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Model checking can be used to verify temporal properties of hybrid automata. However, model checking is not decidable in general. We overcome this difficulty by considering a durational graph abstraction, for which model checking is decidable. The contribution of this paper is to show that, given a hybrid automaton and the durational graph abstraction, there exists a simulation relation between the two systems. This approach allows checking properties such as safety, but also timing properties of hybrid automata. We apply our framework to a relevant case study in the context of air traffic management (ATM). For an extended version of this paper refer to [A. D'Innocenzo et al., 2007].

In this paper a controller based on the so-called robust or structurally stable regulation theory is designed. The ground vehicle motion control is reformulated as a tracking problem of a desired reference, generated by an external system. Moreover, the disturbance acting on the vehicle is supposed to be modeled, i.e. unknown but with a known structure, as happens in many typical situations. The use of immersion techniques eliminates the dependence of the controller on parameters, so obtaining a controller ensuring zero tracking error. Since an immersion for the designed control law can not be easily determined, in this paper we consider the immersion of an approximate expression of the control, so obtaining a bounded tracking error.