Viable trajectories for nonconvex differential inclusions with constant delay

Hélène Frankowska (1) , Ihab Haidar (2)

1 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche
2 QUARTZ - Laboratoire QUARTZ

In this paper, we consider a nonconvex differential inclusion with constant delay. We study the existence of viable solutions when the state is constrained to the closure of an open subset of R n. The main contribution is a relaxation result stating that, under some assumptions, each "viable solution" of the convexified inclusion can be approximated by "viable solutions" of the original one. This result is obtained thanks to an extension of the celebrated Filippov's theorem to the case of delay differential inclusions.

Mots clés: Delay differential inclusions; relaxation; state constraints; inward pointing conditions

Domaines: Optimisation et contrôle [math.OC]

Hélène Frankowska, Ihab Haidar. Viable trajectories for nonconvex differential inclusions with constant delay. 14th IFAC Workshop On Time Delay Systems (TDS 2018), Jun 2018, Budapest, Hungary. pp.112-117, ⟨10.1016/j.ifacol.2018.07.208⟩. ⟨hal-01993553⟩