Hybrid systems with continuous-time inputs: subtleties in solution concepts and existence results

Maurice Heemels (1) , Pauline Bernard (2) , Koen J A Scheres (1) , Romain Postoyan (3) , Ricardo G Sanfelice (4)

1 TU/e - Eindhoven University of Technology [Eindhoven]
2 CAS - Centre Automatique et Systèmes
3 CRAN - Centre de Recherche en Automatique de Nancy
4 UC Santa Cruz - University of California [Santa Cruz]

We study solution concepts and their properties for hybrid systems that can flow and jump, affected by continuous-time inputs. While the solution concepts, the existence of solutions and (forward) completeness properties are extensively discussed in the absence of (external) inputs, there are surprisingly few results when inputs are present, certainly in the case where the flow and jump sets depend on the inputs. Given the relevance of this class of hybrid systems for many applications such as hybrid or networked control for plants subject to disturbances or measurement noise, we discuss in this paper notions of solutions in the presence of inputs and show through various examples the subtleties that can occur. Moreover, we provide tools to guarantee the existence of solutions and results to establish completeness properties.

Domaines: Automatique / Robotique

Maurice Heemels, Pauline Bernard, Koen J A Scheres, Romain Postoyan, Ricardo G Sanfelice. Hybrid systems with continuous-time inputs: subtleties in solution concepts and existence results. 60th IEEE Conference on Decision and Control, CDC 2021, Dec 2021, Austin, United States. ⟨hal-03436863⟩