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Math Help - Optimal Control Theory: About the Riccati Dfiferential Equation

  1. #1
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    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.
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  2. #2
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    Can you tell me what does semdefinite means in this context?

    I know what positive definite matrix means.
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  3. #3
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    A positive-semidefinite matrix is a matrix positive one but also with the equality. That is, x' M x \geq 0.
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