Dina Research School

Workshop: Hybrid Systems.

Tune Landboskole, November 28-29 2002.

Introduction

The  workshop is aimed at research students and researchers  which study complex dynamical phenomena as found in life sciences and in highly non-linear and multimodal control tasks. The  purpose is to introduce hybrid systems, a novel modelling framework for such  systems.

Hybrid Systems are dynamical systems which change irregularly between smooth evolutions and discrete transitions. Some examples from the control domain are a driving wheel hitting black ice, a robot detecting an obstacle, or a gearbox with quick shifts; examples from biology are protein synthesis and cell transformations, e.g. within the immune system. Typically, the smooth evolutions are modelled by differential equations and the discrete transitions by state machines (automata).

The basic theory has evolved during the recent decade in  an interplay between control theory and computer science. Control theory has supplied the framework for modelling smooth evolutions by means of differential equations with algebraic constraints, while computer science has supplied automata theory that gives a framework for modelling discrete transitions. In recent years, modelling tools have been developed together with techniques for determining interesting properties such as stability or optimality.

The workshop introduces the fundamental theory, starting with automata, then quickly proceeds to examples and exercises using modelling tools, such that participants get an operational understanding of the framework. We assume that participants are familiar with modelling of dynamical systems by means of ordinary differential equations.
 
The workshop is directed to:

• PhD students in agricultural, biological or biochemical sciences who have to model complex phenomena.
• PhD students in control engineering or theory  who wants to apply hybrid systems in their work.

Author: phd@dina.kvl.dk. Updated: 30 September 2002