Hi Tomer,
I understand that you are trying to solve a optimal control problem, where you have the initial and final conditions.
To solve this in MATLAB, you might use functions such as 'bvp4c' or 'bvp5c', which are designed to solve boundary value problems. You will need to define the differential equations for both the states and the costates, as well as the boundary conditions. The boundary conditions will include the given initial conditions for the states and the final conditions.
You can follow the code template below to proceed further,
function main
% Initial conditions for states
x10 = -5; x20 = -5;
% Final conditions for Lagrange multipliers
lambda1f = 0; lambda2f = 0;
% Make an initial guess for the solution
solinit = bvpinit(linspace(0, 1, 10), @guess);
sol = bvp4c(@odefun, @bcfun, solinit);
end
function dydt = odefun(t, y)
x1 = y(1);
x2 = y(2);
lambda1 = y(3);
lambda2 = y(4);
% System of differential equations
dx1dt = x2;
dx2dt = -x1 + 1.4*x2 - 0.14*x2^3 - 8*lambda2;
dlambda1dt = lambda2 - 2*x1;
dlambda2dt = -lambda1 - 1.4*lambda2 + 3.014*lambda2*x2^2;
% Combine them into a column vector
dydt = [dx1dt; dx2dt; dlambda1dt; dlambda2dt];
end
function res = bcfun(ya, yb)
% Boundary conditions
res = [ya(1) + 5; % x1(0) = -5
ya(2) + 5; % x2(0) = -5
yb(3); % lambda1(T) = 0
yb(4)]; % lambda2(T) = 0
end
function g = guess(t)
% Initial guess for the solution
g = [-5; -5; 0; 0];
end
Modify the 'odefun', 'bcfun', and 'guess' functions as per the conditions. For a comprehensive understanding of the 'bvp4c' function in MATLAB, please refer to the following documentation.
I hope this helps!
