Coding problem for optimal control

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Redwood 2016-5-31

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https://ww2.mathworks.cn/matlabcentral/answers/286511-coding-problem-for-optimal-control

评论： Tarekegn Dinku 2024-1-20

Dear Matlab experts,

I have a coding for optimal control problem, and this is not working. I would like to know how to solve this problem. Thank you very much in advance.

Sincerely yours,

function Bloc1
% State equations
syms x1 x2 p1 p2 u;
Dx1 = x2^2;
Dx2 = -x2 + u;
% Cost function inside the integral
syms g;
g = 0.5*u^0.5*x2^0.5;
% Hamiltonian
syms p1 p2 H;
H = g + p1*Dx1 + p2*Dx2;
% Costate equations
Dp1 = -diff(H,x1);
Dp2 = -diff(H,x2);
% solve for control u
du = diff(H,u);
sol_u = solve(du, 'u');
% Substitute u to state equations
Dx2 = subs(Dx2, u, sol_u);
% convert symbolic objects to strings for using 'dsolve'
eq1 = strcat('Dx1=',char(Dx1));
eq2 = strcat('Dx2=',char(Dx2));
eq3 = strcat('Dp1=',char(Dp1));
eq4 = strcat('Dp2=',char(Dp2));
sol_h = dsolve(eq1,eq2,eq3,eq4);
%%use boundary conditions to determine the coefficients
%    case a: (a) x1(0)=x2(0)=0; x1(2) = 5; x2(2) = 2;
conA1 = 'x1(0) = 0';
conA2 = 'x2(0) = 0';
conA3 = 'x1(2) = 5';
conA4 = 'x2(2) = 2';
sol_a = dsolve(eq1,eq2,eq3,eq4,conA1,conA2,conA3,conA4);
% plot both solutions
figure(1);
ezplot(sol_a.x1,[0 3]); hold on;
ezplot(sol_a.x2,[0 3]);
ezplot(-sol_a.p2,[0 3]);    % plot the control: u=-p2
axis([0 3 -1.6 7]);
text(0.6,0.5,'x_1(t)');
text(0.4,2.5,'x_2(t)');
text(1.6,0.5,'u(t)');
xlabel('time');
ylabel('states');
title('Solutions comparison (case a)');

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Walter Roberson 2016-5-31

Please give more details about the problems you are observing. Are you getting an error message? If not then what is the first output that does not match what you expect?