solve matrix differential equations with ode45

Question

Zicheng Cai 2019-10-2

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回答： Maximilian Behr 2022-12-8

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.

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Zicheng Cai 2019-10-2

编辑：Zicheng Cai 2019-10-3

在 MATLAB Online 中打开

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 2019-10-4

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

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Answer 1

Naveen Shanmuganantham 2020-12-17

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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

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Answer 2

Maximilian Behr 2022-12-8

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/483324-solve-matrix-differential-equations-with-ode45#answer_1123397

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