Error in Fmincon fuction

Example I am solving

Find the optimal state and optimal control based on minimizing the performance index 𝐽=∫ (𝑥(𝑡) − 1/2 𝑢(𝑡)^2 ) 𝑑𝑡 1 0 , 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

ERROR:

On running solve_system_of_equations , I am getting error as :

Error using system_of_equations

Too many output arguments.

Error in fmincon (line 655)

[ctmp,ceqtmp] = feval(confcn{3},X,varargin{:});

Error in solve_system_of_equations (line 44)

x = fmincon(fun,x0,A,bb,Aeq,beq,lb,ub,nonlcon)

Caused by:

Failure in initial nonlinear constraint function evaluation. FMINCON cannot continue.

CODE:

function F = cost_function(x)
global def;
global m;
s=def.k ;
C2=x(1,(s+1):2*s);
u=(C2*m.H)   ;
F=(1/2)*u*u';
    function F = system_of_equations(x)
        global def;
        global m;
        global init;
        
        global P_alpha_1;
        s=def.k ;
        
        C1=x(1,1:s);
        C2=x(1,(s+1):2*s);
        
        
        x1=(C1*P_alpha_1*m.H) + init(1);
        u=(C2*m.H)   ;
        D_alpha1_x1= C1*m.H;
        %     
        M=Haar_matrix(s);
        HC=M(:,s);
        
        %%control law1
        F = horzcat(  D_alpha1_x1   + x1 - u  , ...
            (C1*P_alpha_1*HC) + init(1) - (1/2*((1-exp(-1))^2)))     ;
        
    end
alpha_1=1;

k=8;     %no. of Haar wavelets 
b=2;  %Total number of days to plot
initialize(alpha_1,k,b )
global m;
global init;
global def;

global P_alpha_1;
global P_alpha_2;
P_alpha_1=fractional_operation_matrix(k,alpha_1,b,m.H);
s=def.k;

x0=zeros(3,3*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)

Answer 1

[Walter Roberson]

    function F = system_of_equations(x)

That function only returns one output.

    nonlcon=@system_of_equations;

For fmincon, the nonlinear constraints function must return 2 outputs (and with some options, it would have to return four outputs.)

The first output is for the nonlinear inequality constraints. The second output is for the nonlinear equality constraints. If you do not have any nonlinear equality constraints, you must return the empty array, [] for the second output.

[Kunal Jain]

@Walter Roberson

Thank you for answering my question

In this using x=ones(1,16)

function F = system_of_equations(x)

Result is

F =

0.6768 1.5303 2.0303 2.1768 2.4268 2.7803 2.7803 2.4268 2.2270

But after running solve_system_of_equations I am geting the same above Fmincon error

Can you please explain a bit more what u explained about the the outputs of fmincon more?

Thanks in advance

[Torsten]

The function "system_of_equations" must return two output arguments. You only return one argument, namely F.

Thus the function must read

function [c,ceq] = system_of_equations(x)
  c = ...;
  ceq = ...;
end
  

For the meaning of c and ceq, please refer to the documentation of fmincon, especially for the function in which the nonlinear inequality and equality constraints are defined (usually named "nonlcon").