# Optimal Control Theory: About the Riccati Dfiferential Equation

• June 27th 2010, 02:36 AM
russel
Optimal Control Theory: About the Riccati Dfiferential Equation
Hello there,
I have a problem on optimal control theory which has to do with the Riccati Equation:
$\dot{P}=-PA-A'P+PBR^{-1}B'P-Q, P(T)=F$
where $Q,R$ are symmetric.
The problem asks to show that the solution matrix of the Riccati equation is positive-semidefinite given that $F,Q \ge 0, R>0$.
• June 28th 2010, 11:22 AM
InvisibleMan
Can you tell me what does semdefinite means in this context?

I know what positive definite matrix means.
• June 28th 2010, 01:04 PM
russel
A positive-semidefinite matrix is a matrix positive one but also with the equality. That is, $x' M x \geq 0$.