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Hybrid systems are the result of merging the two most commonly used models for dynamical systems, namely continuous dynamical systems defined by differential equations and discrete-event systems defined by automata. One can view hybrid systems as constrained systems, where the constraints describe the possible process flows, invariants within states, and transitions on the one hand, and to characterize certain parts of the state space (e.g. the set of initial states, or the set of unsafe states) on the other hand. Therefore, it is advantageous to use constraint logic programming (CLP) as an approach to model hybrid systems. In this paper, we provide CLP implementations, that model hybrid systems comprising several concurrent hybrid automata, whose size is only straight proportional to the size of the given system description. Furthermore, we allow different levels of abstraction by making use of hierarchies as in UML statecharts. In consequence, the CLP model can be used for analyzing and testing the absence or existence of (un)wanted behaviors in hybrid systems. Thus in summary, we get a procedure for the formal verification of hybrid systems by model checking, employing logic programming with constraints.

This paper shows how multiagent systems can be modeled by a combination of UML statecharts and hybrid automata. This allows formal system specification on different levels of abstraction on the one hand, and expressing real-time system behavior with continuous variables on the other hand. It is not only shown how multi-robot systems can be modeled by a combination of hybrid automata and hierarchical state machines, but also how model checking techniques for hybrid automata can be applied. An enhanced synchronization concept is introduced that allows synchronization taking time and avoids state explosion to a certain extent.