Optimal control for linear discrete-time systems with Markov perturbations in Hilbert spaces. (English) Zbl 1159.93036

Ungureanu, Viorica Mariela

IMA J. Math. Control Inf. 26, No. 1, 105-127 (2009).

Summary: We discuss a quadratic control problem for linear discrete-time systems with Markov perturbations in Hilbert spaces, which is linked to a discrete-time Riccati equation defined on certain infinite-dimensional ordered Banach space. We prove that under stabilizability and stochastic uniform observability conditions, the Riccati equation has a unique, uniformly positive, bounded on \(\mathbb N\) and stabilizing solution. Based on this result, we solve the proposed optimal control problem. An example illustrates the theory.

MSC:

93E20	Optimal stochastic control
49N05	Linear optimal control problems
60J75	Jump processes (MSC2010)
93C05	Linear systems in control theory
93C55	Discrete-time control/observation systems

Keywords:

discrete-time stochastic systems; stochastic observability; Riccati equation; optimal control