solve matrix differential equations with ode45

I want to use ode to solve for a riccati differential equation. But it seems that it cannot be implemented directly in MATLAB.

is a known matrix. I want to get the S matrix at t by integrating backward in time.

[darova]

Show us your ideas or some attempts?

[Zicheng Cai]

I unrolled the matrix and made it one vector to solve it. I also need to write a separate function to calculate and return the derivatives in a vector.

This is the function I defined to get derivates in a vector form.

function ds=deriv(t,S,A,B,Q_f,Q,R)
% adjust dimension and return S in a vector
Fs=reshape(S,size(Q_f)); % reshape S into matrix form
Rinv=inv(R);
dsv=-Q+Fs*B*Rinv*B'*Fs-Fs*A - A'*Fs; % derivation of S in matrix form
ds=dsv(:);% unroll the matrix to return a vector
end

This reference

https://www.mathworks.com/matlabcentral/answers/331107-how-can-i-solve-a-matrix-differential-equation-within-matlab

is of great help

[darova]

So what do you need help with? oder function looks ok as for me

Answer 1

[Naveen Shanmuganantham]

I understand that you want to solve for a riccati differential equation in MATLAB.

The "CARE" function within the Control System Toolbox solves the matrix Riccati equation.

The following MATLAB Answers link will help you in solving the matrix Riccati differential equation within MATLAB,

https://www.mathworks.com/matlabcentral/answers/94722-how-can-i-solve-the-matrix-riccati-differential-equation-within-matlab

Answer 2

[Maximilian Behr]

The repo https://zenodo.org/record/4460618#.Yt6LGsHP2de contains a solver (Modified Davison-Maki method) to solve the differential Riccati with MATLAB.