Solver not applicable (sedumi)

[Ahmad Sheikh]

here is the code to find observer gain

clc
clf;
%................Declare Matrices and constants............................
A = [1 1;
    -1 1];
C=[1 0];
I = eye(2);
row= 0;
alpha=-100;
beta=-99;
gamma= 450.191;
h1=0.05;
h12=0.25;
mu=0;
%L=[0.0038; 0.5];


yalmip('clear')
%........................Declare%variables.................................
P= sdpvar(2);
Q1= sdpvar(2);
Q2= sdpvar(2);
Q3=sdpvar(2);
Z1=sdpvar(2);
Z2=sdpvar(2);
X=sdpvar(2,1);
epsilon1=sdpvar(1);
epsilon2=sdpvar(1);
%gamma=sdpvar(1);
Z1bar= 1./Z1;
Z2bar= 1./Z2;
Pbar= 1./P;
T1= P*Z1bar * P;
T2= P*Z2bar * P;
T1bar= 1./T1;
T2bar= 1./T2;


% .................LMI (26)..................


LMI1 = blkvar();


%1st Row
LMI1(1,1) = A'*P+P*A+Q1+Q2+Q3-Z1+((row)*(epsilon1)*(I))+((beta)*(epsilon2)*(I));                  
LMI1(1,2) = -X*C;
LMI1(1,3) = Z1;                                                  
LMI1(1,4) = 0;
LMI1(1,5) = P-((epsilon1*I)/2)+((alpha*epsilon2*I)/2);
LMI1(1,6) = h1*A'*P;
LMI1(1,7) = h12*A'*P ;


%2nd Row
LMI1(2,2) = -((1-mu)*Q3+2*Z2);                    
LMI1(2,3) = Z2;
LMI1(2,4) = Z2;
LMI1(2,5) = 0;
LMI1(2,6) = -h1*C'*X';      
LMI1(2,7) = -h12*C'*X';


%3rd Row
LMI1(3,3) = -(Q1+Z1+Z2);
LMI1(3,4) = 0;
LMI1(3,5) = 0;
LMI1(3,6) = 0;
LMI1(3,7) = 0;


%4th Row
LMI1(4,4) = -(Q2+Z2);                    
LMI1(4,5) = 0;
LMI1(4,6) = h1*P;
LMI1(4,7) = h12*P;


%5th Row
LMI1(5,5) = -epsilon2*I;                        
LMI1(5,6) =  h1*P;          
LMI1(5,7) =  h12*P;


%6th Row
LMI1(6,6) = -P*Z1bar * P;
LMI1(6,7) = 0;


%7th Row
LMI1(7,7) = -P*Z2bar * P;


lmi1= sdpvar(LMI1);


% .................LMI (31)..................


LMI2 = blkvar();


%1st Row
LMI2(1,1) = A'*P+P*A+Q1+Q2+Q3-Z1+((row)*(epsilon1)*(I))+((beta)*(epsilon2)*(I));                  
LMI2(1,2) = -X*C;
LMI2(1,3) = Z1;                                                  
LMI2(1,4) = 0;
LMI2(1,5) = P-((epsilon1*I)/2)+((alpha*epsilon2*I)/2);
LMI2(1,6) = P;
LMI2(1,7) = I;
LMI2(1,8) = h1*A'*P;
LMI2(1,9) = h12*A'*P ;


%2nd Row
LMI2(2,2) = -((1-mu)*Q3+2*Z2);                    
LMI2(2,3) = Z2;
LMI2(2,4) = Z2;
LMI2(2,5) = 0;
LMI2(2,6) = 0;
LMI2(2,7) = 0;
LMI2(2,8) = -h1*C'*X';      
LMI2(2,9) = -h12*C'*X';


%3rd Row
LMI2(3,3) = -(Q1+Z1+Z2);
LMI2(3,4) = 0;
LMI2(3,5) = 0;
LMI2(3,6) = 0;
LMI2(3,7) = 0;
LMI2(3,8) = 0;
LMI2(3,9) = 0;


%4th Row
LMI2(4,4) = -(Q2+Z2);                    
LMI2(4,5) = 0;
LMI2(4,6) = 0;
LMI2(4,7) = 0;
LMI2(4,8) = 0;
LMI2(4,9) = 0;


%5th Row
LMI2(5,5) = -epsilon2*I;                        
LMI2(5,6) =  0;          
LMI2(5,7) =  0;
LMI2(5,8) =  0;
LMI2(5,9) =  0;


