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Pré-Publication, Document De Travail Année : 2022

A Converse Robust-Safety Theorem for Differential Inclusions

Résumé

This paper presents converse theorems for robust safety in terms of barrier functions for continuous-time systems modeled by differential inclusions. Appropriate infinitesimal conditions are shown to be both necessary and sufficient under mild conditions on the considered system and the specified safe and unsafe regions. More precisely, for a robustly-safe system, we propose a construction of a barrier function in terms of the time-to-impact function with respect to a specifically constructed reachable set. Using techniques from set-valued and nonsmooth analysis, we show that such a function, although being only semicontinuous, certifies robust safety by verifying a non-infinitesimal condition; namely, a condition involving the system's solutions. Furthermore, we propose to refine the aforementioned construction, using integral techniques available in the literature. As a result, we provide a necessary and sufficient condition for robust safety that is infinitesimal; namely, it involves only the barrier function and the system's right-hand side. In comparison to the existing converse robust safety theorems, our result is more general as it allows the safety region to be unbounded, the right-hand side to be a general continuous set-valued map, and the solutions to be non-unique.

Dates et versions

hal-03853689 , version 1 (15-11-2022)

Identifiants

Citer

Mohamed Maghenem, Masoumeh Ghanbarpour. A Converse Robust-Safety Theorem for Differential Inclusions. 2022. ⟨hal-03853689⟩
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