Morse Theory and Formation Control

Brian D O Anderson (The Australian National University)

SYSTEMS AND CONTROL SERIES

DATE: 2011-05-13
TIME: 11:00:00 - 12:00:00
LOCATION: RSISE Seminar Room, ground floor, building 115, cnr. North and Daley Roads, ANU
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ABSTRACT:
Formation shape control for a collection of point agents is concerned with devising decentralized control laws which will ensure that the formation will move so that certain inter-agent distances assume prescribed values. A number of algorithms based on steepest descent of an error function have been suggested for various problems, and all display the existence of incorrect equilibria, though often the equilibria are saddle points or unstable. This talk introduces Morse theory as a tool for analyzing the number of such equilibria.

Initially a simpler problem is reviewed: that of navigating a point agent using a steepest descent law to a point in a closed two-dimensional region containing obstacles. A key conclusion is that for both the navigation problem and for the formation shape control problem, there will always be incorrect equilibria associated with any steepest descent law.

BIO:
Brian Anderson is Distinguished Professor at ANU and Distinguished Researcher in NICTA. His research interests are currently in formation control, sensor networks and econometric modelling. His past contributions have been in other areas of control as well as circuit theory, signal processing and telecommunications. He was born in Sydney, and received his undergraduate education at the University of Sydney, with majors in pure mathematics and electrical engineering. He subsequently obtained a PhD degree in electrical engineering from Stanford University. Following completion of his education, he worked in industry in Silicon Valley and served as a faculty member in the Department of Electrical Engineering at Stanford University. He was Professor of Electrical Engineering at the University of Newcastle from 1967 until 1981. He is a Fellow of the IEEE, IFAC, Royal Society London, Australian Academy of Science, Australian Academy of Technological Sciences and Engineering, Honorary Fellow of the Institution of Engineers, and Foreign Associate of the US National Academy of Engineering. He holds honorary doctorates from the Universite Catholique de Louvain in Belgium, Swiss Federal Institute of Technology in Zurich, and the universities of Sydney, Melbourne, New South Wales and Newcastle in Australia. He served as President of the International Federation of Automatic Control from 1990 to 1993 and as President of the Australian Academy of Science between 1998 and 2002. His awards include the IEEE Control Systems Award of 1997, the 2001 IEEE James H Mulligan Jr Education Medal, and the Guillemin-Cauer Award from the IEEE Circuits and Systems Society in 1992 and 2001, the Bode Prize of the IEEE Control Systems Society in 1992, the Senior Prize of the IEEE Transactions on Acoustics, Speech and Signal Processing in 1986, and other best paper awards.

MEDIA:
RSISEMorseTheory.ppt