Doing an example find the optimal state and optimal control based on minimizing the performance index, Fmincon error of scalar value
์กฐํ ์: 1 (์ต๊ทผ 30์ผ)
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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 ๐ฝ=โซ (๐ฅ(๐ก) โ 1/2 ๐ข(๐ก)^2 ) ๐๐ก , 0 โค ๐ก โค 1 subject to ๐ข(๐ก) = ๐ฅฬ(๐ก) + ๐ฅ(๐ก) with the condition ๐ฅ(0) = 0, ๐ฅ(1) = 1 2 (1 โ 1/๐ )^ 2 where ๐ฝ๐๐ฅ๐๐๐ก = 0.08404562020 In this example the initial approximation is ๐ฅ1 (๐ก) = 1 2 (1 โ 1/๐ ) ^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)
๋๊ธ ์: 2
Matt J
2022๋
2์ 17์ผ
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.
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