i},$ χ is x _iOr u _i, with subsystem S _iThe continuous model discretize, obtain subsystem S _iDiscrete model M _i' as follows:

$\left\{\begin{array}{c}{x}_i\left((k+1)T_i\right)=F_i(x_i\left({\mathrm{kT}}_i\right),u_i\left({\mathrm{kT}}_i\right),z_i\left({\mathrm{kT}}_i\right))\\ x_i\left(k_0{T}_i\right)=x_{i,0}\end{array}\right.$

And interconnection constraint: $z_i\left({\mathrm{kT}}_i\right)=H_i({\tilde{x}}_1\left({\mathrm{kT}}_i\right),\&CenterDot;\&CenterDot;\&CenterDot;,{\tilde{x}}_N\left({\mathrm{kT}}_i\right)),$ Wherein, k=k ₀, k ₀+ 1 ..., k _f, k ₀And k _fBe natural number, and k ₀＜k _f, x _{I, 0}Be t=k ₀T _iState initial value constantly, J=1,2 ..., N, j ≠ i represents with T _iFor the sampling period to subsystem S _jState variable x _j(t) carry out that virtual sampling obtains, if T _j≤ T _i, the problem that does not then exist sampled value to lack; If T _j＞T _i, then the time point that does not overlap in sampling will the situation of sampled value disappearance occur, and the sampled value of disappearance replaces with the last sampled value, promptly ${\tilde{x}}_j\left({\mathrm{kT}}_i\right)=x_j\left(k^{\&prime;}{T}_j\right),$ k′T _j≤kT _i≤(k′+1)T _j。

Described step 4) comprises:

Adopt the model prediction method of PREDICTIVE CONTROL, at t=kT _iConstantly, utilize subsystem S _iDiscrete model to subsystem S _iAt following t=(k+1) T _iTo t=(k+P _i) T _iThe system action of time period is predicted:

$\left\{\begin{array}{c}{\stackrel{\&OverBar;}{x}}_i\left((k+l+1)T_i\right)=F_i({\stackrel{\&OverBar;}{x}}_i\left((k+l)T_i\right),u_i\left((k+l)T_i\right),z_i\left((k+l)T_i\right))\\ {\stackrel{\&OverBar;}{x}}_i\left({\mathrm{kT}}_i\right)=x_{i,0}\left({\mathrm{kT}}_i\right)\end{array}\right.$

And $z_i\left((k+l)T_i\right)=H_i({\stackrel{\&OverBar;}{x}}_1\left((k+l)T_i\right),\&CenterDot;\&CenterDot;\&CenterDot;,{\stackrel{\&OverBar;}{x}}_N\left((k+l)T_i\right)),$ l＝0，1，…，P _i-1

Obtain

L=0,1 ..., P _i-1, the model prediction method of employing PREDICTIVE CONTROL utilizes measured value to predicting the outcome

Carry out feedback compensation, obtain

That is:

l＝0，…，P _i-1

γ wherein _iBe feedback correcting coefficient; e _iReflected subsystem S _iVirtual condition x _iWith the model prediction state

Between deviation, that is: $e_i\left({\mathrm{kT}}_i\right)={\stackrel{\&OverBar;}{x}}_i\left({\mathrm{kT}}_i\right)-x_i\left({\mathrm{kT}}_i\right),$ Quantity of state X with each subsystem _iBe decomposed into two subset X _i ^CAnd X _i ^I, promptly for subsystem S _i, that part of state variable that definition directly influences the related input of at least one related subsystem is subsystem S _iOutside association status subclass $X_i^C\stackrel{\mathrm{\&Delta;}}{=}\{x_i^C\&Element;X_i|\&Exists;j\&Element;\{\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,N\},z_j=H_j(\&CenterDot;\&CenterDot;\&CenterDot;,{\tilde{x}}_i^C,\&CenterDot;\&CenterDot;\&CenterDot;)\};$ Definition subsystem S _iAll the other state variables be the internal state subclass $X_i^I\stackrel{\mathrm{\&Delta;}}{=}\{x_i^I\&Element;X_i\backslash X_i^C\};$ By above-mentioned definition, subsystem S _iState equation can be rewritten as:

Wherein

If subsystem S _iAt t=kT _iThe objective function that is optimized control is:

If λ _i ^IAnd λ _i ^CBe respectively about formula

And formula Association's state, then utilize yojan state space decomposition algorithm solving-optimizing problem J _{I, k}As follows: the initial value of given all subsystem controls variablees, even $u_i\left((k+l)T_i\right)={\hat{u}}_i\left((k+l)T_i\right),$ L=0,1 ..., P _i-1, i=1,2 ..., N is according to subsystem S _iDiscrete model calculate corresponding subsystem S _iThe status predication initial track

${\mathrm{\&lambda;}}_i^C\left((k+l)T_i\right)={\widehat{\mathrm{\&lambda;}}}_i^C\left((k+l)T_i\right),$ $z_i^C\left((k+l)T_i\right)={\hat{z}}_i^C\left((k+l)T_i\right),$ Carry out iterative computation as follows:

Iterative step 1: find the solution following dimensionality reduction optimization problem about subsystem internal state and control:

If the optimal control solution of above-mentioned optimization problem is Corresponding internal state track is

L=0,1 ..., P-1;

