How to make the right constraint settings

[yunjiandaiju]

Here's my code.
`clc;
clear;
X=[1 0.5 -0.25;0 1 1];
U=[-1 -1];
X_0=[1 0.5;
0 1];

X_1=[0.5 -0.25;
1 1];
T1=inv(X_0)
X_1T1
K1=UT1
P = sdpvar(2,2,'full');
A=X_0P;
B=X_1P;
LMI1=[A B
B' A]
LMI2=[A-A']
Cons = [LMI1>=0,LMI2==0]
objective = [];
sol = optimize(Cons,objective);
P=double(P)
`
My LMI1 should be a matrix inequality constraint, why am I viewing it as an elemental constraint.

[yunjiandaiju]

clc;
clear;
X=[1 0.5 -0.25;0 1 1];
U=[-1 -1];
X_0=[1 0.5;
     0  1];

X_1=[0.5 -0.25;
      1    1];
T1=inv(X_0)
X_1*T1
K1=U*T1
P = sdpvar(2,2,'full');
A=X_0*P;
B=X_1*P;
LMI1=[A  B
      B' A]
LMI2=[A-A']
Cons = [LMI1>=0,LMI2==0]
objective = [];
sol = optimize(Cons,objective);
P=double(P)

[johanlofberg]

You cannot model it like that. YALMIP will see a non-symmetric costraint in the second constraint and thus interpret as elementwise

However, I am 99% sure you simply try to implement the wrong model, i.e. the derivation of the thing that ends up in (20) is wrong as it almost never looks like that and X_theta would be symmetric by construction if theory done properly

[yunjiandaiju]

But the constraint considers X_*theta=(X_*theta)^T,which considers him symmetric, so the second constraint is also a symmetric matrix.

[yunjiandaiju]

I need to solve for a theta value, the first constraint requires X_*theta to be symmetric, the second is a symmetric constraint, how should I go about defining the constraints, X_ and X+ are known.

[johanlofberg]

You are confusing constraint and solution. The constraint is non-symmetric (and thus not interpreted as an LMI) but you have added an additional constraint asking for the solution to be symmetric. YALMIP analyzes the constraints, not the possible solutions (impossible, as that is for the solver to find)

[a b;b' a]>=0 will be elementwise if a is non-symmetric, and is still so even if you add a == a'. To fool YALMIP, you will have to introduce a new symmetric decision variable z and use the model [z b;b' z]>=0, a == z

But as I said, I think your model is wrong, coming either from a missing symmetric part in some previous Lyapunov reasoning, erroneously trying to apply semidefinite programming to reason about eigenvalues of non-symmetric matrices, or some incorrect application of trying to linearize a quadratic semidefinite constraint. Impossible to say without you revealing where your constraints come from

[johanlofberg]

BTW regardless the model is ill-posed as P=0 would be feasible (if it was a correct model...).

[yunjiandaiju]

Okay, thank you very much for answering my question