Doing an example find the optimal state and optimal control based on minimizing the performance index, Fmincon error of scalar value

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Example to find the optimal state and optimal control based on minimizing the performance index. I have written the code but the error shown in fmincon is "Supplied objective function must return a scalar value." I have checked the matrices but still the error is there. I have attached te codes, kindly tell how to resolve the problem.
EXAMPLE:
Find the optimal state and optimal control based on minimizing the performance index 𝐽=∫ (𝑥(𝑡) − 1/2 𝑢(𝑡)^2 ) 𝑑𝑡 , 0 ≤ 𝑡 ≤ 1 subject to 𝑢(𝑡) = 𝑥̇(𝑡) + 𝑥(𝑡) with the condition 𝑥(0) = 0, 𝑥(1) = 1 2 (1 − 1/𝑒 )^ 2 where 𝐽𝑒𝑥𝑎𝑐𝑡 = 0.08404562020 In this example the initial approximation is 𝑥1 (𝑡) = 1 2 (1 − 1/𝑒 ) ^2
CODES:
File1;
function F = cost_function(x)
global def;
global m;
% global P_alpha_1;
s=def.k ;
C3=x(1,(s+1):2*s);
;
u=(C3*m.H) ;
F=(x-(1/2)*(u*u'));
File 2:
function F = system_of_equations(x)
global def;
global m;
global init;function F = system_of_equations(x)
global def;
global m;
global init;
global P_alpha_1;
s=def.k ;
C1=x(1,1:1);
C3=x(1,(s+1):s);
x1=('C1*P_alpha_1*m.H') + init(1);
u=('C3*m.H') ;
D_alpha1_x1= 'C1*m.H';
M=Haar_matrix(s);
HC=M(:,s);
%%control law1
% F = horzcat( D_alpha1_x1 - u , ...
F = horzcat( D_alpha1_x1 - u , ...
('C1*P_alpha_1*HC') + init(1) - (1/2*((1-exp(-1))^2)) ) ;
end
File 3:
alpha_1=1;
k=8; %no. of Haar wavelets
b=1; %Total number of days to plot
initialize(alpha_1,k,b )
global m;
global init;
global def;
global P_alpha_1;
P_alpha_1=fractional_operation_matrix(k,alpha_1,b,m.H);
s=def.k;
% C3=x(1,((2*s)+1):3*s);
% u=(C3*m.H) ;
% cost function=(1/2)*u.^2;
x0=zeros(2,2*s);
% system_of_equations(x)
A = [];
bb = [];
Aeq = [];
beq = [];
lb = [];
ub = [];
fun = @cost_function;
nonlcon=@system_of_equations;
x = fmincon(fun,x0,A,bb,Aeq,beq,lb,ub,nonlcon)
  2 Comments
Kunal Jain
Kunal Jain on 17 Feb 2022
Edited: Kunal Jain on 18 Feb 2022
@Matt J Thanks for answering my question.
I am not able to run the code here on community. It shows the no code when I click on Run button..
Please tell what should I do?

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Answers (1)

Catalytic
Catalytic on 17 Feb 2022
Edited: Catalytic on 17 Feb 2022
Do as the error message says. Test your cost function on its own and make sure it returns a scalar value before applying fmincon.
  1 Comment
Kunal Jain
Kunal Jain on 17 Feb 2022
@Catalytic Thanks for responding my query.
I tried running the cost function alone and I am getting a value as :
F = cost_function(zeros(1,16))
F =
1.4018e+04
Can you tell then why I am still getting fmincon error?

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