function with myblackbox using fminunc

Question

Ali Esmaeilpour 2019-8-30

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https://ww2.mathworks.cn/matlabcentral/answers/478240-function-with-myblackbox-using-fminunc

评论： Matt J 2019-8-30

Hello guys! I got a Function F(y(x)) = sum (( yref-y(x))^2) and x(1) = q and x(2)=r and x=[q;r] and yref=0. I wanted to code this function to be used in a multi-objective optimization etc.

my initial idea is:

function F = myblackbox(x)
q = x(1)
r = x(2);
yref = 0;
y = solvemyoptimizationproblem(q,r);
F = somefunctionofy(y);

but i don't know how to use fminunc here to do a blackbox optimization and how to replace those things to have F(y(x)) correctly.

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Answer 1

Matt J 2019-8-30

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/478240-function-with-myblackbox-using-fminunc#answer_389768

编辑：Matt J 2019-8-30

在 MATLAB Online 中打开

lsqnonlin would be better suited to this,

x0=[q_guess,r_guess];
x=lsqnonlin( @(x) yfunction(x(1),x(2))-yref, x0);

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Ali Esmaeilpour 2019-8-30

在 MATLAB Online 中打开

how can I find a function for my closed-loop response y? I got closed-loop response:

y = [-2,-2.06844254709663,-2.10111830954110,-2.10207250524360,-2.07526182090699,-2.02451336009587,-1.95348936029213,-1.86566104239566,-1.76428609501489,-1.65239283602609,-1.53276900719044,-1.40795510853059,-1.28024204134041,-1.15167219215486,-1.02404365938112,-0.898917175767882,-0.777625266347119,-0.661283291728917,-0.550801952158784,-0.446900918848503,-0.350123272116316,-0.260850455112571,-0.179317482440462,-0.105628171524862,-0.0397701935839232,0.0183702310931665,0.0689941424455793,0.112376278061898,0.148852238329798,0.178806457148514,0.202661035909770,0.220865478976649,0.233887353198917,0.242203878667164,0.246294444722945,0.246634033866838,0.243687526483402,0.237904851041483,0.229716937775089,0.219532428513973,0.207735091324267,0.194681885774748,0.180701622852288,0.166094162756435,0.151130093813326,0.136050836531366,0.121069118234489,0.106369765666474,0.0921107653476128,0.0784245442470077,0.0654194263502996,0.0531812239571451,0.0417749259245079,0.0312464485645638,0.0216244182313353,0.0129219582599530,0.00513845621642096,-0.00173870934149472,-0.00773250023679152,-0.0128746228204809,-0.0172040168372426,-0.0207654382076332,-0.0236081426698606,-0.0257846749601092,-0.0273497662907451,-0.0283593408257317,-0.0288696309906560,-0.0289363993725932,-0.0286142641583750,-0.0279561239979665,-0.0270126774854485,-0.0258320316788283,-0.0244593937199454,-0.0229368391498630,-0.0213031503020680,-0.0195937183993203,-0.0178405024207615,-0.0160720382595013,-0.0143134917503068,-0.0125867493914005,-0.0109105408257964,-0.00930058753949017,-0.00776977247844266,-0.00632832582476125,-0.00498402235945812,-0.00374238646270093,-0.00260690103919371,-0.00157921715665090,-0.000659361544098163,0.000154060515616681,0.000863668978079722,0.00147312127494728,0.00198693439542896,0.00241031792821887,0.00274901888833613,0.00300917888601873,0.00319720397995884,0.00331964734521793,0.00338310467267475,0.00339412212095973];

Ali Esmaeilpour 2019-8-30

在 MATLAB Online 中打开

I give you the code that I got this close-loop response from and mux1 adn mux2 are closed-loop responses I mean y=mux1 in the following program:

