Chaotic and random point processes: analysis, design and application to hybrid systems

Processes characterised by point events occurring in time are called point processes. Emissions from a radioactive source, action potential in a nerve fibber, traffic flow passing through a designated location on the highway, are all examples of point processes. In our tutorial we firstly discuss point processes associated with deterministic chaotic dynamics of hybrid systems such as power electronic circuits, systems involving switches, impacting mechanical systems, continuous systems controlled by discrete logic (aircraft auto-pilot modes, thermostats, chemical plants with on-off valves and pumps, automobile automatic transmissions). An understanding of bifurcations (qualitative change in a system's dynamical behaviour) is very important for the operation and control of any system. In this tutorial, we seek to develop a theoretical understanding of the bifurcation phenomena that occur in hybrid systems. We'll show that such systems yield piecewise smooth maps under sampled-data model...