Section: New Results

Lur'e set-valued dynamical systems

Participants : Bernard Brogliato, Christophe Prieur, Alexandre Vieira.

Lur'e systems are quite popular in Automatic Control since the fifties. Set-valued Lur'e systems possess a static feedback nonlinearity that is a multivalued function. We study in [31] state observers for particular Lur'e systems which are Moreau's sweeping processes modelling Lagrange dynamics with frictionless unilateral constraints. The observers are themselves set-valued (first order sweeping process with measures), a complete analysis (existence of solutions, stability of the error system) is led. In [51], we extend previous results in the team and also more recently by Camlibel and Schumacher, to solve the problem of output regulation for evolution variational inequalities (in a convex analysis setting). In the PhD thesis of A. Vieira, we attack the problem of optimal control of linear complementarity systems. In the first part of this thesis, the case when the LCS is equivalent to an ODE with Lipschitz continuous right-hand side, is treated. Starting from first-order necessary conditions stated in a broad context by Clarke, we show that the Pontryagin's conditions are a mixed LCS, that yield so-called MPEC problems.