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

被引：0
作者：
Wang, Guangchen [1 ]
Wang, Wencan [1 ,2 ]
机构：
[1] Shandong Univ, Sch Control Sci & Engn, Jinan 250061, Peoples R China
[2] Wuhan Text Univ, Sch Math & Phys Sci, Wuhan 430200, Peoples R China
来源：
IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2024年 / 69卷 / 11期
基金：
国家重点研发计划; 中国国家自然科学基金;
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; LIABILITY MANAGEMENT; MAXIMUM PRINCIPLE; REGULATORS; ASSET;
D O I：
10.1109/TAC.2024.3389559
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
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.
引用
收藏
页码：7449 / 7462
页数：14
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