O-minimal hybrid systems (2000) [58 citations — 7 self]
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@ARTICLE{Lafferriere00o-minimalhybrid,author = {Gerardo Lafferriere and George J. Pappas and Shankar Sastry},
title = {O-minimal hybrid systems},
journal = {Mathematics of Control, Signals, and Systems},
year = {2000},
volume = {13},
pages = {1--21}
}
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Abstract:
Abstract. A unified approach to decidability questions for verification algorithms of hybrid systems is obtained by the construction of a bisimulation. Bisimulations are finite state quotients whose reachability properties are equivalent to those of the original infinite state hybrid system. In this paper, we introduce the notion of o-minimal hybrid systems, which are initialized hybrid systems whose relevant sets and flows are definable in an o-minimal structure. We prove that o-minimal hybrid systems always admit finite bisimulations. We then present a list of o-minimal structures which captures most hybrid systems known to admit finite bisimulations as well as present new classes of hybrid systems with more complex dynamics for which finite bisimulations exist.
Citations
| 1393 | A theory of timed automata – Alur, Dill - 1994 |
| 449 | The algorithmic analysis of hybrid systems – Alur, Courcoubetis, et al. - 1995 |
