Groupe d’études et de recherche en analyse des décisions

Epsilon controllability of nonlinear systems on Polytopes

Mohamed Helwa Université McGill, Canada

Première présentation

In this talk we introduce the notion of epsilon controllability of nonlinear systems on polytopes, which formalizes approximate mutual accessibility problems of nonlinear systems under safety constraints. After motivating our study, we show that if one constructs a polytopic cover of a given polytope, representing the intersection of the safety constraints, such that the affine system resulting from the linearization of the nonlinear system inside each polytopic region of the cover is in-block controllable, then starting from any initial state in the interior of the given polytope, one can steer the nonlinear system to an epsilon neighborhood of any final state in the interior of the polytope in finite time, where epsilon depends on the size of the polytopic regions of the cover. We then study a hierarchy of covers, representing the nonlinear system at different levels of accuracy, and provide a constructive algorithm for achieving approximate mutual accessibility of nonlinear systems under safety constraints.

We also provide an illustrative example to clarify the main results of the talk.

Deuxième présentation

On the generation of conditional densities in nonlinear filtering for McKean-Vlasov systems