MATLAB: Concerning some error For Loop in the optimal control problem

There's error ezplot(sol_a.x1,[0 1]) in my code below for solving a special optimal control problem
% State equations
syms x1 x2 p1 p2 u;
for i=0:0.1:1
Dx1 = -2*x2+u;
Dx2 = 2*x1;
% Cost function inside the integral
syms g;
g = u^2;
% 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
Dx1 = subs(Dx1, 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
conA1 = 'x1(0) = 3-i';
conA2 = 'x2(0) = 3-i';
conA3 = 'x1(1) = 0.5-(0.5)*i';
conA4 = 'x2(1) = 0.5-(0.5)*i';
sol_a = dsolve(eq1,eq2,eq3,eq4,conA1,conA2,conA3,conA4);
% plot solutions
figure(1);
ezplot(sol_a.x1,[0 1]); 
axis([0 1 -4 3]);
hold on;
end
When I run the above code for every value i=0,0.1,…,1 separately, it works, but for "For Loop" it won't work.

Best Answer

Inside a quoted string 'i' the symbolic engine will always interpret 'i' as sqrt(-1) and never as the current value of i
You should assume that you are no longer permitted to pass character vectors to dsolve and rewrite everything to symbolic expressions
You are doing some invalid calculations. Dx1 only makes sense if x1 is a function, but if it is a function then you cannot take the derivative of H with respect to it. Taking the derivative of a function with respect to a function is an invalid operation in normal calculus and requires Calculus of Variations instead. Unknown functions cannot be assumed to be independent, especially in a situation like this where the functions are being defined by their relationships to each other.
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