Groupe d’études et de recherche en analyse des décisions

What is the Lagrangian for nonlinear filtering?

Prashant Girdharilal Mehta University of Illinois at Urbana-Champaign, États-Unis

Prashant G. Mehta

Présentation sur YouTube

There is a certain magic in writing the variational form of the equations in physics and engineering. The most classical of these ‘magics’ is the Lagrange’s formulation of the Newtonian mechanics. An accessible modern take on this and more appears in the Feb 2019 issue of The New Yorker: https://www.newyorker.com/science/elements/a-different-kind-of-theory-of-everything?reload=true

My talk is concerned with a variational (optimal control-type) formulation of the problem of nonlinear filtering/estimation. Such formulations are referred to as duality between optimal estimation and optimal control. The first duality principle appears in the seminal (1961) paper of Kalman-Bucy, where the problem of minimum variance estimation is shown to be dual to a linear quadratic optimal control problem.

In my talk, I will present a new generalization of the Kalman-Bucy duality theory to nonlinear filtering. I will use this duality to (a) define detectability, and (b) obtain results on stability of the nonlinear filter.

This is joint work with Jin-Won Kim and Sean Meyn. The talk is based on the following papers: https://arxiv.org/pdf/1903.11195.pdf and https://arxiv.org/pdf/2103.14631.pdf.

Bio: Prashant Mehta is a Professor in the Coordinated Science Laboratory and the Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign (UIUC). He received his Ph.D. in Applied Mathematics from Cornell University in 2004. He was the co-founder and the Chief Science Officer of the startup Rithmio whose gesture recognition technology was acquired by Bosch Sensortec in 2017. Prior to his academic appointment at UIUC in 2005, he worked at United Technologies Research Center (UTRC) where he invented the symmetry-breaking solution to suppress combustion instabilities. This solution — which helped solve a sixty-year old open problem — has since become an industry standard and is widely deployed in jet engines and afterburners sold by Pratt & Whitney.

Prashant Mehta received the Outstanding Achievement Award at UTRC for his contributions to modeling and control of combustion instabilities in jet-engines. His students have received the Best Student Paper Awards at the IEEE Conference on Decision and Control in 2007, 2009 and most recently in 2019; and have been finalists for these awards in 2010 and 2012. He has served as an Associate Editor for the IEEE Transactions on Automatic Control (2019-), the Systems and Control Letters (2011-14), and the ASME Journal of Dynamic Systems, Measurement and Control (2012-16).