Hello, I’m attempting to solve an optimal control problem using the fmincon function however I have very little experience with it. I’m wondering if there is some fundamental flaw to my code or if there is a more obscure mistake like using the trapz function for integration. My current batch of code is no longer spitting out errors so trying to troubleshoot my way to a solution has slowed down.
The problem is as follows:

And here is the code:
%% Optimization
clear all
close all
clc

%Initialize constants
global U tspan N div
tspan = 10;
div = 10;
N = tspan*div;

control_ic = [linspace(0, 10, 1/5*N), linspace(10, 0, 4/5*N)]; %Control profile guess
%% Routine
u_t = fmincon(@fun, control_ic, [], [],[],[], [], [], [], optimoptions(‘fmincon’, ‘MaxFunctionEvaluations’, 1e5))

function [J] = fun(u) %Objective function
global U tspan div
U = u;
dynamic_ic = [2;2]; %Initial Conditions

[t, X] = ode45(@dynamics, [0 tspan], dynamic_ic); %Find x, xd using u
x = X(:, 1);
xd = X(:, 2);

x_cost = trapz(tspan/length(t), 2*x.^2 + 2*xd.^2); %Calculate objective function
finalx_cost = x(length(x))^2;
control_cost = trapz(div^(-1), .1*u.^2);

J = x_cost + finalx_cost + control_cost;
end

%System Dynamics
function [X] = dynamics(t, x)
global U tspan N
xd = x(2);
vd = -.2*x(2) – 3*x(1) + interp1(linspace(0, tspan, N), U, t);
X = [xd; vd];
endHello, I’m attempting to solve an optimal control problem using the fmincon function however I have very little experience with it. I’m wondering if there is some fundamental flaw to my code or if there is a more obscure mistake like using the trapz function for integration. My current batch of code is no longer spitting out errors so trying to troubleshoot my way to a solution has slowed down.
The problem is as follows:

And here is the code:
%% Optimization
clear all
close all
clc

%Initialize constants
global U tspan N div
tspan = 10;
div = 10;
N = tspan*div;

control_ic = [linspace(0, 10, 1/5*N), linspace(10, 0, 4/5*N)]; %Control profile guess
%% Routine
u_t = fmincon(@fun, control_ic, [], [],[],[], [], [], [], optimoptions(‘fmincon’, ‘MaxFunctionEvaluations’, 1e5))

function [J] = fun(u) %Objective function
global U tspan div
U = u;
dynamic_ic = [2;2]; %Initial Conditions

[t, X] = ode45(@dynamics, [0 tspan], dynamic_ic); %Find x, xd using u
x = X(:, 1);
xd = X(:, 2);

x_cost = trapz(tspan/length(t), 2*x.^2 + 2*xd.^2); %Calculate objective function
finalx_cost = x(length(x))^2;
control_cost = trapz(div^(-1), .1*u.^2);

J = x_cost + finalx_cost + control_cost;
end

%System Dynamics
function [X] = dynamics(t, x)
global U tspan N
xd = x(2);
vd = -.2*x(2) – 3*x(1) + interp1(linspace(0, tspan, N), U, t);
X = [xd; vd];
end Hello, I’m attempting to solve an optimal control problem using the fmincon function however I have very little experience with it. I’m wondering if there is some fundamental flaw to my code or if there is a more obscure mistake like using the trapz function for integration. My current batch of code is no longer spitting out errors so trying to troubleshoot my way to a solution has slowed down.
The problem is as follows:

And here is the code:
%% Optimization
clear all
close all
clc

%Initialize constants
global U tspan N div
tspan = 10;
div = 10;
N = tspan*div;

control_ic = [linspace(0, 10, 1/5*N), linspace(10, 0, 4/5*N)]; %Control profile guess
%% Routine
u_t = fmincon(@fun, control_ic, [], [],[],[], [], [], [], optimoptions(‘fmincon’, ‘MaxFunctionEvaluations’, 1e5))

function [J] = fun(u) %Objective function
global U tspan div
U = u;
dynamic_ic = [2;2]; %Initial Conditions

[t, X] = ode45(@dynamics, [0 tspan], dynamic_ic); %Find x, xd using u
x = X(:, 1);
xd = X(:, 2);

x_cost = trapz(tspan/length(t), 2*x.^2 + 2*xd.^2); %Calculate objective function
finalx_cost = x(length(x))^2;
control_cost = trapz(div^(-1), .1*u.^2);

J = x_cost + finalx_cost + control_cost;
end

%System Dynamics
function [X] = dynamics(t, x)
global U tspan N
xd = x(2);
vd = -.2*x(2) – 3*x(1) + interp1(linspace(0, tspan, N), U, t);
X = [xd; vd];
end optimization, fmincon, ode45 MATLAB Answers — New Questions

​