Indefinite Linear-Quadratic Optimal Control of Mean-Field Stochastic Differential Equation With Jump Diffusion: An Equivalent Cost Functional Method

• 成果类型: Article
• 署名作者: Wang, Guangchen; Wang, Wencan
• 署名单位: Shandong University; Wuhan Textile University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3389559
• 发表日期: 2024
• 页码: 7449-7462
• 关键词: costs; Stochastic processes; optimal control; Riccati equations; PROCESS CONTROL; mathematical models; Diffusion processes; Equivalent cost functional; existence and uniqueness of solution to mean-field forward-backward stochastic differential equation with jump diffusion (MF-FBSDEJ); indefinite MF-LQJ problem; Riccati equation; stochastic Hamiltonian system

摘要

In this article, we consider a linear-quadratic optimal control problem of mean-field stochastic differential equation with jump diffusion, which is also called as an mean-field linear-quadratic problem with jump diffusion (MF-LQJ) problem. Here, cost functional is allowed to be indefinite. We use an equivalent cost functional method to deal with the MF-LQJ problem with indefinite weighting matrices. Some equivalent cost functionals enable us to establish a bridge between indefinite and positive-definite MF-LQJ problems. With such a bridge, solvabilities of stochastic Hamiltonian system and Riccati equations are further characterized. Optimal control of the indefinite MF-LQJ problem is represented as a state feedback via solutions of Riccati equations. As a by-product, the method provides a new way to prove the existence and uniqueness of solution to mean-field forward-backward stochastic differential equation with jump diffusion, where existing methods in literatures do not work. Some examples are provided to illustrate our results.