Help with Riccati equation

Question

Mikle Frolov 2023-5-29

评论： Mikle Frolov 2023-6-1

% Define the Riccati equation and initial conditions

A = [0 1; -1 0]; Q = [1 0; 0 1]; R = 1; P0 = [1 0; 0 1];

% Determine the integral manifold

[V,D] = eig(Q);

M = V * sqrt(inv(D));

% Define the ODE function for numerical integration

f = @(t,P) -A' * P - P * A + P * B * inv(R) * B' * P + Q;

% Solve the ODE on the manifold

[t,P] = ode45(@(t,P) M \ f(t,M * P * M') * M', [0 10], M * P0 * M');

% Plot the solution trajectory on the manifold

plot(P(:,1,1), P(:,2,2));

xlabel('P_{11}');

ylabel('P_{22}');

title('Solution Trajectory on Manifold');

matlab complains about ode45 but I can’t figure out the reason for 2 days already((

Answer 1

Alan Stevens 2023-5-29

You haven't defined B (in the function definition)

Mikle Frolov 2023-6-1

Thank you for the answer it halped a lot