Solve the Riccati eqn symbolically

Hi folks

I want to solve the Riccati equation symbolically. For example, I have 4 state variables in Q and 2 inputs in R lqr weights.

Q=diag([q11 q22 q33 q44]);
R=diag([r11 r22]);

The Riccati equation is

A'*P+P*A-P*B*(inv( R ))*B'*P+Q=0

A:4x4 matrix , B:4x2 matrix

I want to solve that equation with respect to "P" matrix variable.

In other words, the answer should be like P=(...) and that should contain the variables q11 q22 q33 q44 and r11 r22. Is there anyone who can help? I appreciate all answers,

Thank you

Answer 1

[Walter Roberson]

http://www.mathworks.com/matlabcentral/newsreader/view_thread/65295

[Walter Roberson]

Unfortunately Internet Archive seems to be having difficulty at the moment, so I have not tracked down an alternative source for this.

[Walter Roberson]

Not the link that used to exist, but related topics:

https://www.mathworks.com/matlabcentral/answers/8200-riccati-differential-equation

https://www.mathworks.com/help/symbolic/mupad_ref/ode-solve.html (caution: you cannot use this directly inside of MATLAB; you have to use a MuPAD notebook, or you need to use evalin(symengine)

https://ieeexplore.ieee.org/document/4788881

https://jncf2018.lip6.fr/files/slides/bouzidi.pdf

[Walter Roberson]

It appears that the original link was probably intended to refer to the discussion that can currently be found at https://groups.google.com/forum/m/#!topic/comp.soft-sys.matlab/lteUP95r03E