講座主題：Pareto Optimality in Infinite Horizon Mean-Field Stochastic Cooperative Linear-Quadratic Difference Games
專家姓名：張維海
工作單位：山東科技大學(xué)自動(dòng)化學(xué)院
講座時(shí)間：2023年3月25日 8:00-8:45
講座地點(diǎn)：數(shù)學(xué)院三樓大會(huì)議室 (騰訊會(huì)議846-534-645)
主辦單位：煙臺(tái)大學(xué)數(shù)學(xué)與信息科學(xué)學(xué)院
內(nèi)容摘要：
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.
主講人介紹：
張維海，山東科技大學(xué)電氣與自動(dòng)化工程學(xué)院二級(jí)教授、博導(dǎo),，兩個(gè)聘期的山東省“泰山學(xué)者” 特聘教授,。主要研究領(lǐng)域?yàn)殡S機(jī)控制、魯棒控制,、模糊控制,，強(qiáng)化學(xué)習(xí)。主持和承擔(dān)國(guó)家自然科學(xué)基金重點(diǎn)項(xiàng)目,、面上項(xiàng)目,、省自然科學(xué)基金重點(diǎn)項(xiàng)目等省部級(jí)以上項(xiàng)目10多項(xiàng)，發(fā)表SCI 期刊論文200余篇,，在CRC和Springer出版社出版英文專著2部,。連續(xù)2年入選全球前 2% 頂尖科學(xué)家“終身科學(xué)影響力排行榜”榜單（2021年，2022年）,。獲教育部自然科學(xué)二等獎(jiǎng)2項(xiàng)（首位）和山東省自然科學(xué)二等獎(jiǎng)2項(xiàng)（首位）,、山東省高等學(xué)校優(yōu)秀科研成果獎(jiǎng)一等獎(jiǎng)2項(xiàng)。作為指導(dǎo)教師獲得山東省優(yōu)秀博士學(xué)位論文6篇,，山東省優(yōu)秀研究生科技創(chuàng)新成果一等獎(jiǎng)1項(xiàng),。當(dāng)選山東省有突出貢獻(xiàn)的中青年專家、山東省第三屆優(yōu)秀研究生指導(dǎo)教師和青島市拔尖人才,。目前是中國(guó)自動(dòng)化學(xué)會(huì)控制理論專業(yè)委員會(huì)委員,、信息物理系統(tǒng)專業(yè)委員會(huì)委員，中國(guó)工業(yè)與應(yīng)用數(shù)學(xué)學(xué)會(huì)系統(tǒng)與控制專委會(huì)副主任委員,，山東省自動(dòng)化學(xué)會(huì)常務(wù)理事,，IEEE 高級(jí)會(huì)員。
