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Solvability and asymptotic behavior of generalized Riccati equations arising in indefinite stochastic LQ controls

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4 Author(s)
Ait Rami, M. ; Dept. of Syst. Eng. & Eng. Manage., Chinese Univ. of Hong Kong, Shatin, China ; Xi Chen ; Moore, J.B. ; Xun Yu Zhou

The optimal control problem in a finite time horizon with an indefinite quadratic cost function for a linear system subject to multiplicative noise on both the state and control can be solved via a constrained matrix differential Riccati equation. In this paper, we provide general necessary and sufficient conditions for the solvability of this generalized differential Riccati equation. Furthermore, its asymptotic behavior is investigated along with its connection to the generalized algebraic Riccati equation associated with the linear quadratic control problem in finite time horizon. Examples are presented to illustrate the results established

Published in:

Automatic Control, IEEE Transactions on  (Volume:46 ,  Issue: 3 )

Date of Publication:

Mar 2001

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