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arXiv · 1710.08483

On the Relaxation of Hybrid Dynamical Systems

Tyler Westenbroek·S. Shankar Sastry·Humberto Gonzalez
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Abstract

Hybrid dynamical systems have proven to be a powerful modeling abstraction, yet fundamental questions regarding the dynamical properties of these systems remain. In this paper, we develop a novel class of relaxations which we use to recover a number of classic systems theoretic properties for hybrid systems, such as existence and uniqueness of trajectories, even past the point of Zeno. Our relaxations also naturally give rise to a class of provably convergent numerical approximations, capable of simulating through Zeno. Using our methods, we are also able to perform sensitivity analysis about nominal trajectories undergoing a discrete transition -- a technique with many practical applications, such as assessing the stability of periodic orbits.

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Tyler Westenbroek, S. Shankar Sastry, Humberto Gonzalez. 2017-10-23. On the Relaxation of Hybrid Dynamical Systems. https://arxiv.org/abs/1710.08483

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