Talk:Beginning with CVX

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</pre>
</pre>
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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.
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.
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Thanks a lot for all the ideas, they all are greats.
Thanks a lot for all the ideas, they all are greats.
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I'm at work so I can't programm now, I will do it later.
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I don't know how to initialice Epsilon1 and Epsilon2 I'm going to research in the references of my article (Cross fingers)
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At the paper puts:
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normalized eigenvectors: v_W. And
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<pre>
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v_W ' * W * v_W >= Epsilon1
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</pre>
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v_W its a matrix, and Epsilon1 I think its an escalar, so a good idea could be:
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<pre>[ v_W ] = eig ( full ( W ) )
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....
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v_W_1 = v_W( : , 1 ) / norm ( v_W ( : , 1 ) ) ;
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-
v_W_2 = v_W( : , 2 ) / norm ( v_W ( : , 2 ) ) ;
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-
v_W_3 = v_W( : , 3 ) / norm ( v_W ( : , 3 ) ) ;
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-
v_W_4 = v_W( : , 4 ) / norm ( v_W ( : , 4 ) ) ;
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-
....
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v_W_1 ' * W * v_W_1 >= Epsilon1
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v_W_2 ' * W * v_W_2 >= Epsilon1
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v_W_3 ' * W * v_W_3 >= Epsilon1
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-
v_W_4 ' * W * v_W_4 >= Epsilon1
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-
....
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</pre>
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or
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<pre>[ v_W ] = eig ( full ( W ) )
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....
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v_W( : , 1 ) = v_W( : , 1 ) / norm ( v_W ( : , 1 ) ) ;
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v_W( : , 2 ) = v_W( : , 2 ) / norm ( v_W ( : , 2 ) ) ;
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v_W( : , 3 ) = v_W( : , 3 ) / norm ( v_W ( : , 3 ) ) ;
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v_W( : , 4 ) = v_W( : , 4 ) / norm ( v_W ( : , 4 ) ) ;
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-
....
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v_W ' * W * v_W >= Epsilon1 * eye ( 4 );
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....
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</pre>
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I haven't Matlab here so it could be horrible.
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--------------------------------------------------------------------
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Thanks for the ideas it's great. Thank you very much :D.
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I have an answer, how to calculate the normalized eigenvector.
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Maybe? <pre>[v_W]=eig(full(W))/norm ....</pre>
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I've changed Epsilon1, Epsilon2, they aren't a variable, I think they are constants.
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I'm going to see how to initialice (I'm going to research in the references of my article (Cross fingers)
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Thanks a lot again.
Thanks a lot again.
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<pre>
<pre>
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%0)Initialization
clear all;
clear all;
n=2; m=1;
n=2; m=1;
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A_a=3*eye(2*n,2*n)
A_a=3*eye(2*n,2*n)
B_a=4*eye(2*n,2*m)
B_a=4*eye(2*n,2*m)
 +
 +
%1)1
W=eye(4)
W=eye(4)
R=(zeros(2,4))
R=(zeros(2,4))
 +
%2)2
H=W*A_a'+A_a*W-B_a*R-R'*B_a'
H=W*A_a'+A_a*W-B_a*R-R'*B_a'
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lamda_H=max(eig(H))
lamda_H=max(eig(H))
-
Epsilon1=1;
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Epsilon1=11;
-
Epsilon2=1;
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Epsilon2=0.1;
if(lamda_W>=Epsilon1)
if(lamda_W>=Epsilon1)
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end
end
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%3)3
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%v_W=eig(W)/(abs(eig(W)))
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[v_W,D] = eig( full ( W ) )
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%v_W=eig(full(W))/abs(full(W))%%normalized eigenvector :|
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[v_H,D] = eig( full ( H ) )
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%v_H=eig(H)/max(eig(H))
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while para==0
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[v_W,D] = eig(W)
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v_W_1 = v_W( : , 1 ) / norm ( v_W ( : , 1 ) ) ;
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[v_H,D] = eig(H)
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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_H_1 = v_H( : , 1 ) / norm ( v_H ( : , 1 ) ) ;
 +
v_H_2 = v_H( : , 2 ) / norm ( v_H ( : , 2 ) ) ;
 +
v_H_3 = v_H( : , 3 ) / norm ( v_H ( : , 3 ) ) ;
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v_H_4 = v_H( : , 4 ) / norm ( v_H ( : , 4 ) ) ;
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 +
%4a)4a
if ( Epsilon1 - lamda_W )>(lamda_H+Epsilon2)
if ( Epsilon1 - lamda_W )>(lamda_H+Epsilon2)
 +
Caso=1 %For know where am I
cvx_begin
cvx_begin
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variables p1 p2 W(4,4) R(2,4)
variables p1 p2 W(4,4) R(2,4)
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subject to
subject to
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W(1,1)<=p1
 
