Non-Smooth and Zeno Trajectories for Hybrid System Algebra

in: Universität Augsburg Technical Report, Institute of Computer Science, University of Augsburg, March 2006

Abstract:
Hybrid systems are heterogeneous systems characterised by the interaction of discrete and continuous dynamics. In this paper we compare a slightly extended version of our earlier algebraic approach to hybrid systems to other approaches. We show that hybrid automata, which are probably the standard tool for describing hybrid systems, can conveniently be embedded into our algebra. But we allow general transition functions, not only smooth ones. Moreover we embed other models and point out some important advantages of the algebraic approach. In particular, we show how to easily handle Zeno effects, which are excluded by most other authors. The development of the theory is illustrated by a running example and a larger case study.