I need to solve this problem as per screenshot below
The objective is to find the matrices P(k) and Y(k) for k=0,1,2,… N-1 such as the constraints are satisfied. (niu and rho are selected by me depending on the desired accuracy). Since those matrices are time varying, I tried to solve the problem in a loop in this way.
for i = 1:N
X_2 = [x1(:,i+1) x2(:,i+1) x3(:,i+1)];
X_1 = [x1(:,i) x2(:,i) x3(:,i)];
[P(:,:,i+1)-eye(n), X_2*Y(:,:,i); Y(:,:,i)'*X_2', P(:,:,i)] == semidefinite(2*n); X_1*Y(:,:,i) == P(:,:,i); P(:,:,i) - niu*eye(n) >= 0; P(:,:,i) - rho*eye(n) <= 0;
However, the code seems not to work and I can’t get a feasible solution. Is it due to the code or more like the model? Because I don’t seem to find a problem.
Thank you in advance