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- Title
Linear quadratic optimal control problems for stochastic evolution equations in infinite horizon.
- Authors
Lü, Qi
- Abstract
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.
- Subjects
STOCHASTIC control theory; ALGEBRAIC equations; RICCATI equation; EVOLUTION equations; ADMISSIBLE sets
- Publication
Mathematical Control & Related Fields, 2024, Vol 14, Issue 4, p1
- ISSN
2156-8472
- Publication type
Academic Journal
- DOI
10.3934/mcrf.2024017