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W(2,2)<=p1
 
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W(1,1)>=Epsilon1
 
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W(2,2)>=Epsilon1
 
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W(3,3)==W(1,1)
 
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W(4,4)==W(2,2)
 
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R(1,1)>=-p2
 
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R(1,1)<=p2
 
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R(2,3)==R(1,1)
 
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R(1,2)>=-p2
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W(1,1)<=p1
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R(1,2)<=p2
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W(2,2)<=p1
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R(2,4)==R(1,2)
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W(1,1)>=Epsilon1
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W(2,2)>=Epsilon1
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W(3,3)==W(1,1)
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W(4,4)==W(2,2)
 +
 
 +
R(1,1)>=-p2
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R(1,1)<=p2
 +
R(2,3)==R(1,1)
 +
R(1,2)>=-p2
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R(1,2)<=p2
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R(2,4)==R(1,2)
H=W*A_a'+A_a*W-B_a*R-R'*B_a'
H=W*A_a'+A_a*W-B_a*R-R'*B_a'
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W - Epsilon1*eye(2*n) == semidefinite(2*n);
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v_W'*W*v_W - Epsilon1*eye(2*n) == semidefinite(2*n);
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Epsilon2*eye(2*n) + H == -semidefinite(2*n);
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v_W'*W*v_W>=Epsilon1*eye(4)
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cvx_end
cvx_end
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else
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else %4b)4b
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Caso = 2
cvx_begin
cvx_begin
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subject to
subject to
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W(1,1)>=Epsilon1
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W(1,1)>=Epsilon1
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W(2,2)>=Epsilon1
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W(2,2)>=Epsilon1
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W(1,1)<=p1
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W(2,2)<=p1
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W(3,3)==W(1,1)
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W(4,4)==W(2,2)
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W(1,1)<=p1
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R(1,1)>=-p2
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W(2,2)<=p1
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R(1,1)<=p2
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W(3,3)==W(1,1)
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R(2,3)==R(1,1)
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W(4,4)==W(2,2)
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R(1,2)>=-p2
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R(1,2)<=p2
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R(2,4)==R(1,2)
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R(1,1)>=-p2
 
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R(1,1)<=p2
 
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R(2,3)==R(1,1)
 
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R(1,2)>=-p2
 
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R(1,2)<=p2
 
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R(2,4)==R(1,2)
 
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H=W*A_a'+A_a*W-B_a*R-R'*B_a'
H=W*A_a'+A_a*W-B_a*R-R'*B_a'
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W - Epsilon1*eye(2*n) == semidefinite(2*n);
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Epsilon2*eye(2*n) + v_H'*H*v_H == -semidefinite(2*n);
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Epsilon2*eye(2*n) + H == -semidefinite(2*n);
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-
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v_H'*H*v_H<=-Epsilon2*eye(4)
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cvx_end
cvx_end
end
end
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lamda_W=min(eig(full(W)))
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lamda_W = min ( eig ( full ( W ) ) )
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lamda_H=max(eig(H))
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lamda_H = max ( eig ( full ( H ) ) )
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% v_W=eig(full(W))/max(eig(full(W)))%%Cálculo del normalized eigenvector
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R
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% v_H=eig(H)/max(eig(H))
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W=full(W)
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K=R/W
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%STOP
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</pre>
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if(lamda_W>=Epsilon1)
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if(lamda_H<=-Epsilon2) para=1
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else para = 0
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end
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else para =0
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end
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end
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R
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W
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K=R/W</pre>
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Revision as of 09:16, 5 February 2009

lamda_W=eig(full(W))

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 don't know how to initialice Epsilon1 and Epsilon2 I'm going to research in the references of my article (Cross fingers)

Thanks a lot again.

Here is the new code: 

%0)Initialization
clear all;
n=2; m=1;

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

%1)1
W=eye(4)
R=(zeros(2,4))

%2)2
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=11;
Epsilon2=0.1;

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

    %3)3
    [v_W,D] = eig( full ( W ) )
    [v_H,D] = eig( full ( H ) )
    
    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_H_1 = v_H( : , 1 ) / norm ( v_H ( : , 1 ) ) ;
    v_H_2 = v_H( : , 2 ) / norm ( v_H ( : , 2 ) ) ;
    v_H_3 = v_H( : , 3 ) / norm ( v_H ( : , 3 ) ) ;
    v_H_4 = v_H( : , 4 ) / norm ( v_H ( : , 4 ) ) ;

    %4a)4a
if ( Epsilon1 - lamda_W )>(lamda_H+Epsilon2)
    Caso=1 %For know where am I

    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'
        
        v_W'*W*v_W - Epsilon1*eye(2*n) == semidefinite(2*n);

cvx_end

else %4b)4b

    Caso = 2
    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'
        
        Epsilon2*eye(2*n) + v_H'*H*v_H == -semidefinite(2*n);        

cvx_end
end

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

R
W=full(W)
K=R/W
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