Getting error in fmincon with below code how to correct it

% Constants
m = 1; % mass of the rocket (kg)
x_target = 10; % target displacement (m)
t_final = 10; % final time (s)

% Objective function: integral of thrust squared
objective = @(F) integral(@(t) F(t).^2, 0, t_final);

% Initial guess for thrust profile (constant thrust)
%F0 = @(t) 0.0;  % Initial guess for thrust profile is a zero vector
F0 = 0.0; 

% Constraints
nonlcon = @(F) rocket_constraints(F, t_final, m, x_target);

% Solve optimization problem
options = optimoptions('fmincon', 'Display', 'iter');
F_opt = fmincon(objective, F0, [], [], [], [], [], [], nonlcon, options);

Array indices must be positive integers or logical values.

Error in solution>@(t)F(t).^2 (line 7)
objective = @(F) integral(@(t) F(t).^2, 0, t_final);

Error in integralCalc/iterateScalarValued (line 314)
fx = FUN(t);

Error in integralCalc/vadapt (line 132)
[q,errbnd] = iterateScalarValued(u,tinterval,pathlen);

Error in integralCalc (line 75)
[q,errbnd] = vadapt(@AtoBInvTransform,interval);

Error in integral (line 87)
Q = integralCalc(fun,a,b,opstruct);

Error in solution>@(F)integral(@(t)F(t).^2,0,t_final) (line 7)
objective = @(F) integral(@(t) F(t).^2, 0, t_final);

Error in fmincon (line 563)
initVals.f = feval(funfcn{3},X,varargin{:});

Caused by:
Failure in initial objective function evaluation. FMINCON cannot continue.

Answer 1

[Matt J]

You seem to be trying to minimize over a space of functionals, F. You cannot do that with fmincon. The objective must be a function of an unknown parameter vector in and the initial point x0 must be a vector in

[Charuka]

Objective function defined as below and changing F0 for variable gives error as well

objective = @(F) integral(@(t) F(t).^2, 0, t_final);

F0 = @(t) 0.0;

[Matt J]

As well it should. Again, you cannot minimize over function spaces.

[Walter Roberson]

fmincon() passes a vector the length of F0 to the objective function.

Your objective function takes that vector and tries to run an integration, with the integration trying to index the vector.

[Charuka]

Thanks I will relook in to it

Answer 2

[Torsten]

If you define F0 = 0, "fmincon" will use one scalar value as input F to "objective" and "nonlcon". Thus the use of F as a function handle or function doesn't make sense.

[Charuka]

Changing F0 doesnt solve the problem as well, Tried doing this

% Constants
m = 1; % mass of the rocket (kg)
x_target = 10; % target displacement (m)
t_final = 10; % final time (s)

% Objective function: integral of thrust squared
objective = @(F) integral(@(t) F(t).^2, 0, t_final);

% Initial guess for thrust profile (constant thrust)
F0 = @(t) 0.0;  % Initial guess for thrust profile is a zero vector

% Constraints
nonlcon = @(F) rocket_constraints(F, t_final, m, x_target);

% Solve optimization problem
options = optimoptions('fmincon', 'Display', 'iter');
F_opt = fmincon(objective, F0, [], [], [], [], [], [], nonlcon, options);

[Torsten]

The inputs to "objective" and "nonlcon" must be vectors of parameters to be optimized, not functions or function handles.

So you will have to parametrize your function to be integrated and optimize these parameters.

If you don't know how to do that, I suggest you license TOMS software which focusses on solving optimal control problems with MATLAB:

https://tomopt.com/docs/propt/tomlab_propt008.php

[Charuka]

Thank you, I will try it