Linear quadratic optimal control problems for stochastic evolution equations in infinite horizon.

Lü, Qi

We study linear quadratic optimal control problems for stochastic evolution equations in an infinite horizon with constant coefficients. We first give a characterization of the non-emptiness of the admissible control set for all initial states by an operator-valued algebraic Lyapunov equation. Then we demonstrate the equivalence between the existence of an optimal control with suitable a prori bound and the existence of an optimal feedback control. This stands in contrast to the stochastic linear quadratic optimal control problems in a finite time horizon. Finally, we prove that the optimal feedback control can be determined via a generalized operator-valued algebraic Riccati equation.

STOCHASTIC control theory; ALGEBRAIC equations; RICCATI equation; EVOLUTION equations; ADMISSIBLE sets

Mathematical Control & Related Fields, 2024, Vol 14, Issue 4, p1

2156-8472

Academic Journal

10.3934/mcrf.2024017