Algebraic Riccati Tensor Equations with Applications in Multilinear Control Systems
张国峰（香港理工大学）
报告时间：2025年9月16日星期二 14：30-15：30
报告地点：沙河主楼E806
报告摘要: In this talk, we study continuous-time Multilinear time invariant (MLTI) control systems, where inputs, states and outputs are all tensors endowed with the Einstein product. We define Hamiltonian tensors and symplectic tensors, and we establish the Schur-Hamilton 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 semi-definite 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.
报告人简介：Guofeng Zhang received his B.Sc. degree and M.Sc. degree from Northeastern University, Shenyang, China, in 1998 and 2000 respectively. He received a Ph.D. degree in Applied Mathematics from the University of Alberta, Edmonton, Canada, in 2005. During 2005–2006, he was a Postdoc Fellow at the University of Windsor, Windsor, Canada. He joined the School of Electronic Engineering of the University of Electronic Science and Technology of China, Chengdu, China, in 2007. From April 2010 to December 2011, he was a Research Fellow at the Australian National University. He is currently a Professor in the Department of Applied Mathematics at the Hong Kong polytechnic University. His research interests include quantum information and control, sampled-data control and nonlinear dynamics.
邀请人：崔春风
