Talk:Beginning with CVX

From Wikimization

lamda_W=eig(full(W))

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Some one tell to me to upload the article that I'm reading for all the people could read it. I didn't know how to upload it, so I scan it and upload like some images (jpg). If it's wrong just tell to me and I will move or re-upload like jpg. The images are pag1 to pag7.

The paper its: Pole assignment of linear uncertain systems in a sector via a lyapunov - tipe approach. D. Arzeiler, J. Bernussou and G. Garcia. IEEE transactions automatic control, vol 38, nº 7, July 1993.

Thanks a lot for all the ideas, they all are greats.

I'm at work so I can't programm now, I will do it later.

At the paper puts:

normalized eigenvectors: v_W. And

v_W ' * W * v_W >= Epsilon1

v_W its a matrix, and Epsilon1 I think its an escalar, so a good idea could be:

[ v_W ] = eig ( full ( W ) )
....
v_W_1 = v_W( : , 1 ) / norm ( v_W ( : , 1 ) ) ;
v_W_2 = v_W( : , 2 ) / norm ( v_W ( : , 2 ) ) ;
v_W_3 = v_W( : , 3 ) / norm ( v_W ( : , 3 ) ) ;
v_W_4 = v_W( : , 4 ) / norm ( v_W ( : , 4 ) ) ;
....
v_W_1 ' * W * v_W_1 >= Epsilon1
v_W_2 ' * W * v_W_2 >= Epsilon1
v_W_3 ' * W * v_W_3 >= Epsilon1
v_W_4 ' * W * v_W_4 >= Epsilon1
....

or

[ v_W ] = eig ( full ( W ) )
....
v_W( : , 1 ) = v_W( : , 1 ) / norm ( v_W ( : , 1 ) ) ;
v_W( : , 2 ) = v_W( : , 2 ) / norm ( v_W ( : , 2 ) ) ;
v_W( : , 3 ) = v_W( : , 3 ) / norm ( v_W ( : , 3 ) ) ;
v_W( : , 4 ) = v_W( : , 4 ) / norm ( v_W ( : , 4 ) ) ;
....
v_W ' * W * v_W >= Epsilon1 * eye ( 4 ); 
....

I haven't Matlab here so it could be horrible.

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Thanks for the ideas it's great. Thank you very much :D.

I have an answer, how to calculate the normalized eigenvector.

Maybe?

[v_W]=eig(full(W))/norm ....

I've changed Epsilon1, Epsilon2, they aren't a variable, I think they are constants.

I'm going to see how to initialice (I'm going to research in the references of my article (Cross fingers)

Thanks a lot again.

Here is the new code:

clear all;
n=2; m=1;

A_a=3*eye(2*n,2*n)
B_a=4*eye(2*n,2*m) 
W=eye(4)
R=(zeros(2,4))

H=W*A_a'+A_a*W-B_a*R-R'*B_a'

lamda_W=min(eig(full(W)))
lamda_H=max(eig(H))

Epsilon1=1;
Epsilon2=1;

if(lamda_W>=Epsilon1)
    if(lamda_H<=-Epsilon2)     para=1
    else para = 0
    end
else para =0
end


%v_W=eig(W)/(abs(eig(W)))
%v_W=eig(full(W))/abs(full(W))%%normalized eigenvector :|
%v_H=eig(H)/max(eig(H))


while para==0
    
    [v_W,D] = eig(W)
    [v_H,D] = eig(H)
    
if ( Epsilon1 - lamda_W )>(lamda_H+Epsilon2)

    cvx_begin
   
    variables p1 p2 W(4,4) R(2,4)
    
    minimize (p1+p2)
    
    subject to
  
            W(1,1)<=p1
            W(2,2)<=p1
            W(1,1)>=Epsilon1
            W(2,2)>=Epsilon1
            W(3,3)==W(1,1)
            W(4,4)==W(2,2)
       
            R(1,1)>=-p2
            R(1,1)<=p2
            R(2,3)==R(1,1)

            R(1,2)>=-p2
            R(1,2)<=p2
            R(2,4)==R(1,2)
     
        H=W*A_a'+A_a*W-B_a*R-R'*B_a'
        
        W - Epsilon1*eye(2*n) == semidefinite(2*n);
        Epsilon2*eye(2*n) + H == -semidefinite(2*n);
        
        v_W'*W*v_W>=Epsilon1*eye(4)

cvx_end

else 

    cvx_begin
    
    variables p1 p2 W(4,4) R(2,4)
    
    minimize (p1+p2)
    
    subject to
        
            W(1,1)>=Epsilon1
            W(2,2)>=Epsilon1

            W(1,1)<=p1
            W(2,2)<=p1
            W(3,3)==W(1,1)
            W(4,4)==W(2,2)

      
                R(1,1)>=-p2
                R(1,1)<=p2
                R(2,3)==R(1,1)
                
                R(1,2)>=-p2
                R(1,2)<=p2
                R(2,4)==R(1,2)
         
        H=W*A_a'+A_a*W-B_a*R-R'*B_a'
        
        W - Epsilon1*eye(2*n) == semidefinite(2*n);
        Epsilon2*eye(2*n) + H == -semidefinite(2*n);        
        
        v_H'*H*v_H<=-Epsilon2*eye(4)

cvx_end
end

lamda_W=min(eig(full(W)))
lamda_H=max(eig(H))

% v_W=eig(full(W))/max(eig(full(W)))%%Cálculo del normalized eigenvector
% v_H=eig(H)/max(eig(H))

%STOP
if(lamda_W>=Epsilon1)
    if(lamda_H<=-Epsilon2)     para=1
    else para = 0
    end
else para =0
end
        
end

R
W
K=R/W