题目：Pareto Optimality in Infinite Horizon Mean-Field Stochastic Cooperative Linear-Quadratic Difference Games

报告人：张维海，教授，山东科技大学

时间： 2025年11月9日

线下方式：信息与通信工程学院319，13:30-14:30

线上方式：腾讯会议，958-646-929

报告摘要

This talk is concerned with the mean-field stochastic cooperative linear quadratic (LQ) dynamic difference game in an infinite time horizon. First, the necessary and sufficient conditions for the stability in the mean-square sense, and the stochastic Popov-Belevith-Hautus (PBH) eigenvector tests for exact observability and exact detectability of mean-field stochastic linear difference systems are derived by the H-representation technique. Second, the relation between the solvability of the cross-coupled generalized Lyapunov equations (CC-GLEs) and exact observability, exact detectability, and stability of the mean-field dynamic system is well characterized. It is then shown that the cross-coupled algebraic Riccati equations (CC-ARES) admit a unique positive definite (positive semi-definite, respectively) solution under exact observability (exact detectability, respectively), which is also a feedback stabilizing solution. Furthermore, all Pareto optimal strategies and solutions can be respectively derived via the solutions to the weighted CC-ARES (WCC-AREs) and the weighted cross-coupled algebraic Lyapunov equations (WCC-ALEs). Finally, a practical application on the computation offloading in the multi-access edge computing network MECN) is presented to illustrate the proposed theoretical results.

报告人简介

张维海，山东科技大学电气与自动化工程学院二级教授、博导，两个聘期的山东省“泰山学者”特聘教授。主要研究领域为随机控制、鲁棒控制、模糊控制，强化学习。主持和承担国家自然科学基金重点项目、面上项目、省自然科学基金重点项目等省部级以上项目10多项，发表SCI期刊论文200余篇，在CRC和Springer出版社出版英文专著2部。连续2年入选全球前2%顶尖科学家“终身科学影响力排行榜”榜单(2021年，2022 年)。获教育部自然科学二等奖2项(首位)和山东省自然科学二等奖2项(首位)、山东省高等学校优秀科研成果奖一等奖2项。作为指导教师获得山东省优秀博士学位论文6篇，山东省优秀研究生科技创新成果一等奖1项。当选山东省有突出贡献的中青年专家、山东省第三届优秀研究生指导教师和青岛市拔尖人才。目前是中国自动化学会控制理论专业委员会委员、信息物理系统专业委员会委员，中国工业与应用数学学会系统与控制专委会副主任委员，山东省自动化学会常务理事，IEE高级会员。