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Approximate Computation of Reach Sets in Hybrid Systems

D. Ravi·R. K. Shyamasundar
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Abstract

One of the most important problems in hybrid systems is the {\em reachability problem}. The reachability problem has been shown to be undecidable even for a subclass of {\em linear} hybrid systems. In view of this, the main focus in the area of hybrid systems has been to find {\em effective} semi-decision procedures for this problem. Such an algorithmic approach involves finding methods of computation and representation of reach sets of the continuous variables within a discrete state of a hybrid system. In this paper, after presenting a brief introduction to hybrid systems and reachability problem, we propose a computational method for obtaining the reach sets of continuous variables in a hybrid system. In addition to this, we also describe a new algorithm to over-approximate with polyhedra the reach sets of the continuous variables with linear dynamics and polyhedral initial set. We illustrate these algorithms with typical interesting examples.

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D. Ravi, R. K. Shyamasundar. 2002-02-07. Approximate Computation of Reach Sets in Hybrid Systems. https://arxiv.org/abs/cs/0202006

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