Iterative step 2: by following system of equations

Can try to achieve λ _{I, new} ^I((k+l) T _i), and ${\hat{v}}_i\left((k+l)T_i\right)=v_i\left({\hat{x}}_{i,\mathrm{new}}^I\left((k+l)T_i\right)\right),{\hat{u}}_{i,\mathrm{new}}\left((k+l)T_i\right),{\hat{z}}_i\left((k+l)T_i\right),$ The iteration following formula

The outside association status prediction locus that obtains upgrading

Iterative step 3: by following system of equations

Can try to achieve λ _{I, new} ^C((k+l) T _i);

Iterative step 4: upgrade ${\hat{z}}_i\left((k+l)T_i\right)=z_i\left((k+l)T_i\right),$ Order ${\hat{u}}_i\left((k+l)T_i\right)={\hat{u}}_{i,\mathrm{new}}\left((k+l)T_i\right),$ ${\hat{x}}_i^I\left((k+l+1)T_i\right)={\hat{x}}_{i,\mathrm{new}}^I\left((k+l+1)T_i\right),$ ${\hat{x}}_i^C\left((k+l+1)T_i\right)={\hat{x}}_{i,\mathrm{new}}^C\left((k+l+1)T_i\right),$ Return iterative step 1, restrain until iterative process.

The present invention is directed to the big system of the complex industrial of forming by the interconnection subsystem of different time yardstick, proposed a kind of dispersion optimization control scheme of practical.According to the inconsistent characteristics of each subsystem sampling computation period, adopt the forecast Control Algorithm of variable window length, both improved the Control and Optimization performance, take into account the simplicity and the real-time of calculating again, simultaneously, for the correlation signal that lacks because of sampling between the speed subsystem, use the initial value method of substitution to estimate.When each optimization time window carries out rolling optimization, adopt yojan state space decomposition algorithm to realize the distributed control of interconnected big system, decompose by state space in the subsystem after decomposition, further reduce the scale of computation optimization, help improving the real-time of calculating.This method has fast convergence rate, counting yield height, optimize remarkable advantages such as performance is good.

Description of drawings

Fig. 1 is the ironmaking processes schematic flow sheet.

Embodiment

The optimal control of large-scale industry process such as chemical industry, oil, metallurgy etc. plays an important role to increasing output, minimizing raw materials consumption, energy efficient and raising product, and characteristics such as that these objects have usually is non-linear, large time delay, high dimension use conventional control device can't reach the control effect of expection usually.On the other hand, each subsystem of forming big system can't be expressed with unified markers because difference in dynamic characteristics and other a variety of causes present different yardsticks in time, and this has further increased the complex nature of the problem.And in the practical study application process, most of researchist ignores this characteristic usually, uses identical markers to be optimized calculating, and this will make the control effect descend, and will cause control performance to worsen when serious.The present invention is directed to this class speed and mix big system, be intended to set up a kind of simple and practical dispersion forecast Control Algorithm, the contradiction between processing controls performance optimization preferably and the calculating real-time.In the selection of optimizing time domain, the present invention adopts the optimal way of variable time length of window, has alleviated control performance optimization and calculating real-time contradiction between the two in the computation optimization dexterously.And the associated variable that lacks during for computation optimization adopts the initial value method of substitution to supply, and has reasonable and easy to operate advantage.When carrying out distributed optimization, adopt yojan state space decomposition algorithm that big system is carried out coordination optimization, compare with common composition decomposition algorithm, further reduced the computation optimization scale, improved the real-time of calculating.

The dispersion forecast Control Algorithm of the big system of scale complex of many time comprises the steps:

1) supposes that the big system S of scale complex of many time has been divided into N the different subsystem S of inter-related dynamic perfromance _i, i=1,2 ..., N, N＞1, subsystem S _iContinuous model be M _i, continuous model M _iVariable comprise state variable x _i, control variable u _i, associated variable z _i, wherein, associated variable z _iExpression subsystem S _j, j=1,2 ..., N, j ≠ i is to subsystem S _iCoupling, satisfy static equality constraint z _i(t)=h _i(x ₁(t) ..., x _I-1(t), x _I+1(t) ..., x _N(t)), in addition, subsystem S _iContinuous model M _iAlso comprise static inequality constrain and dynamic equality constraint, use the inequality constrain transformation approach subsystem S _iThe static inequality constrain of continuous model be converted into subsystem S _iThe dynamic equality constraint of continuous model;

2) according to subsystem S _iDynamic perfromance determine subsystem S _iSampling period T _i, and T _iSatisfy T _i=T _Min* a _i, $T_{\min }=\underset{i=\mathrm{1,2},...,N}{\min }\left\{T_i\right\},$ a _iBe natural number, with T _iBe the sampling period, utilize forward-difference method subsystem S _iContinuous model in dynamic equation constrained approximation discretize; To static equality constraint z _i(t)=h _i(x ₁(t) ..., x _I-1(t), x _I+1(t) ..., x _N(t)), with T _iFor becoming after the sampling period discretize $z_i=\left({\mathrm{kT}}_i\right)=h_i({\tilde{x}}_1\left({\mathrm{kT}}_i\right),\&CenterDot;\&CenterDot;\&CenterDot;,{\tilde{x}}_{i-1}\left({\mathrm{kT}}_i\right),{\tilde{x}}_{i+1}\left({\mathrm{kT}}_i\right),\&CenterDot;\&CenterDot;\&CenterDot;,{\tilde{x}}_N\left({\mathrm{kT}}_i\right)),$ K=k ₀, k ₀+ 1 ..., k _f, k ₀And k _fBe natural number, and k ₀＜k _f,

