Dipartimento di Ingegneria Elettrica ed Elettronica
Università di Cagliari, Italy

NEWS: Course begins on TUE 1 March.

Schedule 2011 Lectures will be held from March 1 to April 1. This is the tentative schedule (may vary according to the requirements of the registered students).

	MONDAY	h. 15-17	Room B (biennio)
	TUESDAY	h. 15-17	Room B (biennio)
	THURSDAY	h. 9-11	Room B (biennio)

No class on: : TUE 15 March, THU 17 March.

Goals

The course is devoted to the study of hybrid systems, i.e., systems where a discrete event dynamics (modeled, say, by a finite state automaton) is strictly coupled with a time-driven dynamics (modeled, say, by a differential equation). Systems of this type can be found in many application domains: automotive systems (automatic transmission, cruise control systems, semi-active suspensions), mechanical systems (gears, friction models, gain switching systems), chemical systems (batch reactors), electrical systems (static converters, systems with switches or non linearities), communications (buffer control, wireless networks), automation (control using PLC, supervisory control, manufacturing systems), transportation (modeling and control of urban traffic and railways networks), embedded systems.

Hybrid systems have a great modeling power, being capable of describing physical systems at different level of abstraction, and their study presents many challenging theoretical problems: this is why the interest in hybrid systems has constantly been growing in the last years, both in academia and in industry.

The reference models studied in this course are: hybrid automata, timed automata, and switched systems. The students will learn to: (a) model complex systems, taken from different application domains, using hybrid automata and simulated their behavior using software tools; (b) study the reachability set of timed automata and related models; (c) analyze the stability of switched systems and design stabilizing switching laws for this class of systems.

The course, targeted to PhD and Master students, is offered in English. It can be offered in Italian if all registered students request it.

Syllabus

• Systems classification: time-driven systems, discrete event systems, hybrid systems. (2 h)
• Examples of hybrid systems. (2 h)
• Hybrid automata: deterministic and nondeterministic; controlled and autonomous (3 h)
• Evolution of hybrid automata: existence and uniqueness of a solution; zenonicity, spatial regularization and minimal dwell-time; simulation using SIMULINK and MODELICA. (5 h)
• State transition systems: reachability, equivalence classes and bisimulation. Timed automata: region graph and determination of the reachability set. Classes of hybrid automata: multirate automata; rectangular automata; initialized automata and decidability of properties by reduction to timed automata. (6 h)
• Switched linear systems and stability: common Lyapunov function, multiple Lyapunov functions, quadratic stability, stability under slow switching. (6 h)

Homeworks 2010 [Hw1] [Hw2] [Hw3]

Evaluation Graded homeworks or a final project.