How can I solve the Riccati equation with a variable?

I have the fixed value of A,B,Q and a variable R. How can I determine the solution of the Riccati equation P as a function of r？

A=[0 1 0;0 0 1;0 0 0];
B=[0;0;0];
Q=[1 0 0;0 0 0;0 0 0];
R=r;
eqn= A'*P+P*A+Q-P*B*R^(-1)*B'*P==0

Answer 1

[Jaynik]

Hi @senhan yao,

For determining the solution of the Riccati equation, you can use the "care" or "icare" function from the "Control System Toolbox". These functions are used to compute unique solution for the given equation.

As per the documentation, starting in R2019a, it is recommended to use the "icare" function to solve the equation as it has improved accuracy through better scaling. Here is a sample code you can refer:

A = [0 1 0; 0 0 1; 0 0 0];
B = [0; 0; 0];
Q = [1 0 0; 0 0 0; 0 0 0];
R = r;

% Solving the Riccati equation using care
[P1, ~, ~] = care(A, B, Q, R);

% Solving the Riccati equation using icare
[P2,~,~,info] = icare(A, B, Q, R);

You can refer the following documentation to know more about each functions:

• care: https://www.mathworks.com/help/control/ref/care.html
• icare: https://in.mathworks.com/help/control/ref/icare.html