How to find steady state solution of recatti equation

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shahin sharafi 2022-4-16

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评论： shahin sharafi 2022-4-17

采纳的回答： Torsten

在 MATLAB Online 中打开

hi everyone,

I want to find solution of algebric equations as below:

-A_Star'*x-x*A-Q+x*G*x ... where x is the solution of this equation

where A_Star, A Q and G are defined as below:

N=50;
a1=1; a2=1;
tau=1;
A=zeros(N+1,N+1);
A=diag(-N/tau*ones(N+1,1)) + diag(N/tau*ones(N,1),-1);
A(1,1)=a1;
A(1,N+1)=a2;
B=zeros(N+1,1);
B(1)=1;
Q=zeros(N+1,N+1);Q(1,1)=1;
R=1;
W=zeros(N+1,N+1);
W=diag(tau/N*ones(N+1,1));
W(1,1)=1;
G=B*R*B'; 
A_Star=inv(W)*A'*W; 

Thank you in advance for your helps,

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采纳的回答

Torsten 2022-4-16

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https://ww2.mathworks.cn/matlabcentral/answers/1698050-how-to-find-steady-state-solution-of-recatti-equation#answer_944130

If it's a Riccati equation, use "icare" or "idare".

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Torsten 2022-4-16

在 MATLAB Online 中打开

The following code seems to work:

N=50;
a1=1; a2=1;
tau=1;
A=zeros(N+1,N+1);
A=diag(-N/tau*ones(N+1,1)) + diag(N/tau*ones(N,1),-1);
A(1,1)=a1;
A(1,N+1)=a2;
B=zeros(N+1,1);
B(1)=1;
Q=zeros(N+1,N+1);Q(1,1)=1;
R=1;
W=zeros(N+1,N+1);
W=diag(tau/N*ones(N+1,1));
W(1,1)=1;
G=B*R*B';
A_Star=inv(W)*A'*W;
X0 = ones((N+1)^2,1);
X = fsolve(@(X)fun(X,N,A_Star,A,Q,G),X0)
X = reshape(X,N+1,N+1);
norm(-A_Star'*X-X*A-Q+X*G*X)
function res = fun(X,N,A_Star,A,Q,G)
  X = reshape(X,N+1,N+1);
  res = -A_Star'*X-X*A-Q+X*G*X;
  res = res(:);
end