May 21, 2010, 1100 Webb

An observed nonlinear dynamics is observable if the mapping from initial condition to output trajectory is one to one. The standard tool for checking observability is the observability rank condition but this only gives a yes or no answer. It does not measure how observable or unobservable the system is. Moreover it requires the ability to differentiate the dynamics and the observations. We introduce new tools, the local unobservability index and the local estimation condition number, to measure the degree of observability or unobservability of a system. To compute these one only needs the ability to simulate the system. We apply these tools to find the best location to put a sensor to observe the flow induced by two point vortices.

Arthur J. Krener received the PhD in Mathematics from the University of California, Berkeley in 1971. From 1971 to 2006 he was at the University of California, Davis. He retired in 2006 as a Distinguished Professor of Mathematics. Currently he is a Distinguished Visiting Professor in the Department of Applied Mathematics at the Naval Postgraduate School. His research interests are in developing methods for the control and estimation of nonlinear dynamical systems and stochastic processes. Professor Krener is a Fellow of the IEEE and of SIAM. His 1981 IEEE Transactions on Automatic Control paper with Isidori, Gori-Giorgi and Monaco won a Best Paper Award. The IEEE Control Systems Society chose his 1977 IEEE Transactions on Automatic Control paper with Hermann as one of 25 Seminal Papers in Control in the last century. He was a Fellow of the John Simon Guggenheim Foundation for 2001-2. In 2004 he received the W. T. and Idalia Reid Prize from SIAM for his contributions to control and system theory. He was the Bode Prize Lecturer at 2006 IEEE CDC. His research has been continuously funded since 1975 by NSF, NASA, AFOSR and ONR. In 1988 he founded the SIAM Activity Group on Control and Systems Theory and was its first Chair. He was again Chair of the SIAG CST in 2005-07. He chaired the first SIAM Conference on Control and its Applications in 1989 and the same conference in 2007 both in San Francisco. He also co-chaired the Nonlinear Control Design Symposium held at Lake Tahoe in 1996. He has served as an Associate Editor for the SIAM Journal on Control and Optimization and for the SIAM book series on Advances in Design and Control.