How to solve a matrix Riccati equation that depends on a nonlinear system?

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

Answer 1

[Matt J]

You can try FSOLVE, but you would need a sufficiently good initial guess.