J=1,2 ..., N, j ≠ i represents with T _iFor the sampling period to subsystem S _jState variable x _j(t) carry out the value that virtual sampling obtains, obtain subsystem S _iDiscrete model M _i', if T _j≤ T _i, the problem that does not then exist sampled value to lack; If T _j＞T _i, then the time point that does not overlap in sampling will the situation of sampled value disappearance occur, and the sampled value of disappearance replaces with the last sampled value;

3) the rolling optimization method of employing PREDICTIVE CONTROL is at t=kT _iConstantly, to subsystem S _iAt following t=(k+1) T _iTo t=(k+P _i) T _iThe system action of time period predicts and optimizes, wherein P _iBe subsystem S _iAt t=kT _iConstantly carry out the prediction time domain of rolling optimization, L _t=P _iT _iBe t=kT _iThe time window length of moment rolling optimization is by t=kT _iParticipate in the subsystem S of optimization constantly _tIn the slowest subsystem S _s, T _s≤ T _l, S _l∈ S _tDetermine, i.e. L _t=T _sP, P are constant, the minimum prediction time domain that expression allows; Subsystem S _iThe rolling optimization frequency be

4) model prediction and the feedback compensation method of employing PREDICTIVE CONTROL are at t=kT _iConstantly, utilize subsystem S _iDiscrete model to subsystem S _iAt following t=(k+1) T _iTo t=(k+P _i) T _iThe system action of time period is predicted, utilizes measured value to carry out feedback compensation to predicting the outcome.Use yojan state space decomposition algorithm to find the solution subsystem S _iAt following t=(k+1) T _iTo t=(k+P _i) T _iThe optimal control problem J of time period _{I, k}, realize the decentralised control of the big system of scale complex of many time.

Described step 1) comprises:

If subsystem S _iContinuous model M _iAs follows:

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{x}}_i\left(t\right)=f_i(x_i\left(t\right),u_i\left(t\right),z_i\left(t\right))\\ g_i(x_i\left(t\right),z_i\left(t\right),u_i\left(t\right))\&GreaterEqual;0\\ x_i\left(t_0\right)=x_{i,0}\end{array}\right.,$ t ₀≤t≤t _f

Wherein, x _iBe subsystem S _iState variable, u _iBe subsystem S _iControl variable, z _iBe subsystem S _iAssociated variable, and satisfy equation: z _i(t)=h _i(x ₁(t) ..., x _N(t)), f _iBe subsystem S _iThe dynamic equality constraint that satisfies, g _iBe subsystem S _iThe static inequality constrain of satisfying, t ₀And t _fBe respectively the initial and termination time of system, x _{I, 0}Be x _iOriginal state, for subsystem S _iStatic inequality constrain g _i(x _i(t), z _i(t), u _i(t)) 〉=0, the new state variable x of definition _{S, i}(t), satisfy equation:

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{x}}_{s,i}\left(t\right)=f_{s,i}(x_i\left(t\right),u_i\left(t\right),z_i\left(t\right))={\left[G_i\left(t\right)\right]}^2\mathrm{\&sigma;}\left(G_i\left(t\right)\right)\\ x_{s,i}\left(t_0\right)=0\end{array}\right.$

Wherein σ () is a step function, satisfies:

$\mathrm{\&sigma;}(G_i\left(t\right)=\left\{\begin{array}{cc}0,& G_i\left(t\right)\&GreaterEqual;0\\ K_{s,i}& G_i\left(t\right)<0\end{array}\right.$

K wherein _{S, i}Be a constant, terminal condition is:

$x_{s,i}\left(t_f\right)={\&Integral;}_{t_0}^{t_f}{G}_i^2\left(t\right)\mathrm{\&sigma;}\left(G_i\left(t\right)\right)\mathrm{dt}=0$

Subsystem model M then _iCan be expressed as the form of following augmented state equation:

${\stackrel{\&CenterDot;}{x}}_i\left(t\right)=F_i(x_i\left(t\right),u_i\left(t\right),z_i\left(t\right))\stackrel{\mathrm{\&Delta;}}{=}\left[\begin{array}{c}{f}_i(x_i\left(t\right),u_i\left(t\right),z_i\left(t\right))\\ G_i^2\left(t\right)\mathrm{\&sigma;}\left(G_i\left(t\right)\right)\end{array}\right]$

And z _i(t)=h _i(x ₁(t) ..., x _NAnd x (t)) _i(t ₀)=x _{I, 0}, wherein $x_i^T\left(t\right)\stackrel{\mathrm{\&Delta;}}{=}[x_i\left(t\right),x_{s,i}\left(t\right)]$ Be subsystem S _iThe augmented state vector.

