Formations of mobile agents, including unmanned airborne vehicles, may often be used to localize objects in the environment, and many control problems arise. For example, often, such formations should take up a particular shape. What needs to be measured and what needs to be controlled to maintain a prescribed shape? Can control be distributed, i.e. can one arrange for each agent just to observe its neighbors and act appropriately, and yet have the whole formation behave correctly? How can a desired shape be established? What is the effect of noise distorting the measurements? How can an entire formation shape be preserved while the formation translates from A to B? The resolution of these questions draws ideas from diverse mathematical subfields, including graph theory, dynamical systems, Riemannian manifolds and Morse theory. The lecture will illustrate a number of these problems, particularly the mathematical tools involved in resolving them.

 

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 in 1966.  Following graduation, he joined the faculty at Stanford University and worked as Vidar Corporation of Mountain View, California, as staff consultant. He then returned to Australia to become department chair in electrical engineering at the University of Newcastle. He moved to the Australian National University in 1982, as the first engineering professor at that university. He is now Emeritus Professor at the Australian National University, Distinguished Professor in Hangzhou Dianzi University and Distinguished Researcher in Data61-CSIRO, formerly NICTA. During his period in academia, he spent significant time working for the Australian Government, with this service including membership of the Prime Minister’s Science Council under the chairmanship of three prime ministers. He also served on advisory boards or boards of various companies, including the world’s major supplier of cochlear implants,  Cochlear Corporation, where he was a director for ten years. His awards include the IFAC Quazza Medal in 1999, 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 IEEE and other best paper prizes, including Automatica. He is a Fellow of the Australian Academy of Science, Australian Academy of Technological Sciences and Engineering,  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 was IFAC President from 1990 to 1993, having served earlier in various IFAC roles, including Editor of Automatica. He was President of the Australian Academy of Science from 1998 to 2002. His current research interests are in distributed control, sensor networks and econometric modelling.