UTRC CDS Lecture: Mohamed Ali Belabbas, Geometric approach to optimal sensor and actuator placement
Friday, September 18, 2015
1146 A V Williams
301 405 6576
UTRC Control and Dynamical Systems Invited Lecture
A geometric approach to optimal sensor and actuator placement
Mohamed Ali Belabbas
Electrical and Computer Engineering Department
University of Illinois, Urbana-Champaign
Estimators for linear systems are ubiquitous, with applications in fields ranging from engineering to biology to economics. The Kalman filter is known to be the optimal estimator of the state when the noise is additive and Gaussian. Because its performance is limited by the sensors to which it is paired, it is natural to seek an optimal sensor for the Kalman filter. The problem is however not convex and, as a consequence, many ad hoc methods have been used over the years to design sensors. We show in this talk how, by using a geometric approach, one can obtain and characterize optimal sensors. Precisely, we exhibit a positive definite operator which optimal sensors have to commute with. We furthermore describe a gradient algorithm to find optimal sensors, and prove its convergence. This optimal sensor yields the lowest possible estimation error for measurements with a fixed signal to noise ratio. The results presented here also apply to the dual problem of optimal actuator design.
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 System, Sparse Systems, Geometric control theory and data science. He was a recipient of the 2014 NSF Career Award.