Described step 2) comprising:

According to subsystem S _iDynamic perfromance determine subsystem S _iSampling period T _i, and T _iSatisfy T _i=T _Min* a _i, $T_{\min }=\underset{i=\mathrm{1,2},...,N}{\min }\left\{T_i\right\},$ a _iBe natural number, with T _iBe the sampling period, utilize forward-difference method $\stackrel{\&CenterDot;}{\mathrm{\&chi;}}\left(t\right)\&ap;\frac{\mathrm{\&chi;}\left((k+1)T_i\right)-\mathrm{\&chi;}\left({\mathrm{kT}}_i\right)}{T_i},$ χ is x _iOr u _i, with subsystem S _iThe continuous model discretize, obtain subsystem S _iDiscrete model M _i' as follows:

$\left\{\begin{array}{c}{x}_i\left((k+1)T_i\right)=F_i(x_i\left({\mathrm{kT}}_i\right),u_i\left({\mathrm{kT}}_i\right),z_i\left({\mathrm{kT}}_i\right))\\ x_i\left(k_0{T}_i\right)=x_{i,0}\end{array}\right.$

And interconnection constraint: $z_i\left({\mathrm{kT}}_i\right)=H_i({\tilde{x}}_1\left({\mathrm{kT}}_i\right),\&CenterDot;\&CenterDot;\&CenterDot;,{\tilde{x}}_N\left({\mathrm{kT}}_i\right)),$ Wherein, k=k ₀, k ₀+ 1 ..., k _f, k ₀And k _fBe natural number, and k ₀＜k _f, x _{I, 0}Be t=k ₀T _iState initial value constantly,

J=1,2 ..., N, j ≠ i represents with T _iFor the sampling period to subsystem S _jState variable x _j(t) carry out that virtual sampling obtains, if T _j≤ T _i, the problem that does not then exist sampled value to lack; If T _j＞T _i, then the time point that does not overlap in sampling will the situation of sampled value disappearance occur, and the sampled value of disappearance replaces with the last sampled value, promptly ${\tilde{x}}_j\left({\mathrm{kT}}_i\right)=x_j\left(k^{\&prime;}{T}_j\right),$ k′T _j≤kT _i≤(k′+1)T _j。

Described step 4) comprises:

Adopt the model prediction method of PREDICTIVE CONTROL, at t=kT _iConstantly, utilize subsystem S _iDiscrete model to subsystem S _iAt following t=(k+1) T _iTo t=(k+P _i) T _iThe system action of time period is predicted:

$\left\{\begin{array}{c}{\stackrel{\&OverBar;}{x}}_i\left((k+l+1)T_i\right)=F_i({\stackrel{\&OverBar;}{x}}_i\left((k+l)T_i\right),u_i\left((k+l)T_i\right),z_i\left((k+l)T_i\right))\\ {\stackrel{\&OverBar;}{x}}_i\left({\mathrm{kT}}_i\right)=x_{i,0}\left({\mathrm{kT}}_i\right)\end{array}\right.$

And $z_i\left((k+l)T_i\right)=H_i({\stackrel{\&OverBar;}{x}}_1\left((k+l)T_i\right),\&CenterDot;\&CenterDot;\&CenterDot;,{\stackrel{\&OverBar;}{x}}_N\left((k+l)T_i\right)),$ l＝0，1，…，P _i-1

Obtain

L=0,1 ..., P _i-1, the model prediction method of employing PREDICTIVE CONTROL utilizes measured value to predicting the outcome

Carry out feedback compensation, obtain

That is:

L=0 ..., P _i-1

γ wherein _iBe feedback correcting coefficient; e _iReflected subsystem S _iVirtual condition x _iWith the model prediction state Between deviation, that is: $e_i\left({\mathrm{kT}}_i\right)={\stackrel{\&OverBar;}{x}}_i\left({\mathrm{kT}}_i\right)-x_i\left({\mathrm{kT}}_i\right),$ Quantity of state X with each subsystem _iBe decomposed into two subset X _i ^CAnd X _i ^I, promptly for subsystem S _i, that part of state variable that definition directly influences the related input of at least one related subsystem is subsystem S _iOutside association status subclass $X_i^C\stackrel{\mathrm{\&Delta;}}{=}\{x_i^C\&Element;X_i|\&Exists;j\&Element;\{\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,N\},z_j=H_j(\&CenterDot;\&CenterDot;\&CenterDot;,{\tilde{x}}_i^C,\&CenterDot;\&CenterDot;\&CenterDot;)\};$ Definition subsystem S _iAll the other state variables be the internal state subclass $X_i^I\stackrel{\mathrm{\&Delta;}}{=}\{x_i^I\&Element;X_i\backslash X_i^C\};$ By above-mentioned definition, subsystem S _iState equation can be rewritten as:

Wherein

If subsystem S _iAt t=kT _iThe objective function that is optimized control is:

According to maximal principle, establish subsystem S _iThe Hamilton function be:

$H_{i,k}={\mathrm{\&Phi;}}_i(x_i^I\left((k+l)T_i\right),x_i^C\left((k+l)T_i\right),u_i\left((k+l)T_i\right))$

$+{\mathrm{\&lambda;}}_i^I\left((k+l+1)T_i\right)F_i^I\left(x_i^I\left(\right(k+l)T_i\right),u_i\left((k+l)T_i\right),w_i\left((k+l)T_i\right))$

$+{\mathrm{\&lambda;}}_i^C\left((k+l+1)T_i\right)F_i^C\left(x_i^C((k+l)T_i\right),v_i\left((k+l)T_i\right))$

