CN112000005A - Target-shooting solving method for slope economy cruise switching control parameters - Google Patents

Target-shooting solving method for slope economy cruise switching control parameters Download PDF

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CN112000005A
CN112000005A CN202010611444.4A CN202010611444A CN112000005A CN 112000005 A CN112000005 A CN 112000005A CN 202010611444 A CN202010611444 A CN 202010611444A CN 112000005 A CN112000005 A CN 112000005A
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施树明
乔少锋
林楠
岳柄剑
孟凡钰
白明慧
王槊
张博识
马晓帆
李云霞
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Abstract

The invention provides a target shooting solving method for a slope economic cruise switching control parameter, which is characterized in that a target shooting equation is constructed by utilizing an optimal control principle and known boundary conditions to obtain unknown initial state variables, the unknown initial state variables and the known initial variables form initial state variables of a system equation together, the initial state values of the system equation are solved under the frame of the target shooting method by utilizing methods such as a genetic algorithm, a particle swarm optimization method, a homotopy method and the like, the specific switching time of longitudinal force control in the process of the vehicle slope economic cruise is obtained, and the problem of difficulty in solving under the condition of relatively complex unknown switching sequence or switching process is solved.

Description

Target-shooting solving method for slope economy cruise switching control parameters
Technical Field
The invention belongs to the technical field of automobile economy cruise control, and particularly relates to a target-shooting solving method for a slope economy cruise switching control parameter.
Background
The economic cruising on the sloping road is a hot point of the research of the current intelligent vehicle, and has wide market application prospect. The control applied to the real vehicle is mostly judged based on the rule of experience, and needs the support and the perfection of theoretical research.
The existing theoretical model emphasizes the influence of the nonlinearity of an engine on economic cruising, pays more attention to the continuous control process of driving, and ignores the problem of switching of driving and braking control. In the specific slope cruising problem, under the condition of comprehensively considering the driving and braking conditions, the control rate of the whole system can be deduced by using an extreme value principle according to a system state equation and an objective function on the basis of an optimal control theory and according to a system state equation and an objective function, and slope economical cruising is found to be typical bang-bang control or bang-arc-bang control, namely state switching between driving, sliding and braking. In a specific scene, under the condition that a state equation and the optimal control rate are known, the key for obtaining the optimal road section switching sequence and switching time is to solve the initial value of the co-modal state by using a numerical method.
The solution of the co-modal initial value is substantially an edge value problem, the shooting method is a method commonly used for solving the edge value problem, the complete initial condition is constructed by selecting and adjusting the initial value, the edge value problem is converted into the initial value problem to be solved, and the initial value problem is close to the given boundary condition, but conventional numerical algorithms such as the Runge Kuta and the Newton iteration used in the traditional shooting method are commonly used for solving mathematical models with simple structures, and the problem of difficult solution often exists for complex models with nonlinearity and discontinuity.
With the appearance of some intelligent optimization algorithms such as genetic algorithm, particle swarm optimization and the like, the phenomenon of 'dead circulation' caused by the fact that a common numerical iteration method is easy to get into a local minimum trap is well overcome through simulating a natural process, and the numerical iteration method has strong global optimization capability and provides an effective scheme for solving the complex problems. The genetic algorithm (GA, NSGA II and the like) references the mechanisms of natural heredity and natural selection in the biological world, is simple, is an efficient intelligent search method which does not need any initial information and can seek global optimal solution, has strong robustness, and is suitable for processing the complex nonlinear problem which is not solved well by the traditional search algorithm. Particle Swarm Optimization (PSO) is an emerging algorithm, has many similarities with genetic algorithm, is suitable for the problem of continuous function extremum, and has strong global search capability for nonlinear and multimodal problems. The homotopy method is a method based on numerical extension thought, and for some special complex non-linear discontinuous problems, when the problems cannot be solved by using a genetic algorithm and a particle swarm method, the solving difficulty can be effectively reduced by means of the homotopy method.
Disclosure of Invention
The invention aims to provide a method for solving target shooting of a slope economic cruise switching control parameter, which is characterized in that a target shooting equation is constructed according to an optimal control principle, the target shooting equation is solved by utilizing an optimization algorithm under the framework of a target shooting method, the specific switching time of longitudinal force control in the vehicle slope economic cruise process is obtained, and the problem of difficulty in solving under the condition of unknown switching sequence or relatively complex switching process is solved.
