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

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)
        

[Matt J]

It would be easiest if you run the code here in the forum, rather than on your local computer. That way, we can all see what it's doing in the same environment.

[Kunal Jain]

@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?

Answer 1

[Catalytic]

Do as the error message says. Test your cost function on its own and make sure it returns a scalar value before applying fmincon.

[Kunal Jain]

@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?