Duality theory for nonlinear filtering

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• Prashant G. Mehta, Coordinated Science Laboratory and University of Illinois at Urbana-Champaign
• Monday 27 February 2023, 14:00-15:00
• 611.

If you have a question about this talk, please contact Giordano Scarciotti.

Abstract: There is a fundamental dual relationship between estimation and control. The dual relationship is expressed in two interrelated manners: (i) Duality between observability and controllability; and (ii) Duality between optimal estimation (filtering) and optimal control. The second item means expressing one type of problem as another type of problem. In our work, the main interest is to convert a filtering problem into a control problem.

In my talk, I will describe an extension of the duality theory to hidden Markov models (HMM) with white noise observations. I will quickly review the classical Kalman’s duality (taught as part of any introductory course in Linear Systems Theory) and discuss the difficulty in extending the duality to nonlinear stochastic systems (HMMs). After describing the extension, I will close my talk with an application of the duality theory for the purposes of nonlinear filter stability analysis.

This is joint work with Jin Won Kim. The talk is based on the following papers: https://arxiv.org/abs/2208.06586 and https://arxiv.org/abs/2208.06587

Biography: Prashant Mehta is a Professor in the Coordinated Science Laboratory (CSL) 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 serves 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).

This talk is part of the Control and Power Seminars series.

This talk is included in these lists:

• 611
• Andrea Picciau's list
• Control and Power Seminars

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