Special Session 158: From PDE control to the qualitative study of (random) dynamical systems

Robust control of linear systems under small parameter variation
Pierre Lissy
CERMICS, Ecole nationales des ponts et chausses
France
Co-Author(s):    Sylvain Ervedoza and Yannick Privat
Abstract:
In this talk, I will discuss insensitization problems for linear controlled evolutions under small parameter variations. The goal is to design a control which both drives the nominal system to a prescribed target and cancels the first-order sensitivity of the final state with respect to the parameter. I will present an abstract framework, in which this question is recast as a controllability problem for a coupled state-sensitivity cascade system. In finite dimension, I will give a complete characterization in terms of a Kalman-type rank condition. I will also illustrate the approach on PDE examples, including the heat equation with uncertain diffusion and the wave equation with uncertain potential.