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Symmetry Abstractions for Hybrid Systems and their Applications

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Document pages: 23 pages

Abstract: A symmetry of a dynamical system is a map that transforms one trajectory toanother trajectory. We introduce a new type of abstraction for hybrid automatabased on symmetries. The abstraction combines different modes in a concreteautomaton A, whose trajectories are related by symmetries, into a single modein the abstract automaton B. The abstraction sets the guard and reset of anabstract edge to be the union of the symmetry-transformed guards and resets ofthe concrete edges. We establish the soundness of the abstraction using aforward simulation relation (FSR) and present several examples. Our abstractionresults in simpler automata, that are more amenable for formal analysis anddesign. We illustrate an application of this abstraction in making reachabilityanalysis faster and enabling unbounded time safety verification. We show how afixed point of the reachable set computation of B can be used to answerreachability queries for A, even if the latter visits an infinite and unboundedsequences of modes. We present our implementation of the abstractionconstruction, the fixed point check, and the map that transforms abstractreachable sets to concrete ones in a software tool. Finally, we show theadvantage of our method over existing ones, and the different aspects of ourabstraction, in a sequence of experiments including scenarios with linear andnonlinear agents following waypoints.

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