Modeling and Control of Hybrid Systems

Recent technological innovations have caused a considerable interest in the study of dynamical processes of a mixed continuous and discrete nature. Such processes are called hybrid systems and are characterized by the interaction of time-continuous models (governed by differential or difference equations) on the one hand, and logic rules and discrete-event systems (described by, e.g., automata, finite state machines, etc.) on the other. A hybrid system also arises in practice when continuous physical processes are controlled via embedded software that intrinsically has a finite number of states only (e.g., on/off control).

This course provides an introduction to modeling, analysis, and control of hybrid systems.

The main topics considered are:

* General introduction, examples of hybrid systems and motivation

* Modeling frameworks (automata, hybrid automata, piecewise-affine systems, complementarity systems, mixed logic dynamical systems, Petri nets)

* Properties and analysis of hybrid systems (well-posedness, Zeno behavior, stability, liveness, safety, ...)

* Control of hybrid systems (switching controllers, model predictive control)

* Verification and tools