difficulties with penlab solver

[Ryad BOUKHARI]

Hi,

I want to solve an LMI constraint using " penlab ", and i have three matrices constraints (SDPs are : P11, P12, P2), when i run the Matlab-file, Matlab keep busy and it not return solution, even if i keep it for a long time.

I want to know, if my device isn't enough performant, or i maked mistake(s) in my program ???

With my thanks.

the code:

close all

clear all

clc

%%% the differents constants

u=0.7;

Sf10=60712.7*u;

Sf20=4814*u;

Sr10=60088*u;

Sr20=3425*u;

m=1500;

Vx=20;

Iz=2208;

L2=1.4625;

L1=1.0065;

Is=5;

Iw=0.4;

a11=(-(2*(Sf10+Sr10))/m*Vx);

a12=-1+((2*(L2*Sr10-L1*Sf10))/m*Vx^2);

a13=(2*(L2*Sr10-L1*Sr10))/Iz;

a14=(-2*(L2^2*Sr10+L1^2*Sf10))/Iz*Vx;

a21=(-(2*(Sf20+Sr20))/m*Vx);

a22=-1+((2*(L2*Sr20-L1*Sf20))/m*Vx^2);

a23=(2*(L2*Sr20-L1*Sr20))/Iz;

a24=(-2*(L2^2*Sr20+L1^2*Sf20))/Iz*Vx;

b11=2*Sf10/m*Vx;

b12=2*L1*Sf10/Iz;

b13=1/m*Vx;

b14=Iw/Iz;

b21=2*Sf20/m*Vx;

b22=2*L1*Sf20/Iz;

%%% the matrices of system

A1=[a11 a12 0 0;a13 a14 0 0;0 1 0 0;Vx Is Vx 0];

B1=[b11 1/m*Vx 0;b12 Iw/Iz 0;0 0 -Vx;0 0 -Is*Vx];

A2=[a21 a22 0 0;a23 a24 0 0;0 1 0 0;Vx Is Vx 0];

B2=[b21 1/m*Vx 0;b22 Iw/Iz 0;0 Iw/Iz 0;0 0 -Is*Vx];

C=[1 0 0 0;0 1 0 0;0 0 1 0;0 0 0 1];

D=[[0;0;0;0],[0;0;0;0],[0;0;0;0]];

Bd=[1 0 0 0;0 1 0 0;0 0 1 0;0 0 0 1];

%%% SDP Variables

P11=sdpvar(4,4,'symmetric');

P12=sdpvar(4,4,'symmetric');

P2=sdpvar(4,4,'symmetric');

N1=sdpvar(4,4);

N2=sdpvar(4,4);

V=sdpvar(4,4);

lm=sdpvar(1,1);

u=sdpvar(1,1);

o=sdpvar(1,1);

gg1=P11*A1;

gg2=P11*A2;

Del11=gg1+gg1'+N1*C'+C*N1'+eye(4);

Del12=gg2+gg2'+N1*C'+C*N1'+eye(4);

Del21=N1'-P12'*C*A1-N2*C;

Del22=N1'-P12'*C*A2-N2*C;

%% System under the Schur complement

S1=[Del12 Del22' ((A1-A2)'*P11)';Del22 N2+N2' (-(A1-A2)'*C'*P12)';(A1-A2)'*P11 -(A1-A2)'*C'*P12 P2*A1'+A1*P2'];

M1=[(B1-B2)'*P11 -(B1-B2)'*C'*P12 B1'*P2;Bd'*P11 -Bd'*C'*P12 Bd'*P2;V*C zeros(4) zeros(4)];

R1=[u*eye(4) zeros(4) zeros(4,3);zeros(4) lm*eye(4) zeros(4,3);zeros(3,4) zeros(3,4) o*eye(3)];

S2=[Del11 Del21' ((A2-A1)'*P11)';Del21 N2+N2' (-(A2-A1)'*C'*P12)';(A2-A1)'*P11 -(A2-A1)'*C'*P12 P2*A2'+A2*P2'];

M2=[(B2-B1)'*P11 -(B2-B1)'*C'*P12 B2'*P2;Bd'*P11 -Bd'*C'*P12 Bd'*P2;V*C zeros(4) zeros(4)];

R2=[u*eye(4) zeros(4) zeros(4,3);zeros(4) lm*eye(4) zeros(4,3);zeros(3,4) zeros(3,4) o*eye(3)];

%% SDP solve

Sys=[[S1-M1'*R1*M1]<=0];

Sys=[Sys, [S2-M2'*R2*M2]<=0];

Sys=[Sys, P12>=0, P11>=0, P2>=0, lm>=0, u>=0];

opt=sdpsettings('solver','penlab');

yalmipdiagnostics=optimize(Sys)

N1=double(N1);

N2=double(N2);

P11=double(P11);

P12=double(P12);

P2=double(P2);

RR=inv(inv(P12)*N2-C*inv(P11)*N1);

tet=inv(P11)*N1*RR;

E=[eye(4)+tet*C tet;RR*C RR]

Y=inv(E)  

[Johan Löfberg]

penlab has bugs which causes it to stall. This has been reported to the developers but has not been fixed.

All I can suggest is that you tweak various penlab options to see if things improve etc.

BTW, note that your code now generates N1 and N2 as symmetric. I don't think you want that.

http://users.isy.liu.se/johanl/yalmip/pmwiki.php?n=Tutorials.Basics

[Johan Löfberg]

and it doesn't make sense to say LMI when you specifically use penlab as 2 of your constraints aren't LMIs