The purpose of the invention is realized by the following technical scheme:
a target-shooting solving method for a slope economy cruise switching control parameter comprises the following specific steps:
s1, establishing an optimal control model of the slope economic cruise;
s1.1, constructing an equality constraint equation of an optimal control system according to a balance relation of driving force and running resistance, wherein the form is as follows:
Figure BDA0002561035010000021
wherein x isiIs a state variable;
Figure BDA0002561035010000022
means xiDerivative of fiObtaining a relational expression of the variable value of the state; n is the number of state variables
S1.2, constructing an objective function considering driving brake energy consumption, road speed limit and time efficiency, wherein the form is as follows:
Figure BDA0002561035010000023
wherein, t0、tfIn the beginning and end time, L is a mathematical expression for unifying instantaneous energy consumption of driving and braking, and sigma is a time factor;
s1.3, constructing a Hamiltonian according to a state equation and an objective function, wherein the form is as follows:
H＝L+σ+λ×f(x) (3)
wherein, λ is n dimension covariate, f (x) is the relational expression for obtaining the n dimension state variable value;
s1.4, solving the optimal control rate F of the system according to the minimum value principlel *Respectively solving partial derivatives of state variables by using a Hamiltonian, changing an original state equation from n dimension to 2n dimension without changing the form, wherein a new state equation of the system is as follows:
Figure BDA0002561035010000031
s2, constructing a shooting equation;
s2.1, constructing system dynamics according to the optimal control rate and a system equation: substituting the optimal control rate into a state equation (4), assuming that the initial value of the co-modal state and the operation simulation time are known, and solving a system dynamics equation by using a numerical algorithm to obtain a state quantity and a Hamilton value in the operation simulation time under the specific initial value of the co-modal state;
s2.2, calculating the system tail end deviation under the specific co-modal initial value by utilizing system dynamics, constructing a targeting equation as follows,
Figure BDA0002561035010000032
wherein Htf、vtf、stfIs the end state quantity H calculated by using the system dynamics under a specific initial value of the co-statef、vf、sfIs the known end constraint of the system;
s3, solving an initial value by using an optimization algorithm;
s3.1, converting the shooting equation into a target function in an optimization algorithm;
according to the optimal control theory, the system dynamics is calculated to obtain the system tail end state and the tail end Hamilton value H under the specific initial co-modal valuefGiven end state (v)f,sf) The deviation between the target and the target is used as an optimization target, and the target shooting equation is converted into a target in an optimization algorithm. The form is as follows:
fga＝k1|Htf|+k2|vtf-vf|+k3|stf-sf| (6)
wherein k is1、k2、k3Is a proportionality coefficient, Htf、vtf、stfIs the end time tfCorresponding hamiltonian value, velocity, displacement;
s3.2, selecting an optimization method and setting parameters;
s3.3, substituting the objective function into the corresponding optimization algorithm to obtain the unknown initial co-modal value lambda in the system equation according to the complexity of the selected mathematical models0、λv0. Then the obtained initial value of co-state is determineds0、λv0And a known state initial value (v)t0、st0) And substituting the optimal road section switching sequence and the optimal road section switching time into a system equation.
As a more excellent technical scheme of the invention: when the mathematical model is a complex nonlinear multi-peak continuity mathematical model, the step S3.2 selects an optimization method to solve a coordination initial value by using a particle swarm optimization method, and parameters such as the number of the population, the inertia weight, the position limit, the speed limit and the like in the particle swarm optimization are set.
As a more excellent technical scheme of the invention: when the mathematical model is a complex nonlinear discontinuous model, the step S3.2 selects an optimization method to select a genetic algorithm to solve initial values, and parameters such as population size, iteration times, intersection, variation and the like in the genetic algorithm are set.
The beneficial effects are as follows:
the method utilizes an optimal control principle and known boundary conditions to construct a shooting equation to obtain unknown initial state variables, the unknown initial state variables and the known initial variables form the initial state variables of the system equation together, and intelligent optimization methods such as genetic algorithm, particle swarm optimization, homotopy method and the like are utilized to solve initial state values of the covariance under the frame of the shooting method, so that the problem of difficulty in solving under the condition of complex unknown switching sequence or switching process is solved.
