Distinguished ICON Seminar by Prof. Brian D. O. Anderson (ANU)

Title: Extrema without Convexity (and Stability without Lyapunov)

Time & Location:  1:00pm-3:00pm at ARMS 1010 with Zoom https://purdue-edu.zoom.us/j/98158458681

Agenda: Afternoon Coffee (1:00-1:30pm), Seminar (1:30-2:30pm), Q&A(2:30-3:00pm)

Abstract:  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 of a variable x which may live in an arbitrary n-dimensional manifold. Under some circumstances, the theory can establish uniqueness of a minimum before that minimum is even found. 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, and the nature of equilibria of formation shape control problems.

Bio: 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 is an Emeritus Professor at the Australian National University (having retired as Distinguished Professor in 2016), having been appointed as ANU’s first engineering professor in 1981. His awards include 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 was a recipient of the IFAC Quazza Medal in 1999. He is a Fellow of the Australian Academy of Science, the Australian Academy of Technological Sciences and Engineering, the Royal Society (London), 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. 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, epidemic modelling, social networks and econometric modelling. He also served as a director on company boards, including the world’s largest supplier of implantable hearing devices, Cochlear Ltd, and as an advisor to government, including membership of the Prime Minister’s Science Council under three prime ministers.

Recording: https://youtu.be/Z2QDV5KpqKQ