I have a problem with the differential Riccati matrix equation in optimal control. As we all know, for a cost function $J = \frac{1}{2}x(t_f)^T S_f x(t_f) + \frac{1}{2} \int_{0}^{t_f}(x^T Q x + u^T R u) dt$ ; if we set Q , $S_f$ are seimi-positive definite, R is positive. Then, the solution of the differential Riccati matrix equation $ -\dot{P} = PA + A^T P - P B R^{-1} B^T P + Q $ should be semi-positive definite. Is there any conditions to guarantee a positive definite solution of above equation.
2026-03-26 21:54:01.1774562041
solution of the differential riccati matrix equation in optimal control
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