λ wherein _i ^IAnd λ _i ^CBe respectively about formula $\mathrm{\&Delta;}{x}_i^I\left((k+1)T_i\right)=F_i^I(\mathrm{\&Delta;}{x}_i^I\left({\mathrm{kT}}_i\right),\mathrm{\&Delta;}{u}_i\left({\mathrm{kT}}_i\right),w_i\left({\mathrm{kT}}_i\right))$ And formula $\mathrm{\&Delta;}{x}_i^C\left((k+1)T_i\right)=F_i^C(\mathrm{\&Delta;}{x}_i^C\left({\mathrm{kT}}_i\right),v_i\left({\mathrm{kT}}_i\right))$ Association's state.Subsystem S then _iOptimal control solution should satisfy following first-order condition:

$\left\{\begin{array}{c}\frac{{\&PartialD;H}_{i,k}}{{\&PartialD;x}_i^I\left((k+l)T_i\right)}={\mathrm{\&lambda;}}_i^I\left((k+l)T_i\right)=\frac{{\&PartialD;\mathrm{\&Phi;}}_i}{{\&PartialD;x}_i^I\left((k+l)T_i\right)}+{\mathrm{\&lambda;}}_i^I\left((k+l+1)T_i\right)\frac{{\&PartialD;F}_i^I}{{\&PartialD;x}_i^I\left((k+l)T_i\right)}+{\mathrm{\&lambda;}}_i^C\left((k+l+1)T_i\right)\frac{{\&PartialD;F}_i^C}{{\&PartialD;v}_i}\frac{{\&PartialD;v}_i}{{\&PartialD;x}_i^I\left((k+l)T_i\right)}\\ {\mathrm{\&lambda;}}_i^I\left((k+P_i)T_i\right)=\frac{{\&PartialD;\mathrm{\&Gamma;}}_i}{{\&PartialD;x}_i^I\left((k+P_i)T_i\right)}\end{array}\right.$

$\left\{\begin{array}{c}\frac{{\&PartialD;H}_{i,k}}{{\&PartialD;x}_i^C(k+l)}={\mathrm{\&lambda;}}_i^C\left((k+l)T_i\right)=\frac{{\&PartialD;\mathrm{\&Phi;}}_i}{{\&PartialD;x}_i^C\left((k+l)T_i\right)}+{\mathrm{\&lambda;}}_i^I\left((k+l+1)T_i\right)\frac{{\&PartialD;F}_i^I}{{\&PartialD;w}_i}\frac{{\&PartialD;w}_i}{{\&PartialD;x}_i^C\left((k+l)T_i\right)}+{\mathrm{\&lambda;}}_i^C\left((k+l+1)T_i\right)\frac{{\&PartialD;F}_i^C}{{\&PartialD;x}_i^C\left((k+l)T_i\right)}\\ {\mathrm{\&lambda;}}_i^C\left((k+P_i)T_i\right)=\frac{{\&PartialD;\mathrm{\&Gamma;}}_i}{{\&PartialD;x}_i^C\left((k+P_i)T_i\right)}\end{array}\right.$

And

$\frac{{\&PartialD;H}_{i,k}}{{\&PartialD;u}_i\left((k+l)T_i\right)}=\frac{{\&PartialD;\mathrm{\&Phi;}}_i}{{\&PartialD;u}_i\left((k+l)T_i\right)}+{\mathrm{\&lambda;}}_i^I\left((k+l+1)T_i\right)\frac{{\&PartialD;F}_i^I}{{\&PartialD;u}_i\left((k+l)T_i\right)}+{\mathrm{\&lambda;}}_i^C\left((k+l+1)T_i\right)\frac{{\&PartialD;F}_i^C}{{\&PartialD;v}_i}\frac{{\&PartialD;v}_i}{{\&PartialD;u}_i\left((k+l)T_i\right)}=0$

Then can obtain following yojan state space decomposition algorithm: the initial value of given all subsystem controls variablees, even $u_i\left((k+l)T_i\right)={\hat{u}}_i\left((k+l)T_i\right),$ L=0,1 ..., P _i-1, i=1,2 ..., N is according to subsystem S _iDiscrete model calculate corresponding subsystem S _iThe status predication initial track ${\mathrm{\&lambda;}}_i^C\left((k+l)T_i\right)={\widehat{\mathrm{\&lambda;}}}_i^C\left((k+l)T_i\right),$ $z_i^C\left((k+l)T_i\right)={\hat{z}}_i^C\left((k+l)T_i\right),$ Carry out iterative computation as follows:

Iterative step 1: find the solution following dimensionality reduction optimization problem about subsystem internal state and control:

If the optimal control solution of above-mentioned optimization problem is

Corresponding internal state track is

L=0,1 ..., P-1;

Iterative step 2: by following system of equations

Can try to achieve λ _{I, new} ^I((k+l) T _i), and ${\hat{v}}_i\left((k+l)T_i\right)=v_i({\hat{x}}_{i,\mathrm{new}}^I\left((k+l)T_i\right),{\hat{u}}_{i,\mathrm{new}}\left((k+l)T_i\right),{\hat{z}}_i\left((k+l)T_i\right)),$ The iteration following formula

The outside association status prediction locus that obtains upgrading

Iterative step 3: by following system of equations

Can try to achieve λ _{I, new} ^C((k+l) T _i);

Iterative step 4: upgrade ${\hat{z}}_i\left((k+l)T_i\right)=z_i\left((k+l)T_i\right),$ Order ${\hat{u}}_i\left((k+l)T_i\right)={\hat{u}}_{i,\mathrm{new}}\left((k+l)T_i\right),$ ${\hat{x}}_i^I\left((k+l+1)T_i\right)={\hat{x}}_{i,\mathrm{new}}^I\left((k+l+1)T_i\right),$ ${\hat{x}}_i^C\left((k+l+1)T_i\right)={\hat{x}}_{i,\mathrm{new}}^C\left((k+l+1)T_i\right),$ Return iterative step 1, restrain until iterative process.

