Criterion for the convergence of the solution of the Riccati differential equation

“…Moreover, there is a unique optimal control with the following feedback form: (10) Furthermore, the value function is given by (11) Proof: This result is proved in [11,Th. 3.2] for the case when .…”

Section: Theorem 22mentioning

confidence: 89%

“…Although some open problems still remain [23], the asymptotic theory has been well established [26], [10]. However, the indefinite stochastic LQ case remains unexplored.…”

mentioning

confidence: 99%

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

Rami

Chen

Moore

et al. 2001

IEEE Trans. Automat. Contr.

143

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Abstract-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.Index Terms-Asymptotic analysis, generalized Riccati equation, indefinite stochastic linear quadratic (LQ) control, linear matrix inequality, solvability.

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“…It is shown in [10] that since fF 22 ; H 2 g is observable and fF 22 ; G 2 g has no unreachable modes on the j!-axis, P220(t) converges to P max 22 , and thus P 220 (t) converges to P max 22 . Now, we shall prove (11).…”

mentioning

confidence: 99%