How to use fmincon to optimize the objective fun with constraint variables from Simulink model?

问题

I have build a Simulink model for the dynamic and kinematic modeling of the vehicle, the vehicle has to track a reference trajectory, So the objective of the optimization is to minimize the error defined by (y) in "objec_Fun". And the constraint of the vehicle motion is the linear speed, angular speed, linear acceleration, and angular acceleration defined by (c) in "constraint_Fun". And the design parameter is the controller gains.

the vehicle linear and angular speeds must be reached to 8 m/s and -0.8 rad/s respectively as a steady-state.

Firstly; I run the code without nonlinear constraint function c=[], and it gives a perfect result to minimize the error (y) but the linear speed, angular speed, linear acceleration, and angular acceleration are not realistic.

Then I have put a limitation on the speeds and accelerations, but the fmincon can't minimize the errors.

the simulation time is 10 sec, and the symbols of the speeds and accelerations are "VV" and "VVdot". "VV" is 10001*3 matrix the first column is the time, the second is linear speed, and the third is the angular speed.

"VVdot" is 10001*3 matrix the first column is the time, the second is linear acceleration, and the third is the angular acceleration.

Main Matlab File

    global   K1 K2     Roh  delta1 delta2   kx ky   ktheta  VV  VVdot
    K1=1; K2=1;  Roh=1;  delta1=0.00001;   delta2=0.00001;  kx=1;   ky=1;    ktheta=1;
    lb=[0.00      0.00      0.00    0.00001    0.00001  0.00  0.00  0.00  ];
    ub=[0200      0200      0200    0.1        0.1      0200  0200  0200  ];
    x0=[K1   K2     Roh    delta1     delta2     kx   ky    ktheta];
    A=[];    b=[];    Aeq=[];    beq=[];
    options = optimset( 'Algorithm','sqp','Display','iter','PlotFcn','optimplotfval','TolFun',10e-6,'TolCon',10e-6);
    [x,fval,exitflag,output,grad]=fmincon(@objec_Fun,x0,A,b,Aeq,beq,lb,ub,@constraint_Fun,options)

objec_Fun

function y=objec_Fun(x)
global   K1 K2     Roh  delta1 delta2   kx ky   ktheta  VV  VVdot 

K1=x(1);
K2=x(2);
Roh=x(3);
delta1=x(4);
delta2=x(5);
kx=x(6);
ky=x(7);
ktheta=x(8);

%% 
options=simset('SrcWorkspace','current');
sim('DynSMC23092019.slx',[],options);
assignin('base','x',x)
assignin('base','VV',VV)
assignin('base','VVdot',VVdot)
%%

errx=ep.Data(:,1);
erry=ep.Data(:,2);
errtheta=ep.Data(:,3);
errd=sqrt(errx.^2+erry.^2);
N=length(errtheta);
y=(1/N)*(sum(errd.^2+errtheta.^2));
end

constraint_Fun

function [c,ceq]=constraint_Fun(x)

global   K1 K2     Roh  delta1 delta2   kx ky   ktheta   VV  VVdot


K1=x(1);
K2=x(2);
Roh=x(3);
delta1=x(4);
delta2=x(5);
kx=x(6);
ky=x(7);
ktheta=x(8);

c=[max(VV(:,2))-10;          max(abs(VV(:,3)))-1.5 ;...
   max(VVdot(:,2))-(10/3);   max(abs(VVdot(:,3)))-(1.5/3)];

ceq=[];
end

来源：https://stackoverflow.com/questions/58252567/how-to-use-fmincon-to-optimize-the-objective-fun-with-constraint-variables-from

标签

matlab

optimization

simulink