clc;
clear;
close all;
%% Time structure 
t0 = 0;         
tf = 10;        
dt = 0.1;      
time = t0:dt:tf-dt; 
%% System structure  ===> x(k+1) = A*x(k) + B*u(k) + G*w(k)
A = [1.02 -0.1;0.1 0.98];
B = [0.5 0;0.05 0.5];
G = [0.3 0;0 0.3];
[nx,nu] = size(B);
%% MPC parameters
Q = eye(nx);
R = eye(nu)*50;
Qf = eye(nu)*50;
N = 26;
%% Problem parameters
M = blkdiag(Q,R);
w1 = randn(1,100); 
w1 = w1-mean(w1);
muw1 = mean(w1);
sigmaw1 = var(w1);
w2 = randn(1,100); 
w2 = w2-mean(w2);
muw2 = mean(w2);
sigmaw2 = var(w2);
w = [w1;w2];
sigmaw = [sigmaw1 0 ;0 sigmaw2];
x = randn(2,1);
mux{1} = [-2;2];
sigmax{1} = [1,0;0,1];
h1x = [-1/sqrt(5);-2/sqrt(5)];
h2u = [-0.4/sqrt(1.16);1/sqrt(1.16)];
epsilon = 0.5;
g1 = 3;
g2 = 0.2;
c = 0;
%% Main loop
for t = t0:dt:tf-dt
c = c+1;  
sigmax = sdpvar(repmat(nx,1,N+1),repmat(nu,1,N+1));
p = sdpvar(repmat(4,1,N-1),repmat(4,1,N-1));
pN = sdpvar(2,2);
F = sdpvar(repmat(2,1,N+1),repmat(2,1,N+1));
K = sdpvar(repmat(2,1,N+1),repmat(2,1,N+1));
muu = sdpvar(repmat(nu,1,N),repmat(1,1,N));
sigmau = sdpvar(repmat(2,1,N),repmat(2,1,N));
constraint = [];
objective = 0;
for k = 1:N-1   
    mux{k+1} = A*mux{k} + B*muu{k};        
    objective = objective + 1/2*(trace(M*p{k}));         
    constraint2 = [sigmax{k+1} (A*sigmax{k}+B*F{k}) G*sigmaw;(A*sigmax{k}+B*F{k})' sigmax{k} zeros(2);(G*sigmaw)' zeros(2) sigmaw]>=0;
    constraint3 = [sigmau{k} (F{k});(F{k})' sigmax{k}]>=0;
    constraint4 = h1x'*mux{k}<=(1-(0.5*epsilon))*g1-((0.95/2*epsilon*g1*(1-0.95))*h1x'*sigmax{k}*h1x);
    constraint5 = h2u'*muu{k}<=(1-(0.5*epsilon))*g2-((0.95/2*epsilon*g2*(1-0.95))*h2u'*sigmau{k}*h2u);
    constraint6 = [p{k} [sigmax{k};F{k}] [mux{k};muu{k}];[sigmax{k};F{k}]' sigmax{k} zeros(2,1);[mux{k};muu{k}]' zeros(1,2) ones(1)]>=0;
    constraint7 = [F{k} K{k};sigmax{k} eye(2)];
    constraint = [constraint,constraint2,constraint3,constraint4,constraint5,constraint6,constraint7];          
end        
objective = objective + (1/2*trace((trace(Q*pN))));
constraint8 = h1x'*mux{N}<=(1-(0.5*epsilon))*g1-((0.95/2*epsilon*g1*(1-0.95))*h1x'*sigmax{N}*h1x);
constraint9 = [pN-sigmax{N} mux{N};mux{N}' 1];
constraint = [constraint,constraint8,constraint9];
option = sdpsettings('solver','sedumi');
a = optimize (constraint,objective,option);   
u = value(muu{1});
U1(c) = u(1,1);
U2(c) = u(2,1);
U3 = [U1;U2];   
mux3 = value(mux{1});
mux1(c) = mux3(1,1);
mux2(c) = mux3(2,1);
F = value(F{1});
X = value(sigmax{1});
f1{c} = F;
X1{c} = X;
K = F*inv(X);
% K=value(K{1})
K1{c} = K;
K2 = value(K1{c});
x = value(x);
u1 = u+K2*(x-mux3);
u2{c} = u1;
x = A*x+B*u1+G*w(:,c);
mux{1} = value(mux{2});
sigmax{1} = value(sigmax{2});    
ud = value(u2{c});
ud1(c) = ud(1,1);
ud2(c) = ud(2,1);
x1(c) = x(1,1);
x2(c) = x(2,1);       
end
%% Plot results
figure(1)
subplot(4,1,1)
plot(time,ud1,'LineWidth',2)
xlabel('time')
ylabel('ud1')
title('Input signal')
grid on
subplot(4,1,2)
plot(time,ud2,'LineWidth',2)
xlabel('time')
ylabel('ud2')
grid on
subplot(4,1,3)
plot(time,x1,'LineWidth',2)
xlabel('time')
ylabel('x1')
title('State 1')
grid on
subplot(4,1,4)
plot(time,x2,'LineWidth',2)
xlabel('time')
ylabel('x2')
title('State 2')
grid on
figure(2)
subplot(4,1,1)
plot(time,x1,'r',time,mux1,'g','LineWidth',2)
xlabel('time')
legend({'x1','Mean of x1'},'Location','northeast')
grid on
subplot(4,1,2)
plot(time,x2,'r',time,mux2,'g','LineWidth',2)
xlabel('time')
legend({'x2','Mean of x2'},'Location','northeast')
grid on
subplot(4,1,3)
plot(mux1,mux2,'LineWidth',2)
title('State space phase plane')
xlabel('mux1')
ylabel('mux2')
grid on
subplot(4,1,4)
plot(U1,U2,'LineWidth',2)
title('Control space phase plane')
xlabel('U1')
ylabel('U2')
grid on
figure
subplot(4,1,1)
plot(time,mux1,'b','LineWidth',2)
title('Mean of first state')
xlabel('Time')
ylabel('mux1')
grid on
subplot(4,1,2)
plot(time,mux2,'b','LineWidth',2)
title('Mean of second state')
xlabel('Time')
ylabel('mux2')
grid on
subplot(4,1,3)
plot(time,U1,'r','LineWidth',2)
title('First input')
xlabel('Time')
ylabel('U1')
grid on
subplot(4,1,4)
plot(time,U2,'r','LineWidth',2)
title('Second input')
xlabel('Time')
ylabel('U2')
grid on

Ali Esmaeilpour 2019-8-30

so I put that fminsearch at the end of my main code?

Matt J 2019-8-30

fminsearch will search for the optimal x. You put it wherever you need the optimization to occur.

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function with myblackbox using fminunc

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function with myblackbox using fminunc

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