Approximate Computation of Reach Sets in Hybrid Systems
<|reference_start|>Approximate Computation of Reach Sets in Hybrid Systems: 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.<|reference_end|>
@article{ravi2002approximate,
    title={Approximate Computation of Reach Sets in Hybrid Systems},
    author={D. Ravi and R.K. Shyamasundar},
    journal={arXiv preprint arXiv:cs/0202006},
    year={2002},
    archivePrefix={arXiv},
    eprint={cs/0202006},
    primaryClass={cs.LO cs.SE}
}