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SUMMARY:Stabilization of 1D systems of PDEs
DTSTART:20220609T151500
DTEND:20220609T164500
DTSTAMP:20260505T021302Z
UID:656959b11b8821ff7859790e902abc181b02e92e94c9cb76cb826bc0
CATEGORIES:Conferences - Seminars
DESCRIPTION:Prof.  Amaury HAYAT  (Ecole des Ponts Paristech. - FR)\nAbst
 ract:\n\nAs part of control theory\, stabilization consists in finding a w
 ay to make stable a trajectory of a system on which one has some means of 
 action.\nIn this talk\, we will discuss recent advances in stabilization o
 f PDEs\, starting with one of the most natural approaches for nonlinear sy
 stems\, quadratic Lyapunov functions\, to more complex approaches such as 
 Fredholm backstepping. With quadratic Lyapunov functions\, we will focus o
 n hyperbolic systems and see that adding an arbitrarily small viscosity ca
 n have a paradoxical effect\, either robustifying or destroying the stabil
 ity.\n\nBackstepping\, on the other hand\, is a way of looking at the prob
 lem differently: it consists in finding a control operator such that the P
 DE system can be invertibly mapped to a simpler PDE system for which stabi
 lity is known. Surprisingly powerful\, this approach offers the possibilit
 y to deal with very general classes of systems. We will review the origin 
 of the method and present new results that resolve a question opened in 20
 17 and illustrate it on the rapid stabilization of the linearized water-wa
 ve equations.\n 
LOCATION:MA A1 10 https://plan.epfl.ch/?room==MA%20A1%2010
STATUS:CONFIRMED
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