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FIG. 1 is a flow chart of a target solving method for a slope economy cruise switch control parameter of the invention;
fig. 2 is a simulation result in example 1 of the present invention (hill, regardless of brake power consumption, σ ═ 0, LB [ -1; -55; 180], UB [ 0; -45; 200 ]);
fig. 3 is a simulation result in example 1 of the present invention (concave slope, regardless of brake energy consumption, σ ═ 1, LB [ -1; -5; 100], UB [ 0; 0; 115 ]);
fig. 4 is a simulation result in example 1 of the present invention (hill, considering braking energy consumption, σ ═ 0, LB [ -1; -55; 180], UB [ 0; -45; 200 ]);
fig. 5 shows the simulation results in example 1 of the present invention (concave slope, considering braking energy consumption, σ ═ 1, LB [ -1; 0; 100], UB [ 0; 10; 115 ]).
Detailed Description
The process of the present invention is further illustrated in detail by the following examples and figures.
Example 1
Referring to fig. 1, the invention provides a target-shooting-method-based slope economic cruise switching control solving method, taking an integral optimization problem that the tail end state (mileage and speed) is fixed and the tail end time is free in a large slope economic cruise problem, taking a control variable as a whole vehicle driving/braking force model as an example, and referring to a table 1 for related simulation parameters and driving conditions.
TABLE 1
Figure BDA0002561035010000051
The method comprises the following specific steps:
s1, establishing an optimal control model for the economic cruise of the slope
S1.1, constructing an equality constraint equation of an optimal control system according to a balance relation between driving force and each driving resistance;
s1.1.1, according to the longitudinal force balance in the running process of the vehicle, the total longitudinal dynamic model of the whole vehicle is as follows:
Fl＝Ff+Fw+Fi+Fj (7)
wherein, rolling resistance: ffMgf; air resistance:
Figure BDA0002561035010000061
ramp resistance: fiMgi; acceleration resistance: fj＝mav(ii) a m is the mass of the whole vehicle; g is the acceleration of gravity; f is a rolling resistance coefficient; a isvIs the vehicle running acceleration; cDIs the air resistance coefficient; a is the windward area; ρ is the air density; the conversion coefficient of the rotating mass; and i is the sine value of the road slope angle.
S1.1.2, the gradient function selects a linear function, the road elevation curve is an integral curve of the gradient function to the independent variable displacement s, the function can represent the road form with parabolic characteristics, and can be the case of convex slopes or concave slopes, and a linear function is selected to express the road gradient:
i(s)＝as+b (8)
wherein, a and b are road gradient coefficients, and s is displacement.
S1.1.3, establishing an equality constraint equation
Selecting two variables of mileage and speed as state variables of the system, i.e.
Figure BDA0002561035010000062
According to the stress balance of the longitudinal force, the state equation of the system is obtained as follows:
Figure BDA0002561035010000063
wherein the content of the first and second substances,
Figure BDA0002561035010000064
CDis the air resistance coefficient, rho is the air density, A is the frontal area of the automobile;
s1.2, constructing an objective function considering driving brake energy consumption, road speed limit and time efficiency.
S1.2.1, selecting a whole vehicle full-working-condition instantaneous energy consumption model containing driving and braking working conditions, wherein the form is as follows:
L＝c1|Fl|v+c2|Fl|v (10)
wherein c is1≥c2If more than 0 is a undetermined parameter, the driving and braking energy consumption slope is set according to the real or designed driving and braking effect of the vehicle to obtain c1And c2。FlFor longitudinal control of force, Fb max≤Fl≤Ft max，Ft maxFor maximum driving force, Fb maxIs the maximum braking force.
S1.2.2, introducing a time factor sigma, and establishing a time-fuel optimal control model, wherein the objective function form is as follows:
Figure BDA0002561035010000071
s1.3, constructing a Hamiltonian according to a state equation and an objective function:
Figure BDA0002561035010000072
s1.4, solving the optimal control rate F of the system according to the minimum value principlel *And respectively solving the state partial derivatives by using a Hamiltonian, and changing the original state equation from n dimension to 2n dimension.
