Hello there,

I have a problem on optimal control theory which has to do with the Riccati Equation:

$\displaystyle \dot{P}=-PA-A'P+PBR^{-1}B'P-Q, P(T)=F$

where $\displaystyle Q,R$ are symmetric.

The problem asks to show that the solution matrix of the Riccati equation is positive-semidefinite given that $\displaystyle F,Q \ge 0, R>0$.