Characterization of Safety and Conditional Invariance for Nonlinear Systems | IEEE Conference Publication | IEEE Xplore

Characterization of Safety and Conditional Invariance for Nonlinear Systems


Abstract:

This paper investigates sufficient and necessary conditions for safety (equivalently, conditional invariance) in terms of barrier functions. Relaxed sufficient conditions...Show More

Abstract:

This paper investigates sufficient and necessary conditions for safety (equivalently, conditional invariance) in terms of barrier functions. Relaxed sufficient conditions concerning the sign and the regularity of the barrier function are proposed. Furthermore, via a counterexample, the lack of existence of an autonomous and continuous barrier function certifying safety in a class of autonomous systems is shown. As a consequence, guided by converse Lyapunov theorems for only stability, time-varying barrier functions are proposed and infinitesimal conditions are shown to be both necessary as well as sufficient, provided that mild regularity conditions on the system's dynamics holds. Examples illustrate the results.
Date of Conference: 10-12 July 2019
Date Added to IEEE Xplore: 29 August 2019
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Conference Location: Philadelphia, PA, USA

I. Introduction

Beyond stability, the most important property to guarantee in a dynamical system is safety. The safety problem consists in guaranteeing that the system's solutions, when starting from a given set of initial conditions, never reach a given unsafe set [1]. The same property is also called conditional invariance in some earlier works [2]–[5]. Regarding the considered application, reaching the unsafe set can correspond to the impossibility of applying a predefined feedback law [6] or, simply, colliding with an obstacle [7]. Safety analysis is in fact a key step in many control applications.

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References

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