Minimum time control problems for non autonomous differential equations

Olivier Bokanowski (1) , Ariela Briani (2) , Hasnaa Zidani (3)

1 LJLL - Laboratoire Jacques-Louis Lions
2 University of Pisa - Università di Pisa
3 OC - Optimisation et commande

In this paper, we investigate a minimum time problem for controlled non-autonomous differential systems, with dynamics depending on the final time. The minimal time function associated to this problem does not satisfy the dynamic programming principle. However, we will prove that it is related to a standard front propagation problem via the reachability function. Two simple numerical examples are given to illustrate our approach.

Mots clés: Non-autonomous differential equations; Minimum time problem; Hamilton­Jacobi­Bellman equation; Reachability set; Target problem

Domaines: Analyse numérique [cs.NA]

Olivier Bokanowski, Ariela Briani, Hasnaa Zidani. Minimum time control problems for non autonomous differential equations. Systems and Control Letters, 2009, 58 (10-11), pp.742-746. ⟨10.1016/j.sysconle.2009.08.003⟩. ⟨hal-00387803v2⟩