An Introduction to Hybrid Automata
نویسنده
چکیده
ion methods are used to simplify models and make their analysis more tractable. Several equivalence relations have been studied for subclasses of hybrid systems. For example, it can be shown that transition systems of timed automata admit finite state abstractions, called region graphs, that are time-abstract bisimilar, see [AD94] for details. Those equivalence results are used to prove decidability of verification problems on subclasses of hybrid automata [Hen95, HK96] and allow the use of well-known modelchecking procedures that are guaranteed to terminate in the presence of finite quotients [HM00]. Other techniques that are not exact but use overapproximations have been proposed and have proven useful in practice: the approximation schema proposed in Section 4.3 is detailed and proven correct in [HHWT98]. Other interesting works about overapproximations can be found, among others, in [HRP94, AIKY95, ADI03]. 5.4 Control synthesis In this introduction, we have shown how we can model and verify controllers using hybrid automata. In our example, we have proposed a controller for the system and proven that the controller was correct for a list of requirements. A more ambitious goal than algorithmic (controller) verification is algorithmic (controller) synthesis. Here are some references about control synthesis [Won97, AMPS98, CHR02, HK99, HHM99]. 5.5 Semantics and robustness The semantics of hybrid automata that we defined in this chapter can be described as perfect. For example, it is possible to model, with this semantics, a controller that takes a given transition when a variable of the environment has exactly a given value. This can be considered as unrealistic because any implementation of such a controller will measure its environment through sensors that have finite precision. Alternative semantics that can be considered as robust are proposed in [GHJ97, HR00, AB01, Frä99]. 5.6 Tool support and case studies Several tools for the automatic analysis of hybrid automata have been implemented. The tools Kronos [DOTY96] and Uppaal [BLL96] can be used to analyze the subclass of timed automata. The tool HyTech [HHWT97] allows
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تاریخ انتشار 2005