How to solve a matrix Riccati equation that depends on a nonlinear system?
2 views (last 30 days)
Show older comments
Regarding the resolution of the matrix Riccati equation, the problem does not arise if the Jacobian matrice 'A' contain constants (for exemple):
A=[-27,6,-3,9; 2,-6,-2,-6; -5,0,-5,-2; 10,3,4,-11];
B=[0,3; 16,4; -7,4; 9,6];
Q=[6,5,3,4; 5,6,3,4; 3,3,6,2; 4,4,2,6]; R=[4,1; 1,5];
C=Q; B1=B*inv(R)*B'; P=are(A,B1,C),
norm(P*A+A'*P-P*B*inv(R)*B'*P+Q)
But if this same Jacobian matrice result of a nonlinear system with respect to state variables x, y and z. Thus, this matrice will depend of these variables: for exemple, the matrix 'A' will contain constants and also variables: A=[-27x,6,-3y,9; 2,-6,-2,-6; -5,0,-5z,-2; 10,3,4z,-11]
which makes the resolution the matrix Riccati equation difficult.
Magdalin
0 Comments
Answers (1)
Matt J
on 30 Dec 2014
You can try FSOLVE, but you would need a sufficiently good initial guess.
0 Comments
See Also
Categories
Find more on Matrix Computations in Help Center and File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!