How to solve a Riccati Control (differential) Equation?
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Hi everyone! First time writing in this forum :)
My problem is that I have to solve the Riccati Control Equation, of the form:
dS/dt = -A' S -S A - Q + S G S
where A' is the transpose. A, S, Q and G are real matrices in R^(N x N). I need the steady state solution of this equation (within a real time simulink scheme, but this for now is not necessary).
Should I use a ODE solver? But how i define the function with matrices? and what about the timespan?
Thank you for your help!
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Answers (2)
Giovanni Mottola
on 4 Oct 2016
You don't need to solve a differential equation. "Steady-state" means the solution (here, the matrix S) remains constant, which means that the derivative is zero. Substituting dS/dt=0 in your equation we get:
0= -A' S -S A - Q + S G S
which is an algebraic problem (no derivatives involved) in N x N equations and N x N unknowns.
This can be solved directly. You may define a function func.m as follows:
function diff = func( A, Q, G, x )
diff = A.'*x+x*a+Q-x*G*x;
end
Then from the command window define your initial guess x0 and call:
fsolve(@(x) func(A, Q, G, x), x0)
The alternative would be to use the "care" command ( http://it.mathworks.com/help/control/ref/care.html ), but you first have to find the vector B such that B*B.'=G.
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jalal khodaparast
on 23 Oct 2019
I want to solve a complex differential Riccati equation numerically. I used ODE45 and ODE15s but The solution has unstable oscillation.
How can I solve a differential Riccati equation with complex values?
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