Embodiment

Ironmaking production procedure shown in Figure 1 is a typical complex large system, form by 5 operations (subsystem) such as ore-burden process, coal blending process, ore sintering process, carbonization of coal process, blast furnace ironmaking processes, relate to a large amount of process variable with complicated related, and the dynamic perfromance of each subsystem differs very big.When arbitrary production link in the system is subjected to external disturbance or operating conditions change,, only adopt local control to be difficult to overcome effectively this departing from because the correlation between subsystem will make other link also depart from the ordinary production state.

The present invention adopts the production data of certain steel plant, utilize the dispersion forecast Control Algorithm of the big system of scale complex of many time that is proposed that this ironmaking flow process has been carried out global coordination optimization control calculating, and the validity by the computer simulation experiment verification algorithm, emulation shows, this method has fast convergence rate, the counting yield height is optimized performance and is waited remarkable advantage well.

Following table has provided the input/output signal and the optimization aim explanation of each subsystem among Fig. 1.

Variable dimension that each subsystem relates to and signal update cycle such as following table are listed:

Claims (4)

1. One kind for a long time between the dispersion forecast Control Algorithm of the big system of scale complex, it is characterized in that comprising the steps:

   1) supposes that the big system S of scale complex of many time has been divided into N the different subsystem S of inter-related dynamic perfromance _i, i=1,2 ..., N＞1, subsystem S _iContinuous model be M _i, continuous model M _iVariable comprise state variable x _i, control variable u _i, associated variable z _i, wherein, associated variable z _iExpression subsystem S _j, j=1,2 ..., N, j ≠ i is to subsystem S _iCoupling, satisfy static equality constraint z _i(t)=h _i(x ₁(t) ..., x _I-1(t), x _I+1(t) ..., x _N(t)), in addition, subsystem S _iContinuous model M _iAlso comprise static inequality constrain and dynamic equality constraint, use the inequality constrain transformation approach subsystem S _iThe static inequality constrain of continuous model be converted into subsystem S _iThe dynamic equality constraint of continuous model;

   2) according to subsystem S _iDynamic perfromance determine subsystem S _iSampling period T _i, and T _iSatisfy T _i=T _Min* a _i, $T_{\min }=\underset{i=\mathrm{1,2},...,N}{\min }\left\{T_i\right\},$ a _iBe natural number, with T _iBe the sampling period, utilize forward-difference method subsystem S _iContinuous model in dynamic equation constrained approximation discretize; To static equality constraint z _i(t)=h _i(x ₁(t) ..., x _I-1(t), x _I+1(t) ..., x _N(t)), with T _iFor becoming after the sampling period discretize $z_i\left({\mathrm{kT}}_i\right)=h_i({\tilde{x}}_1\left({\mathrm{kT}}_i\right),\&CenterDot;\&CenterDot;\&CenterDot;,{\tilde{x}}_{i-1}\left({\mathrm{kT}}_i\right),{\tilde{x}}_{i+1}\left({\mathrm{kT}}_i\right),\&CenterDot;\&CenterDot;\&CenterDot;,{\tilde{x}}_N\left({\mathrm{kT}}_i\right)),k=k_0,k_0+1,...,k_f,$ k ₀And k _fBe natural number, and k ₀＜k _f, ${\tilde{x}}_j\left({\mathrm{kT}}_i\right),j=\mathrm{1,2},...,N,$ J ≠ i represents with T _iFor the sampling period to subsystem S _jState variable x _j(t) carry out the value that virtual sampling obtains, obtain subsystem S _iDiscrete model M _i', if T _j≤ T _i, the problem that does not then exist sampled value to lack; If T _j＞T _i, then the time point that does not overlap in sampling will the situation of sampled value disappearance occur, and the sampled value of disappearance replaces with the last sampled value;

   3) the rolling optimization method of employing PREDICTIVE CONTROL is at t=kT _iConstantly, to subsystem S _iAt following t=(k+1) T _iTo t=(k+P _i) T _iThe system action of time period predicts and optimizes, wherein P _iBe subsystem S _iAt t=kT _iConstantly carry out the prediction time domain of rolling optimization, L _t=P _iT _iBe t=kT _iThe time window length of moment rolling optimization is by t=kT _iParticipate in the subsystem S of optimization constantly _tIn the slowest subsystem S _s, T _s≤ T _l, S _l∈ S _tDetermine, i.e. L _t=T _sP, P are constant, the minimum prediction time domain that expression allows; Subsystem S _iThe rolling optimization frequency be

   

   4) model prediction and the feedback compensation method of employing PREDICTIVE CONTROL are at t=kT _iConstantly, utilize subsystem S _iDiscrete model to subsystem S _iAt following t=(k+1) T _iTo t=(k+P _i) T _iThe system action of time period is predicted, utilizes measured value to carry out feedback compensation to predicting the outcome.Use yojan state space decomposition algorithm to find the solution subsystem S _iAt following t=(k+1) T _iTo t=(k+P _i) T _iThe optimal control problem J of time period _{I, k}, realize the decentralised control of the big system of scale complex of many time.
2. 2. the dispersion forecast Control Algorithm of the big system of a kind of scale complex of many time according to claim 1 is characterized in that described step 1) comprises:

