Towards Modelling of Hybrid Systems

The article is an attempt to use methods of category theory and topology for analysis of hybrid systems. We use the notion of a directed topological space (Grandis, 2003); it is a topological space together with a set of privileged paths. Dynamical systems are examples of directed topological spaces. A hybrid system consists of a number of dynamical systems that are glued together according to information encoded in the discrete part of the system. Motivated by Ames and Sastry (2005) we develop a definition of a hybrid system as a functor from the category generated by a transition system to the category of directed topological spaces. Its directed homotopy colimit (geometric realization) is a single directed topological space. The behavior of hybrid systems can be then understood in terms of the behavior of dynamical systems through the directed homotopy colimit