S1.4.1, according to the principle of minimum value, the optimal control rate of the system is the control rate when the Hamiltonian (12) takes minimum time, and the optimal control rate F of the systeml *Comprises the following steps:
Figure BDA0002561035010000073
wherein
Figure BDA0002561035010000074
S1.4.2, respectively obtaining the partial derivatives of the state quantities (s, v) by using a Hamiltonian, linearizing the expression of the air resistance,
Figure BDA0002561035010000075
is the set average speed. Expanding the state equation set of the original system from 2 dimensions to 4 dimensions, wherein the state equation of the final system is as follows:
Figure BDA0002561035010000076
s2, constructing a shooting equation
And S2.1, constructing system dynamics according to a system equation and the optimal control rate.
Will optimize the control rate Fl *Substituting into equation of state (14) to assume a co-modal initial value λs0、λv0And running simulation time tfAs is known, the state equation is solved by solving the function of ode45 in Matlab, and numerical solution simulation is carried outThe step size is selected to be 0.01s, and the relative tolerance precision is 10-5Absolute tolerance accuracy of 10-7So as to obtain the running state v corresponding to any time t in the simulation time under the specific collaborative initial valuet、stAnd Hamilton value Ht。
And S2.2, calculating the system tail end deviation under the specific co-modal initial value by utilizing system dynamics, and constructing a target shooting equation.
According to the optimal control principle, when the terminal Hamilton value H f0 and set end state vf＝23，sfAt 3000, the vehicle is able to achieve economical cruising under prescribed conditions. Selecting and adjusting unknown co-modal initial value variable lambdas0、λv0And running simulation time tfSubstituting into the optimal control rate (13) and the system dynamics equation (14) to solve for the time tfCorresponding state quantities and Hami end values. At the initial value lambda of the ideal specific co-states0、λv0And running simulation time tfThen, the corresponding terminal state quantity H is obtainedtf、vtf、stfWith a known terminal quantity Hf、vf，sfIs 0, the targeting equation is constructed as follows:
Figure BDA0002561035010000081
wherein Hf＝0、vf＝23，sf＝3000
S3, solving initial value by using optimization algorithm
The mathematical model corresponding to the selected scene in this embodiment 1 is a non-linear discontinuous mathematical model, and therefore, a genetic algorithm is selected to solve the initial value.
S3.1, converting the shooting equation into an objective function of an optimization algorithm
Selecting and adjusting unknown co-modal initial value variable lambdas0、λv0And running simulation time tfSubstituting the obtained product into a system state equation to solve, selecting a numerical value solution simulation step length of 0.01s, and setting the relative tolerance precision to 10-5Absolute tolerance accuracy of 10-7To obtainTo the corresponding end state quantity Htf、vtf、stfThe obtained end state value and the known end quantity H are comparedf、vf，sfAs an optimization quantity, and then constructing an objective function as follows:
fitnessfcn＝400*|vtf-vf|+100*|stf-sf| (16)
s3.2, setting parameters of optimization algorithm
The algorithm used for solving the target equation in the invention is a genetic algorithm, and options parameters in the genetic algorithm are set as follows (parameters not shown are default settings):
limiting times of genetic iteration: 200 of a carrier;
initial population: 70;
number of genetically surviving individuals: 60, adding a solvent to the mixture;
iteration limiting time: 10000;
wherein, linear inequality constraint A and b in the genetic algorithm are empty sets, linear equality constraint Aeq and Beq are empty sets, and nonlinear constraint nonlcon is an empty set.
S3.3, solving the objective function by utilizing an optimization method
Substituting the obtained fitness function into a genetic algorithm function, lambdas0、λv0And running simulation time tfThe range of (d) and the corresponding simulation results are as follows (LB is the lower limit, UB is the upper limit):
(1) convex slope, not considering the braking energy consumption, the time factor sigma is 0, and LB is-1; -55; 180], UB ═ 0; -45; 200], simulation results are shown in FIG. 2;
(2) the method comprises the following steps of (1) concave slope, regardless of braking energy consumption, wherein a time factor sigma is 1, and LB is-1; -5; 100], UB ═ 0; 0; 115], the simulation results are shown in fig. 3;
(3) the convex slope considers the braking energy consumption, the time factor sigma is 0, and LB is [ -1; -55; 180], UB ═ 0; -45; 200], the simulation result is shown in FIG. 4;
(4) the concave slope considers the braking energy consumption, the time factor sigma is 1, and the LB is [ -1; 0; 100], UB ═ 0; 10; 115], the simulation results are shown in fig. 5.