   If subsystem S _iContinuous model M _iAs follows:

   $\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{x}}_i\left(t\right)=f_i(x_i\left(t\right),u_i\left(t\right),z_i\left(t\right))\\ g_i(x_i\left(t\right),z_i\left(t\right),u_i\left(t\right))\&GreaterEqual;0\\ x_i\left(t_0\right)=x_{i,0}\end{array}\right.,t_0\&le;t\&le;t_f$

   Wherein, x _iBe subsystem S _iState variable, u _iBe subsystem S _iControl variable, z _iBe subsystem S _iAssociated variable, and satisfy equation: z _i(t)=h _i(x ₁(t) ..., x _N(t)), f _iBe subsystem S _iThe dynamic equality constraint that satisfies, g _iBe subsystem S _iThe static inequality constrain of satisfying, t ₀And t _fBe respectively the initial and termination time of system, x _{I, 0}Be x _iOriginal state, for subsystem S _iStatic inequality constrain g _i(x _i(t), z _i(t), u _i(t)) 〉=0, the new state variable x of definition _{S, i}(t), satisfy equation:

   $\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{x}}_{s,i}\left(t\right)=f_{s,i}(x_i\left(t\right),u_i\left(t\right),z_i\left(t\right))={\left[G_i\left(t\right)\right]}^2\mathrm{\&sigma;}\left(G_i\left(t\right)\right)\\ x_{s,i}\left(t_0\right)=0\end{array}\right.$

   Wherein σ () is a step function, satisfies:

   $\mathrm{\&sigma;}\left(G_i\left(t\right)\right)=\left\{\begin{array}{cc}0,& G_i\left(t\right)\&GreaterEqual;0\\ K_{s,i}& G_i\left(t\right)<0\end{array}\right.$

   K wherein _{S, i}Be a constant, terminal condition is:

   $x_{s,i}\left(t_f\right)={\&Integral;}_{t_0}^{t_f}{G}_i^2\left(t\right)\mathrm{\&sigma;}\left(G_i\left(t\right)\right)\mathrm{dt}=0$

   Subsystem model M then _iCan be expressed as the form of following augmented state equation:

   ${\stackrel{\&CenterDot;}{x}}_i\left(t\right)=F_i(x_i\left(t\right),u_i\left(t\right),z_i\left(t\right))\stackrel{\mathrm{\&Delta;}}{=}\left[\begin{array}{c}{f}_i(x_i\left(t\right),u_i\left(t\right),z_i\left(t\right))\\ G_i^2\left(t\right)\mathrm{\&sigma;}\left(G_i\left(t\right)\right)\end{array}\right]$

   And z _i(t)=h _i(x ₁(t) ..., x _NAnd x (t)) _i(t ₀)=x _{I, 0}, wherein $x_i^T\left(t\right)\stackrel{\mathrm{\&Delta;}}{=}\left[\begin{array}{cc}{x}_i\left(t\right),& x_{s,i}\left(t\right)\end{array}\right]$ Be subsystem S _iThe augmented state vector.
3. 3. the dispersion forecast Control Algorithm of the big system of a kind of scale complex of many time according to claim 1 is characterized in that described step 2) comprising:

   According to subsystem S _iDynamic perfromance determine subsystem S _iSampling period T _i, and T _iSatisfy T _i=T _Min* a _i, $T_{\min }=\underset{i=\mathrm{1,2},...,N}{\min }\left\{T_i\right\},$ a _iBe natural number, with T _iBe the sampling period, utilize forward-difference method $\stackrel{\&CenterDot;}{\mathrm{\&chi;}}\left(t\right)\&ap;\frac{\mathrm{\&chi;}\left((k+1)T_i\right)-\mathrm{\&chi;}\left({\mathrm{kT}}_i\right)}{T_i},$ χ is x _iOr u _i, with subsystem S _iThe continuous model discretize, obtain subsystem S _iDiscrete model M _i' as follows:

   $\left\{\begin{array}{c}{x}_i\left((k+1)T_i\right)=F_i(x_i\left({\mathrm{kT}}_i\right),u_i\left({\mathrm{kT}}_i\right),z_i\left({\mathrm{kT}}_i\right))\\ x_i\left(k_0{T}_i\right)=x_{i,0}\end{array}\right.$

   And interconnection constraint: $z_i\left({\mathrm{kT}}_i\right)=H_i({\tilde{x}}_1\left({\mathrm{kT}}_i\right),\&CenterDot;\&CenterDot;\&CenterDot;,{\tilde{x}}_N\left({\mathrm{kT}}_i\right)),$ Wherein, k=k ₀, k ₀₊₁..., k _fAnd k _fBe natural number, and k ₀＜k _f, x _{I, 0}Be t=k ₀T _iState initial value constantly, ${\tilde{x}}_j\left({\mathrm{kT}}_i\right),j=\mathrm{1,2},...,N,$ J ≠ i represents with T _iFor the sampling period to subsystem S _jState variable x _j(t) carry out that virtual sampling obtains, if T _j≤ T _i, the problem that does not then exist sampled value to lack; If T _j＞T _i, then the time point that does not overlap in sampling will the situation of sampled value disappearance occur, and the sampled value of disappearance replaces with the last sampled value, promptly ${\tilde{x}}_j\left({\mathrm{kT}}_i\right)=x_j\left(k^{\&prime;}{T}_j\right),$ k′T _j≤kT _i≤(k′+1)T _j。
4. 4. the dispersion forecast Control Algorithm of the big system of a kind of scale complex of many time according to claim 1 is characterized in that described step 4) comprises:

