Séminaire d'Automatique du Plateau de Saclay : Optimal control problems with oscillations, concentrations, and discontinuities.

Séminaire le 19 Octobre 2017, 11h00 à CentraleSupelec (Gif-sur-Yvette) Salle du conseil du L2S - B4.40
Didier Henrion (CNRS Senior Researcher, LAAS-CNRS & Professor, Faculty of Electrical Engineering, Czech Technical University)

Optimal control problems with oscillation (chattering controls) and concentration (impulsive controls) can have integral performance criteria such that concentration of the control signal occurs at a discontinuity of the state signal. Techniques from functional analysis (extensions of DiPerna-Majda measures from the partial differential equations literature) are developed to give a precise meaning of the integral cost and to allow for the sound application of numerical methods. We show how this can be achieved for the Lasserre hierarchy of semidefinite programming relaxations. This includes in particular the use of compactification techniques allowing for unbounded time, state and control.

Bio. Didier Henrion is a CNRS Senior Researcher at LAAS, an engineering laboratory in Toulouse, France. He is also a Professor at the Faculty of Electrical Engineering at the Czech Technical University in Prague, Czechia. Since 1994 he has been developing constructive tools for addressing mathematical problems arising from systems control and optimization.