题目：Morse Theory and its Application to Optimisation and Stabilisation

时间：2023年8月22日14:00-15:00（北京时间）

报告人：Prof. Brian D. O. Anderson, Australian National University

主持人：Prof. Qing-Long Han, Swinburne University of Technology

Zoom Meeting ID：873 9385 4523

The seminar introduces a 1930s development termed Morse theory, which can initially be seen as a tool for obtaining insight into the nature of the extrema (critical points) of a scalar function. The theory can sometimes establish uniqueness of a minimum before that minimum is even found, and without a requirement for convexity of the function. Simple concepts of Morse theory are introduced, illustrated by applications to the detection of a nuclear particle emitter, and the optimization of the realization of a controller in a sampled-data control system. The use of Morse theory for studying differential equations and establishing their stability is then illustrated, with applications to the movement of robots in a sphere world under a potential field, and the nature of equilibria of formation shape control problems.

Brian D. O. Anderson was born in Sydney, Australia, and educated at Sydney University in mathematics and electrical engineering, with PhD in electrical engineering from Stanford University. He was appointed as the first engineering professor at the Australian National University in 1981, retired as Distinguished Professor in 2016, and is now an Emeritus Professor. His awards include the IFAC Quazza Medal of 1999, the IEEE Control Systems Award of 1997, the 2001 IEEE James H Mulligan, Jr Education Medal, and the Bode Prize of the IEEE Control System Society in 1992, as well as several IEEE and other best paper prizes. He is a Fellow of the Australian Academy of Science, the Australian Academy of Technological Sciences and Engineering, the Royal Society, and a foreign member of the US National Academy of Engineering. He holds honorary doctorates from a number of universities, including Université Catholique de Louvain, Belgium, and ETH, Zürich and is an honorary professor of Zheijiang University, Harbin Institute of Technology and Shandong University. He is a past president of the International Federation of Automatic Control and the Australian Academy of Science. His current research interests are in distributed control and localization, nonlinear control, and social networks and econometric modelling. He also served as a director on company boards, including the world’s major supplier of cochlear implants, Cochlear Ltd, and as an advisor to government, including membership of the Prime Minister’s Science Council under three prime ministers. He holds national awards from both Japan and Australia.