You have NaNs in your constraints!, iterating, for loop

Hi, I am trying to run the code, iterating 'e_1' in the bold text. When I don't interate, equally fixing the 'e_1' without for loop, it perfectly works.

What I thought was putting constraints and objective in the for loop, then it gives solutions, Pfeasible, per each 'e_1'

I basically use tool 'YALMIP' to solve optimization problem and the code I run is shown below:

I would be appreciated whatever you give some tips!

%Compare under e_1
%Data-based
ops = sdpsettings('solver','mosek','verbose',1,'debug',1);
Y=sdpvar(2,10);
 
delta = 0.7637;
A= [0.2, 1.3; 0.1, 1.2];
B= [1; 2];
D= [0.45 0.45; 0.3 -0.3];
t=0:9;
U=chirp(t,0.2,3,0.6);
[x] = data_dstate(); %data-based state: xdb
xdb=transpose(x);%X_{0,N}=(2x10)
 
for i=1:10
    dxx(:,i)= A*(x(i,:))' + B*U(1,i) + D*(x(i,:))'*U(1,i);
end
dx= dxx;%X_{1,N}=(2x10)
for i=1:10
    Vv(:,i)= [xdb(1,i)*U(1,i); xdb(2,i)*U(1,i)];
end
V=Vv;%V_{0,N}=(2x10)
 
for e_1=0:0.2:2                                                %BOLD STARTS HERE
    ops = sdpsettings('solver','mosek','verbose',1,'debug',1);
    
    e_2=sdpvar(1,1);
M_2 = [Y*dx'+ dx*Y'+ e_2*delta^2 *eye(2,2), Y*U', zeros(2,2), -Y*V';
    U*Y', -e_1, zeros(1,2), zeros(1,2);
    zeros(2,2), zeros(2,1), -P2./e_1, P2;
    -V*Y', zeros(2,1), P2, -e_2*eye(2,2)];%LMI,(7x7)-data
M=[P1*A'+ A*P1+ B*y'+ y*B'+ e_1*D*P1*D' , y; y' , -e_1];%LMI-model
 
con2 = [e_2>=0, P2>=0, P2==xdb*Y', M_2<=0]; %constraints
con1=[P1>=0, M<=0]; %constraints
 
ob2 = -log(det(P2)); %objective
optimize(con2, ob2, ops)
ob1= -log(det(P1)); %objective
optimize(con1, ob1, ops)
end                                                         %BOLD ENDS HERE
 
%data-based solution
Pfeasible2 = value(P2);%(2x2)
Yfeasible2 = value(Y);%(2x10)
G_k = (Yfeasible2)'/(Pfeasible2);%(10x2)
K_db = U* G_k; %(1x2)
%data-based solution
Pfeasible1 = value(P1);
yfeasible1 = value(y);
K_mb = (yfeasible1)'/(Pfeasible1);% (yfeasible1)'*inv(Pfeasible1);
 
%Figure3-1
plot(e_1,det(Pfeasible2))
hold on 
plot(e_1,det(Pfeasible1))

[Walter Roberson]

Is it the fact that you are iterating, or is it the fact that your e_1 becomes non-zero ?

[Junhwi Mun]

I just noticed e_1 should be nonzero to run the code since one of the term in the matrix M_2 has the denominator 'e_1'. Then when I fix 'e_1' to be colse to zero like 0.01, optimization was working but it doesn't give solutions Pfeasible per each 'e_1', even if I moved the code for Pfeasible and Yfeasible inside of the for loop. It only shows only one solution

Answer 1

[Johan Löfberg]

You are better off posting this question to the YALMIP Google groups, which you did but you never replied to the questions you received there. When you do that, also make sure the code is reproducible (it is not at the moment since data_dstate is some non-standard call)