【Abstract】 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.

【Bio】Prof. Brian D. O. ANDERSON is currently Distinguished Professor (Professor since 1981) of The Australian National University and Distinguished Researcher NICTA (President, 2002-3, Chief Scientist 2003-6).  He got his BSc in 1962 and BE in 1964in Sydney and PhD in Elec Eng Stanford in 1966.   He is a member of Australian Academy of Science (Fellow-1974), Institute of Electrical and Electronics Engineers (Fellow-1975, Life Fellow 2007), Australian Academy of Technological Sciences and Engineering (Fellow-1980), Institution of Engineers, Australia (Honorary Fellow-1985). Royal Society, London (Fellow-1989), National Academy of Engineering, USA (Foreign Member-2002), and International Federation of Automatic Control (Fellow – 2005).   He was Officer of the Order of Australia, 1993 and got Centenary Medal, Government of Australia 2001.   He also held many visiting professorships at leading international universities, including Stanford, Berkeley, Kyoto, Imperial College, ETH. and consult in a wide variety of companies in Australia and abroad.  Moreover, he serves on numerous government committees and boards related to science and technology, and participation in and leadership of government enquiries.  Particularly, he was the President of International Federation of Automatic Control (1990-1993), and Australian Academy of Science (1998-2002).   He got many prizes and awards, including Flinders Lectureship and Medal, Australian Academy of Science, 1992, Guillemin-Cauer Award, IEEE Circuits and Systems Society, 1992, IEEE Control Systems Society Bode Prize, 1992, International Award of Society for Materials Engineering for Resources of Japan, 1994, Life Adviser, International Federation of Automatic Control, 1996, IEEE Control Systems Award, 1997, Quazza Medal, IFAC, 1999, Best Paper Prize, Automatica, 1999,  Distinguished Lecturer, IEEE Control Systems Society, 2001, IEEE James H Mulligan Jr Education Medal, 2001, and Guillemin-Cauer Award, IEEE Circuits and Systems Society, 2001.   He has published 10 books and approximately 1100 papers, and over the five year period 2010-2014, published 50 journal articles, 8 book chapters and 83 conference papers.  His h-index (Google Scholar Citations) is 82.