Solve long matrices equation
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Hello,
please I would like help to solve this equation with matlab ( you can see it in the screenshot). I want to find the matrix P11. All other matrices in the equation are known.
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Answers (2)
cui,xingxing
on 4 May 2024
From your screenshot formulas, you should first prioritize the formulas Manipulation and Simplification, and then try to solve the analytical solution using some of the functions of the Symbolic Math Toolbox™, and if the analytical solution doesn't exist theoretically, you should try to get a numerical solution, which is valuable in a lot of engineering. Secondly, based on your equation, which is in matrix expression form, you should do a specific analysis based on your specific application context to simplify your process.
Finally, see the following link for generalities about the functionality of solving with the Symbolic Math Toolbox™:
John D'Errico
on 4 May 2024
Edited: John D'Errico
on 4 May 2024
This is a classic algebraic Ricatti equation.
How do you solve it in MATLAB? It looks like the care function does that, which is now obsolete, and superceeded by icare. (I hope they never have to come up with a name to supercede icare. What would they use? Maybe ycare? Ok, I know, who cares?)
help icare
As you can see, it handles exactly your problem. Just plug in your matrices. You would have something like this:
Q = 0
S = B
G = 0
X = P11
E = I
A = 2*A
I think I got them right, but it would be worth a quick check, as the form in icare does not have B factored out and paired with R^-1.
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