%6th Row
LMI2(6,6) = -gamma*I;
LMI2(6,7) = 0;
LMI2(6,8) = h1*P;
LMI2(6,9) = h12*P;


%7th Row
LMI2(7,7) = -gamma*I;
LMI2(7,8) = h1*P;
LMI2(7,9) = h12*P;


%8th Row
LMI2(8,8) = -P*Z1bar * P;
LMI2(8,8) = 0;


%9th Row
LMI2(9,9) = -P*Z2bar * P;


lmi2= sdpvar(LMI2);




%LMI3 = blkvar();


%LMI3(1,1) = gamma;


%lmi3= sdpvar(LMI3);


%..................... LMI (36)..............
LMI4 = blkvar();


%1st row


LMI4(1,1) = P ;                  
LMI4(1,2) = I;


%2nd row


LMI4(2,2) =  Pbar;


lmi4= sdpvar(LMI4);


%..................... LMI (36) for i=1....................
LMI5 = blkvar();


%1st row


LMI5(1,1) = Z1 ;                  
LMI5(1,2) = I;


%2nd row


LMI5(2,2) =  Z1bar;


lmi5= sdpvar(LMI5);


%..................... LMI (36) for i=2....................
LMI6 = blkvar();


%1st row


LMI6(1,1) = Z2 ;                  
LMI6(1,2) = I;


%2nd row


LMI6(2,2) =  Z2bar;


lmi6= sdpvar(LMI6);


%..................... LMI (37) for i=1....................
LMI7 = blkvar();


%1st row


LMI7(1,1) = T1 ;                  
LMI7(1,2) = I;


%2nd row


LMI7(2,2) =  T1bar;


lmi7= sdpvar(LMI7);


%..................... LMI (37) for i=2....................
LMI8 = blkvar();


%1st row


LMI8(1,1) = T2 ;                  
LMI8(1,2) = I;


%2nd row


LMI8(2,2) =  T2bar;


lmi8= sdpvar(LMI8);


%..................... LMI (39) for i=1....................
LMI9 = blkvar();


%1st row


LMI9(1,1) = Z1bar ;                  
LMI9(1,2) = Pbar;


%2nd row


LMI9(2,2) =  T1bar;


lmi9= sdpvar(LMI9);


%..................... LMI (39) for i=2....................
LMI10 = blkvar();


%1st row


LMI10(1,1) = Z2bar ;                  
LMI10(1,2) = Pbar;


%2nd row


LMI10(2,2) =  T2bar;


lmi10= sdpvar(LMI10);


%..................... LMI (38) for i=1....................


LMI11 = blkvar();


%1st row


LMI11(1,1) = P*Z1bar*P ;                  
LMI11(1,2) = I;


%2nd row


LMI11(2,2) =  T1bar;


lmi11= sdpvar(LMI11);


%..................... LMI (38) for i=2....................


LMI12 = blkvar();


%1st row


LMI12(1,1) = P*Z2bar*P ;                  
LMI12(1,2) = I;


%2nd row


LMI12(2,2) =  T2bar;


lmi12= sdpvar(LMI12);


constraints=[lmi1<0,lmi2<0,lmi4>0,lmi5>0,lmi6>0,lmi7>0,lmi8>0,lmi9>0,lmi10>0, lmi11>0,lmi12>0];
   
options = sdpsettings('solver','sedumi');
sol = solvesdp(constraints,[trace(Z1*Z1bar + 0.5*P*Z1bar*P*T1bar + 0.5*T1*T1bar + Z2*Z2bar + 0.5*P*Z2bar*P*T2bar + 0.5*T2*T2bar+ P*Pbar)], options);




%solution_Y=value(Y);
P=value(P)
X=double(P)
L= inv(P)*X

Enter code here...

but it is giving NaN at the end...!

[Johan Löfberg]

It's not linear, so it makes no sense to think SeDuMi can solve it.

Even worse, it is not bilinear (hard), polynomial (even harder) but involves divisions etc. i.e, a very nasty semidefinite program.

You have to take a step back and reconsider your whole model. You will not be able to solve the problem in the current form. When deriving models, one strives for linear semidefinite programs. Deriving a polynomial or bilinear is sort of a fail, but can have merits if you have clever methods to address it, and there are local nonlinear SDP solver to *try* to solve it. Here, you've failed even worse as you've had to introduce hadamard divisions etc.