活动时间：2025-11-25 15:30

活动地点：绅士漫画 2432报告厅

主讲人：魏益民

主讲人简介：

魏益民，男，教授，博士生导师。复旦大学数学科学绅士漫画 教授，从事矩阵计算的理论和应用研究二十余年。1997年在复旦大学数学研究所获得理学博士学位，是上海市应用数学重点实验室的研究人员，曾获得上海市高校优秀青年教师和上海市“曙光”学者称号；获得上海市自然科学二等奖、三等奖各一项。在国际学术期刊《Math. Comput.》,《SIAM J. Sci. Comput.》,《SIAM J. Numer Anal.》, 《SIAM J. Matrix Anal. Appl.》,《J. Sci. Comput.》,《IEEE Trans. Auto. Control》,《IEEE Trans.Neural Network Learn. System》, 《Neurocomputing》和《Neural Computation》 等发表论文150余篇; 在EDP Science, Elsevier, Springer, World Scientific和科学出版社等出版英语专著5本。10次入选爱思唯尔“中国高被引学者”榜单。Google学术引用12000余次，H 指数 55。魏益民曾主持国家自然科学基金、教育部博士点基金项目和973项目的子课题；目前正主持国家自然科学基金项目，担任国际学术期刊《Computational and Applied Mathematics》、《Journal of Applied Mathematics and Computing》、《FILOMAT》、《Communications in Mathematical Research》和《高校计算数学学报》的编委。

内容摘要：

In a recent paper by Chen et al. [SIAM J. Control Optim., 59 (2021), pp. 749--776], the authors initiated the control-theoretic study of a class of discrete-time multilinear time-invariant (MLTI) control systems, where system states, inputs, and outputs are all tensors endowed with the Einstein product. They established criteria for fundamental system-theoretic notions such as stability, reachability, and observability through tensor decomposition. Building on this new research direction, the purpose of our paper is to extend the study to continuous-time MLTI control systems. Specifically, we define Hamiltonian tensors and symplectic tensors, and we establish the Schur-Hamiltonian tensor decomposition and the symplectic tensor singular value decomposition (SVD). Based on these concepts, we propose the algebraic Riccati tensor equation (ARTE) and demonstrate that it has a unique positive semidefinite solution if the system is stabilizable and detectable. To find numerical solutions to the ARTE, we introduce a tensor-based Newton method. Additionally, we establish the tensor versions of the bounded real lemma and the small gain theorem. A first-order robustness analysis of the ARTE is also conducted. Finally, we provide a numerical example to illustrate the proposed theory and algorithms.

主持人：秦玉明