|July 21, 2017
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Prof. Ali Belabbas
Electrical and Computer Engineering Department
University of Illinois, USA
Friday 2017-07-21 14:00
IKTD-Seminar-Room 1.264 - Pfaffenwaldring 9 - Campus Stuttgart-Vaihingen
Linear systems with process and observation noises are widely used in engineering and physics to model systems as varied as the stock market and epidemics. Consider the estimation of the state of such systems from the noisy measurements; the Kalman filter is known to be the minimum mean square error estimator when the noises are Gaussian. We address here how to design the sensors that minimize the error afforded by the Kalman filter. This problem of optimal sensor design, which is almost as old as the Kalman filter itself, is however not convex. As a consequence, many ad hoc methods have been used over the years to solve it. We show in this talk how a geometric approach allows us to characterize and obtain the optimal designs exactly. This optimal design yields the lowest possible estimation error from linear measurements with a fixed signal to noise ratio. The approach can be used to solve the dual problem of optimal actuator design to minimize control energy.
M.-A. Belabbas obtained his PhD degree in applied mathematics from Harvard University and his undergraduate degree from Ecole Centrale Paris and University de Louvain. He is currently an assistant professor in the Electrical and Computer Engineering department at the University of Illinois, Urbana-Champaign and the Coordinated Science Laboratory. His research interests are in networked control, geometric control and stochastic systems. He was a recipient of the 2014 NSF Career Award.