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Subject: Equality constraints in LMI..elementwise implementation....reproduction of neural network in Park& Park paper
Date: Fri, 21 Aug 2009 19:26:04 +0000 (UTC)
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Uses LMI toolbox in matlab to implement problem defined by Park & Park  (paper attached).however problem results in infeasibility....

Implementing eq 9 and 10 in park & park paper "An optimization approach to design of cellular neural networks"International Journal of Systems Science, 2000, volume 31, number 12, pages 1585 ? 1591

two problems encountered...
1) y is the problem infeasible in my code whereas feasible results are obtained in aprk & park using GEVP

2) where to use equality constraints to define Tii=0 and T=T'=T|S elementwise as in park & park

I think the structure of my LMI equations using lmivar and lmiterm is correct

The code is as such....



clear all;
clc;
A1=[1 1 1 1 -1 -1 1 -1 -1 1 1 1]';
A2=[1 -1 1 1 1 1 1 -1 1 1 -1 1]';
A3=[1 1 1 1 -1 1 1 1 1 1 -1 -1]';
A4=[-1 1 -1 -1 1 -1 -1 1 -1 -1 1 -1]';
S= [1 1 0 1 1 0 0 0 0 0 0 0; 1 1 1 1 1 1 0 0 0 0 0 0; 0 1 1 0 1 1 0 0 0 0 0 0; 1 1 0 1 1 0 1 1 0 0 0 0; 1 1 1 1 1 1 1 1 1 0 0 0; 0 1 1 0 1 1 0 1 1 0 0 0; 0 0 0 1 1 0 1 1 0 1 1 0; 0 0 0 1 1 1 1 1 1 1 1 1; 0 0 0 0 1 1 0 1 1 0 1 1; 0 0 0 0 0 0 1 1 0 1 1 0; 0 0 0 0 0 0 1 1 1 1 1 1; 0 0 0 0 0 0 0 1 1 0 1 1];
L=1;
U=10;
I= eye(12);
W=ones(12,12);
setlmis([])
T = lmivar(1,[12 1]);
B = lmivar(2,[12 1]);
P = lmivar(1,[12 0]);
Q = lmivar(1,[12 0]);




lmiterm([-1 1 1 T],1,A1*A1'*I);
lmiterm([-1 1 1 B],1,A1'*I);
lmiterm([-1 1 1 P],-1,1);

lmiterm([-2 1 1 T],1,A2*A2'*I);
lmiterm([-2 1 1 B],1,A2'*I);
lmiterm([-2 1 1 P],-1,1);

lmiterm([-3 1 1 T],1,A3*A3'*I);
lmiterm([-3 1 1 B],1,A3'*I);
lmiterm([-3 1 1 P],-1,1);

lmiterm([-4 1 1 T],1,A4*A4'*I);
lmiterm([-4 1 1 B],1,A4'*I);
lmiterm([-4 1 1 P],-1,1);


lmiterm([-5 1 1 Q],1,W);
lmiterm([-5 1 1 T],1,-1);

lmiterm([-6 1 1 Q],1,W);
lmiterm([-6 1 1 T],1,1);

lmiterm([-7 1 1 Q],1,1);
lmiterm([7 1 1 0],L*I);

lmiterm([-8 1 1 0],U*I);
lmiterm([8 1 1 Q],1,I);

lmiterm([-9 1 1 Q],2,1);
lmiterm([9 1 1 P],-1,1);

% lmiterm([-10 1 1 -T],1/2,-1,'s');
% lmiterm([-10 1 1 T],1,1);
% 
% lmiterm([11 1 1 -T],1/2,-1,'s');
% lmiterm([11 1 1 T],1,1);
% [m,n]=size(S);
% for i=1:m
%     for j =1:n
%     if S(i,j)==1
%         T(i,j)=T(i,j);
%     else
%         T(i,j)=0;
%     end
%     if (i==j)
%         T(i,j)=0;
%     else
%         T(i,j)=T(i,j);
%     end
%     end
% end
test_LMIs = getlmis;
[alpha,Qopt]=gevp(test_LMIs,9)