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Solving Matrix Riccati
Posted:
Apr 5, 2013 7:20 PM


I'm new to MATLAB and trying to use ODE45 to find the coefficients of the matrix Riccati equation for a controls problem.
I'm not sure what I'm doing wrong.
I've defined my Riccati equation in a function 'regulator'
%Define matrices function dS=regulator(t,S)
A=[0 1;0 2.972]; B=[0;390]; Q=[(1/(pi^2)) 0;0 30]; R=1;
dS=1*(A'*S+S*AS*B*(R^1)*B'*S+Q);
end
Then I'm just going straight to ODE45, doing something like this:
[t,S]=ode45('regulator',[0 5],[0 0;0 0])
looking for a solution to matrix S.
Can I solve like this or do I have to multiply out all the terms of S? Assuming S is
S = [s11(t) s12(t) ; s12(t) s22(t)];
Any help would be appreciated.



