Help with Riccati equation
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% 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((
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