The above simulation results show that: under a specific optimization scene of the vehicle, a simulation result obtained by GA solution in the targeting method is basically consistent with a simulation result obtained by an analytic method, and the targeting solution method can ensure that the vehicle runs economically under the control rate corresponding to the obtained result and simultaneously solves the problem that the analytic method is difficult to solve under the condition of unknown switching sequence or relatively complex switching process.
The method for solving the slope economic cruise switching control can solve the problem that the solution is difficult under the conditions that the initial and final conditions of the system are partially unknown and the switching process is complex.
In some embodiments, when the mathematical model is a complex nonlinear multimodal continuity mathematical model, the step S3.2 of selecting the optimization method selects a particle swarm optimization method to solve the initial covariance value, and sets parameters such as the population number, the inertial weight, the position limit, the speed limit, and the like in the particle swarm optimization.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting the same, and although the present invention is described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: modifications and equivalents may be made to the embodiments of the invention without departing from the spirit and scope of the invention, which is to be covered by the claims.

Claims (2)

1. A target-shooting solving method for a slope economy cruise switching control parameter is characterized by comprising the following steps: the method comprises the following specific steps:
s1, establishing an optimal control model of the slope economic cruise;
s1.1, constructing an equality constraint equation of an optimal control system according to a balance relation of driving force and running resistance, wherein the form is as follows:
Figure FDA0002561035000000011
wherein x isiAs state variables
Figure FDA0002561035000000012
Means xiDerivative of fiObtaining a relational expression of the variable value of the state; n is the number of state variables;
s1.2, constructing an objective function considering driving brake energy consumption, road speed limit and time efficiency, wherein the form is as follows:
Figure FDA0002561035000000013
wherein, t0、tfIn the beginning and end time, L is a mathematical expression for unifying instantaneous energy consumption of driving and braking, and sigma is a time factor;
s1.3, constructing a Hamiltonian according to a state equation and an objective function, wherein the form is as follows:
H＝L+σ+λ×f(x) (3)
wherein, λ is n dimension covariate, f (x) is the relational expression for obtaining the n dimension state variable value;
s1.4, solving the optimal control rate F of the system according to the minimum value principlel *Respectively solving partial derivatives of state variables by using a Hamiltonian, changing an original state equation from n dimension to 2n dimension without changing the form, wherein a new state equation of the system is as follows:
Figure FDA0002561035000000014
s2, constructing a shooting equation;
s2.1, constructing system dynamics according to the optimal control rate and a system equation: substituting the optimal control rate into a state equation (4), assuming that the initial value of the co-state and the operation simulation time are known, and solving a system dynamics equation by using a numerical algorithm to obtain an operation state v corresponding to any time t in the simulation time under the specific initial value of the co-statet、stAnd Hamilton value Ht；
S2.2, calculating the system tail end deviation under the specific co-modal initial value by utilizing system dynamics, constructing a targeting equation as follows,
Figure FDA0002561035000000021
wherein Htf、vtf、stfIs the end state quantity H calculated by using the system dynamics under a specific initial value of the co-statef、vf，sfIs the known end constraint of the system;
s3, solving an initial value by using an optimization algorithm;
s3.1, converting the shooting equation into a target function in an optimization algorithm;
according to the optimal control theory, the system dynamics is calculated to obtain the system tail end state and the tail end Hamilton value H under the specific initial co-modal valuefGiven end state (v)f,sf) The deviation between the target and the target is used as an optimization target, and a target equation is converted into a target in an optimization algorithm, wherein the form is as follows:
fga＝k1|Htf|+k2|vtf-vf|+k3|stf-sf| (6)
wherein k is1、k2、k3Is a proportionality coefficient, Htf、vtf、stfIs the end time tfCorresponding hamiltonian value, velocity, displacement;
s3.2, selecting an optimization method and setting parameters;
s3.3, substituting the objective function into the corresponding optimization algorithm to obtain the unknown initial co-modal value lambda in the system equation according to the complexity of the selected mathematical models0、λv0Then the obtained initial value of co-state is lambdas0、λv0And a known state initial value vt0、st0And substituting the optimal road section switching sequence and the optimal road section switching time into a system equation.
2. The target solving method for the slope economic cruise switching control parameter as claimed in claim 1, wherein: the optimization method of the step S3.2 is a particle swarm optimization or a genetic algorithm.
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