Optimal control for linear discrete-time systems with Markov perturbations in Hilbert spaces

Ungureanu, Viorica Mariela

doi:10.1093/imamci/dnp001

Cited by 11 publications

(32 citation statements)

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“…The main results of this paper extend the known ones from and provide useful tools for the study of infinite horizon stochastic/nonstochastic optimal control problems with definite/indefinite quadratic cost functionals in both finite and infinite dimensional cases. For example, these results can be used to obtain the infinite dimensional counterpart of the ones in , where, depending upon the class of admissible controls, the corresponding optimal LQ control was obtained with the minimal solution of the associated DTSREs or with the maximal and stabilizing solutions.…”

Section: Introductionsupporting

confidence: 57%

“…As in and , we associate with and the following DTSRE of control (DTSRE‐C) where

E_{i} MathClass-punc: l_{{scriptE}_{H}}^{Z} MathClass-rel\to E_{H} MathClass-punc,

…”

Section: Statement Of the Problem And Motivationmentioning

confidence: 99%

“…discrete‐time systems of Riccati equations (DTSREs) play an important role in the mathematical theory of control. The subject is fully developed with a vast literature especially in the finite dimensional case (see, e.g., . Recently, there was a revival of the study of DTSREs, due in particular to the great development of stochastic control and stochastic game theories.…”

Section: Introductionmentioning

confidence: 99%

“…The DTSREs associated with the optimal control problem for such discrete‐time infinite MJLSs are infinite dimensional, whether the state space of the system is finite dimensional or not. An example can be found in , where the DTSREs are defined on ordered Banach spaces formed by sequences of linear and bounded operators. More complicated DTSREs occur when the MJLSs are also affected by multiplicative noise (see for finite dimensional case).…”

Section: Introductionmentioning

confidence: 99%

“…In fact, each of these nonlinear equations is a system of interconnected Riccati equations, which we call generalized discrete‐time system of Riccati equations or GDTSRE for short. So, many of the DTSREs from can be treated as special cases of GDTSREs. On the other hand, outside the class of GDTSREs we have proposed, there are DTSREs whose properties can also be studied via GDTSREs.…”

Section: Introductionmentioning

confidence: 99%

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Global solutions of a class of discrete‐time backward nonlinear equations on ordered Banach spaces with applications to Riccati equations of stochastic control

Ungureanu

Drăgan

Morozan

2012

Optim Control Appl Methods

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SUMMARYIn this paper, we consider the problem of existence of certain global solutions for general discrete-time backward nonlinear equations, defined on infinite dimensional ordered Banach spaces. This class of nonlinear equations includes as special cases many of the discrete-time Riccati equations arising both in deterministic and stochastic optimal control problems. On the basis of a linear matrix inequalities approach, we give necessary and sufficient conditions for the existence of maximal, stabilizing, and minimal solutions of the considered discrete-time backward nonlinear equations. As an application, we discuss the existence of stabilizing solutions for discrete-time Riccati equations of stochastic control and filtering on Hilbert spaces. The tools provided by this paper show that a wide class of nonlinear equations can be treated in a uniform manner.

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Section: Introductionsupporting

confidence: 57%

“…As in and , we associate with and the following DTSRE of control (DTSRE‐C) where