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Path-complete Lyapunov techniques: when Algebra and Combinatorics meet in Control

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I will present an overview of ‘Path-complete techniques’, which have been developed to analyze stability properties of dynamical systems. These tools rely on concepts from Mathematics, Computer Science, and Optimization. Starting with the pioneering works of Bliman, Ferrari-Trecate, Lee, Dullerud, Daafouz, and others, the full nature of path-complete Lyapunov functions has been progressively understood in the last 20 years, and their range of application is still widening. These Algebro-combinatorial techniques allow in favorable cases to obtain provably efficient algorithms (e.g. for switching systems stability analysis), and are promising for tackling much more general problems, and much more general dynamical systems.

If time permits, I will move to applications in the field of Wireless Control Networks, where again, algebraic and combinatorial arguments allow to push classical unfeasibility boundaries for switching systems control.

I will end by presenting some further questions and potential applications.

Short bio:

Raphaël Jungers is a FNRS Research Associate and Professor at the Université catholique de Louvain, Belgium. His main interests lie in the fields of Computer Science, Graph Theory, Optimization and Control. He received a PhD in mathematical engineering from the Université catholique de Louvain (2008), and an engineering degree in applied mathematics, both from the Ecole Centrale Paris, France (2004), and from the Université catholique de Louvain (2005). He holds a minor degree in Electrical Engineering from the Université catholique de Louvain (2005).

He has held various invited researcher positions, at the Department of Computer Science of the Université Libre de Bruxelles (2008-2009), at the Laboratory for Information and Decision Systems of the Massachusetts Institute of Technology (2009-2010), and at the University of L’Aquila (2011,2013).

He is a FNRS fellow and a BAEF fellow. He is an Associate Editor for the IEEE CSS Conference Editorial Board, and the journals NAHS , Systems and Control Letters, and IEEE Transactions on Automatic Control. He was the recipient of the IBM Belgium 2009 award and a finalist of the ERCIM Cor Baayen award 2011. He was the co-recipient of the SICON best paper award 2013-2014.

This talk is part of the CUED Control Group Seminars series.

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