Séminaire d’Automatique du plateau de Saclay : On generalized homogeneity and time-constrained stabilization of evolution systems.

Séminaire le 25 Avril 2017, 10h00 à CentraleSupelec (Gif-sur-Yvette) Salle du conseil du L2S - B4.40
Andrey polyakov (NON-A team, Inria-Lille-Nord Europe)

Homogeneity is a symmetry of an object (e.g. function or operator) with respect to some transformations (dilations). Nonlinear homogeneous ODEs (ordinary differential equations) form an important class of models of control systems. They appear as local approximations of nonlinear plant and include models of process control, nonholonomic mechanical systems, models with frictions, etc. Being non-linear the homogeneous systems demonstrate properties typical for linear systems, for example, local stability implies the global one, stable homogeneous control system is ISS (input-to-state stable) with respect to measurement noises and additive exogenous disturbance, etc.

This talk is devoted to extension of ideas of homogeneity to evolution systems in Banach/Hilbert spaces. A lot of well-known partial differential equations are homogeneous in a generalized sense, (e.g. heat, wave, Navier-Stocks, Saint-Venant, Korteweg-de Vries, fast diffusion equations). They inherit many important properties of homogeneous ODEs such as  scalability of trajectories or finite-time stability in the case of negative homogeneity degree. Homogeneity allows us to design a universal control for finite-time stabilization of evolution system.

Bio. Andrey Polyakov received PhD degree from Voronezh State University (Russia) in 2005.
He was lecturer (2004-2007) and associate professor (2008-2010) of this university.
In 2007 and 2008 he was a post-doctoral research associate with Automatic Control Department of CINVESTAV (Mexico). From 2010 till 2013 he was researcher with Institute of Control Sciences of Russian Academy of Sciences. Now Andrey Polyakovis Inria researcher with NON-A team of Inria Lille Nord Europe (France). His research interests include
different problems of robust nonlinear control and estimation. He is co-author of the book "Attractive Ellipsoids in Robust Control". He is editor of International Journal of Robust and Nonlinear Control, Journal of Optimization Theory and Applications (JOTA), Automation and Remote Control.