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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.

Hybrid automata are used as standard means for the specification and analysis of dynamical systems. Several researches have approached them to formally specify reactive Multi-agent systems situated in a physical environment, where the agents react continuously to their environment. The specified systems, in turn, are formally checked with the help of existing hybrid automata verification tools. However, when dealing with multi-agent systems, two problems may be raised. The first problem is a state space problem raised due to the composition process, where the agents have to be parallel composed into an agent capturing all possible behaviors of the multi-agent system prior to the verification phase. The second problem concerns the expressiveness of verification tools when modeling and verifying certain behaviors. Therefore, this paper tackles these problems by showing how multi-agent systems, specified as hybrid automata, can be modeled and verified using constraint logic programming(CLP). In particular, a CLP framework is presented to show how the composition of multi-agent behaviors can be captured dynamically during the verification phase. This can relieve the state space complexity that may occur as a result of the composition process. Additionally, the expressiveness of the CLP model flexibly allows not only to model multi-agent systems, but also to check various properties by means of the reachability analysis. Experiments are promising to show the feasibility of our approach.