Hybrid optimal impulse control

Lv，Siyu1; Xiong，Jie2

2022-06-01

10.1016/j.automatica.2022.110233

AUTOMATICA   影响因子和分区

0005-1098

This paper is concerned with an optimal impulse control problem under a hybrid diffusion (or, regime switching) model, where the state of the system consists of a number of diffusions coupled by a continuous-time finite-state Markov chain. The objective is to minimize the expected discounted cost from exerting the impulse control in the infinite horizon. Based on the dynamic programming principle (DPP), the value function of the hybrid optimal impulse control problem is shown to be the unique viscosity solution to the associated Hamilton–Jacobi–Bellman (HJB) equation, which is in the form of a coupled system of variational inequalities. Moreover, a verification theorem as the sufficient condition for optimality of a solution is also established. The optimal impulse control, indicates when and how it is optimal to intervene, is described by the obstacle part of the HJB equation. Finally, the general theoretical results are applied to an optimal cash management problem. The value function in closed-form and an explicit optimal policy are obtained, which exhibit clearly the effect of regime switching on the agent's decision.

HJB equation Markov chain Optimal impulse control Verification theorem Viscosity solution

EI

英语

其他

National Natural Science Foundation of China[11801072];National Natural Science Foundation of China[11831010];National Natural Science Foundation of China[11971267];Fundamental Research Funds for the Central Universities[2242021R41175];National Natural Science Foundation of China[61873325];Natural Science Foundation of Jiangsu Province[BK20180354];Southern University of Science and Technology[Y01286120];

20221311851526

Dynamic programming ; Markov processes ; Variational techniques ; Viscosity

Fluid Flow, General:631.1 ; Calculus:921.2 ; Optimization Techniques:921.5 ; Probability Theory:922.1 ; Physical Properties of Gases, Liquids and Solids:931.2 ; Systems Science:961

ENGINEERING

2-s2.0-85126978710

Scopus

1.School of Mathematics,Southeast University,Nanjing,211189,China
2.Department of Mathematics and National Center for Applied Mathematics (Shenzhen),Southern University of Science and Technology,Shenzhen,518055,China

Lv，Siyu,Xiong，Jie. Hybrid optimal impulse control[J]. AUTOMATICA,2022,140.

Lv，Siyu,&Xiong，Jie.(2022).Hybrid optimal impulse control.AUTOMATICA,140.

Lv，Siyu,et al."Hybrid optimal impulse control".AUTOMATICA 140(2022).