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Solvability and asymptotic behavior of generalized Riccati equations arising in indefinite stochastic LQ controls. (English) Zbl 0992.93097
Summary: 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 infinite time horizon. Examples are presented to illustrate the results established.
MSC:
93E20Optimal stochastic control (systems)
49N10Linear-quadratic optimal control problems
93C05Linear control systems