How to solve the riccati equations in matlab

Question

hsuan wei pan 2020-8-30

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https://ww2.mathworks.cn/matlabcentral/answers/586373-how-to-solve-the-riccati-equations-in-matlab

评论： hsuan wei pan 2020-9-2

我想設計一個LTR觀察器，但是首先我需要求解類似這樣的黎卡提方程：“ Q *（A + I）'+（A + I）* Q-（Q * C'* C * Q / u）+ pi * G * G'“來獲得” Q“，我已經知道” u“” pi“和” A“” C“” G“向量。有人可以告訴我該怎麼做嗎？謝謝！！

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Answer 1

David Wilson 2020-9-2

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https://ww2.mathworks.cn/matlabcentral/answers/586373-how-to-solve-the-riccati-equations-in-matlab#answer_488285

Well, if Google translate is accurate, you seem to want to solve

for the matrix Q. I'm assuming that everything is a matrix with the appropriate dimensions, and that u is a scalar (going by the way you have written this.)

Now the function are.m, (not care.m, since that has been depreciated), solves

for matrix X. Note that this is in the same form as what you have, but of course you need some "translation" from your nomenclature, to Matlab's. In other words

your nomenclature → Matlab

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hsuan wei pan 2020-9-2

thank you very much , I think i solved the problem!!

this is my code

tf( [9.86e12 7.862e16 1.865e20 1.05e24 8.063e26 3.374e30 2.268e32 3.481e35], [1 7336 5.912e07 2.581e11 1.068e15 2.797e18 6.708e21 1.011e25 1.199e28 6.47e30 1.395e33 5.364e35]);

[a,b,c,d] = tf2ss([9.86e12 7.862e16 1.865e20 1.05e24 8.063e26 3.374e30 2.268e32 3.481e35], [1 7336 5.912e07 2.581e11 1.068e15 2.797e18 6.708e21 1.011e25 1.199e28 6.47e30 1.395e33 5.364e35]);

I = eye(11);

pi = 1000;

u = 1;

A = (a+I)' ;

B = c' ;

C = pi*b*b' ;

[Q] = care(A,B,C);

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