Lyapunov-Barrier Characterization of Robust Reach-Avoid-Stay Specifications for Hybrid Systems

Yiming Meng; Jun Liu

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arXiv · 2211.00814

Lyapunov-Barrier Characterization of Robust Reach-Avoid-Stay Specifications for Hybrid Systems

Yiming Meng·Jun Liu

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Abstract

Stability, reachability, and safety are crucial properties of dynamical systems. While verification and control synthesis of reach-avoid-stay objectives can be effectively handled by abstraction-based formal methods, such approaches can be computationally expensive due to the use of state-space discretization. In contrast, Lyapunov methods qualitatively characterize stability and safety properties without any state-space discretization. Recent work on converse Lyapunov-barrier theorems also demonstrates an approximate completeness or verifying reach-avoid-stay specifications of systems modelled by nonlinear differential equations. In this paper, based on the topology of hybrid arcs, we extend the Lyapunov-barrier characterization to more general hybrid systems described by differential and difference inclusions. We show that Lyapunov-barrier functions are not only sufficient to guarantee reach-avoid-stay specifications for well-posed hybrid systems, but also necessary for arbitrarily slightly perturbed systems under mild conditions. Numerical examples are provided to illustrate the main results.

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BibTeX RIS

Yiming Meng, Jun Liu. 2022-11-02. Lyapunov-Barrier Characterization of Robust Reach-Avoid-Stay Specifications for Hybrid Systems. https://arxiv.org/abs/2211.00814

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