Rafael Wisniewski

Department of Control Engineering, Aalborg University, Denmark.

Time: Wednesday 26.4.2006, 15:00
Place: Room B2-109, Fr. Bajersvej 7

Towards Modelling of Hybrid Systems

By a model of a hybrid system we understand a mathematical tool for predicting, with certain accuracy, the future behaviour of the system. The models depend to a great extend on a type of enquiry we wish to undertake. There are models with very little structure who take merely the underlying topological spaces into ccount. They can be applied for majority of hybrid systems. However, they answer only very general questions such as: Is the given system Zeno. Adding the structure of continuous dynamics can help answering more specific questions of reachability and safety. Finally, for control synthesis it might be advantageous to consider the continuous dynamics restricted to piecewise affine dynamical systems.

The program is to understand the space of trajectories/traces of a hybrid system. I will introduce during the presentation a categorical version of a discrete system and a labelled discrete system. To work with the space of trajectories I use the notion of a directed topological space of Marco Grandis. A directed topological space (X,dX) is a topological space X equipped with a directed structure dX, that is a set of continuous paths. The hybrid system is then a number of directed topological spaces, which are glued together in a way encoded in a discrete system.