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Pré-Publication, Document De Travail Année : 2022

On a Strong Robust-Safety Notion for Differential Inclusions

Résumé

This paper proposes a general framework to analyze strong robust safety for differential inclusions. This notion finds a natural motivation in the context of control loops subject to both measurement and actuation disturbances. For this reason, we say that a dynamical system is strongly robustly safe provided that it remains safe in the presence a continuous and positive perturbation, named robustness margin, added to both the argument and the image of the right-hand side. Therefore, in comparison with existing robust-safety notions, where the continuous and positive perturbation is added only to the image if the right-hand side, the proposed notion is shown to be relatively stronger, especially when the right-hand side is a general set-valued map. Furthermore, we distinguish between strong robust safety and an even stronger notion named uniform strong robust safety, which requires the existence of a constant robustness margin. The first part of this paper proposes sufficient conditions for strong and uniform strong robust safety in terms of barrier functions. The proposed conditions involve only the barrier function and the system's right-hand side. The second part establishes the equivalence between strong robust safety and the existence of a continuously differentiable barrier function certifying the notion via an infinitesimal condition. Throughout this paper, examples are provided to support our results.

Dates et versions

hal-03853676 , version 1 (15-11-2022)

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Mohamed Maghenem, Diana Karaki. On a Strong Robust-Safety Notion for Differential Inclusions. 2022. ⟨hal-03853676⟩
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