   Adopt the model prediction method of PREDICTIVE CONTROL, at t=kT _iConstantly, utilize subsystem S _iDiscrete model to subsystem S _iAt following t=(k+1) T _iTo t=(k+P _i) T _iThe system action of time period is predicted:

   $\left\{\begin{array}{c}{\stackrel{\&OverBar;}{x}}_i\left((k+l+1)T_i\right)=F_i({\stackrel{\&OverBar;}{x}}_i\left((k+l)T_i\right),u_i\left((k+l)T_i\right),z_i\left((k+l)T_i\right))\\ {\stackrel{\&OverBar;}{x}}_i\left({\mathrm{kT}}_i\right)=x_{i,0}\left({\mathrm{kT}}_i\right)\end{array}\right.$

   And $z_i\left((k+l)T_i\right)=H_i({\stackrel{\&OverBar;}{x}}_1\left((k+l)T_i\right),\&CenterDot;\&CenterDot;\&CenterDot;,{\stackrel{\&OverBar;}{x}}_N\left((k+l)T_i\right)),l=\mathrm{0,1},...,P_i-1$

   Obtain

   

   L=0,1 ..., P _i-1, the model prediction method of employing PREDICTIVE CONTROL utilizes measured value to predicting the outcome

   

   Carry out feedback compensation, obtain

   

   That is:

   

   γ wherein _iBe feedback correcting coefficient; e _iReflected subsystem S _iVirtual condition x _iWith the model prediction state Between deviation, that is: $e_i\left({\mathrm{kT}}_i\right)={\stackrel{\&OverBar;}{x}}_i\left({\mathrm{kT}}_i\right)-x_i\left({\mathrm{kT}}_i\right),$ Quantity of state X with each subsystem _iBe decomposed into two subset X _i ^CAnd X _i ^I, promptly for subsystem S _i, that part of state variable that definition directly influences the related input of at least one related subsystem is subsystem S _iOutside association status subclass $X_i^C\stackrel{\mathrm{\&Delta;}}{=}\{x_i^C\&Element;X_i|\&Exists;j\&Element;\{\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,N\},$ $z_j=H_j(\&CenterDot;\&CenterDot;\&CenterDot;,{\tilde{x}}_i^C,\&CenterDot;\&CenterDot;\&CenterDot;)\};$ Definition subsystem S _iAll the other state variables be the internal state subclass $X_i^I\stackrel{\mathrm{\&Delta;}}{=}\{x_i^I\&Element;X_i\backslash X_i^C\};$ By above-mentioned definition, subsystem S _iState equation can be rewritten as:

   

   

   Wherein

   

   

   If subsystem S _iAt t=kT _iThe objective function that is optimized control is:

   

   If λ _i ^IAnd λ _i ^CBe respectively about formula

   

   And formula

   

   Association's state, then utilize yojan state space decomposition algorithm solving-optimizing problem J _{I, k}As follows: the initial value of given all subsystem controls variablees, even $u_i\left((k+l)T_i\right)={\hat{u}}_i\left((k+l)T_i\right),l=\mathrm{0,1},\&CenterDot;\&CenterDot;\&CenterDot;,P_i-1,i=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,N,$ According to subsystem S _iDiscrete model calculate corresponding subsystem S _iThe status predication initial track

   

   ${\mathrm{\&lambda;}}_i^C\left((k+l)T_i\right)={\widehat{\mathrm{\&lambda;}}}_i^C\left((k+l)T_i\right),$ $z_i^C\left((k+l)T_i\right)={\hat{z}}_i^C\left((k+l)T_i\right),$ Carry out iterative computation as follows:

   Iterative step 1: find the solution following dimensionality reduction optimization problem about subsystem internal state and control:

   

   If the optimal control solution of above-mentioned optimization problem is

   

   Corresponding internal state track is ${\hat{x}}_{i,\mathrm{new}}^I\left((k+l+1)T_i\right),l=\mathrm{0,1},\&CenterDot;\&CenterDot;\&CenterDot;,P-1;$

   Iterative step 2: by following system of equations

   The attitude prediction locus

   

   Iterative step 3: by following system of equations

   

   Can try to achieve λ _{I, new} ^C((k+l) T _i);

   Iterative step 4: upgrade ${\hat{z}}_i\left((k+l)T_i\right)=z_i\left((k+l)T_i\right),$ Order ${\hat{u}}_i\left((k+l)T_i\right)={\hat{u}}_{i,\mathrm{new}}\left((k+l)T_i\right),$ ${\hat{x}}_i^I\left((k+l+1)T_i\right)={\hat{x}}_{i,\mathrm{new}}^I\left((k+l+1)T_i\right),$ ${\hat{x}}_i^C\left((k+l+1)T_i\right)={\hat{x}}_{i,\mathrm{new}}^C\left((k+l+1)T_i\right),$ Return iterative step 1, restrain until iterative process.

Images