16 21 June 2011
Ph.D.
in Information Technology
Dipartimento
di Elettronica e Informazione
Politecnico di Milano
Lecturers:
|
John
Lygeros ETH Zurich Maria
Prandini Politecnico
di Milano |
Course
description:
|
The aim of this course
is to introduce the student to the area of hybrid systems, that is dynamical systems
characterized by the interaction of different types of dynamics, both
continuous and discrete. The interest in a
systematic study of hybrid systems has been fuelled by recent technological
innovations, which led to the pervasive diffusion of increasingly complex
digital system for the control and supervision of physical systems
(embedded systems represent a significant example in this respect). The study of hybrid
systems is generally more challenging than that of purely discrete or purely
continuous systems, because of the interaction between dynamics of different
nature. In this course, we shall introduce models for hybrid systems, and
describe general methods for investigating properties such as reachability, observability and
stability. Control of hybrid systems will also be addressed according to a reachability analysis approach. Analysis and design
methods will be demonstrated on examples from different application contexts.
Finally, we shall consider stochastic hybrid systems, and discuss recently
developed methods for reachability analysis of this
class of systems where the hybrid dynamics is affected by probabilistic
uncertainty. Students attending the
course should be able to appreciate the diversity of phenomena that arise in
hybrid systems, and understand how concepts that are classical in the theory
of discrete systems, modelled by automata, can
coexist with concepts that are classical in the theory of continuous systems,
modelled by differential equations, in a unifying
framework. |
Structure of the
course:
|
Thursday June 16 (M. Prandini) 11.30 13.00
Introduction
and motivating examples. Definition of hybrid
automaton. [pdf] 14.30 16.00
Execution of a hybrid automaton: Zeno, blocking, and nondeterministic automata. [pdf] Friday June 17 (M. Prandini): 09.30 11.00 Lyapunov
stability. [pdf] 11.30 13.00 Stability for switched
linear systems. [pdf] 14.30
16.00 State observer. [pdf] Monday June 20 (J. Lygeros) 14.30 16.00 Reachability
analysis: definition and deductive methods.
16.30
18.00 Model checking. Tuesday June 21 (J. Lygeros) 9.30
11.00 Reachability with inputs: A game theoretic
perspective. 11.30
13.00 Stochastic hybrid systems.
[pdf] 14.30
16.00 Reachability
analysis. Remarks: Time schedule
does not include breaks but refers to effective lecture-time. |
|
To register to the course, please, send an e-mail to dottoratoinginfo@elet.polimi.it Lectures will take place at the Aula Seminari of the Dipartimento di
Elettronica e Informazione del Politecnico di Milano, via Ponzio 34/5, 20133
Milano. See http://www.dei.polimi.it/presentazione/come_raggiungerci/index.php?&idlang=eng for directions on how to reach the Dipartimento
di Elettronica e Informazione.
|
|
John
Lygeros, Lecture Notes on Hybrid Systems. M.
Branicky. Multiple Lyapunov
functions and other analysis tools for switched and hybrid systems. IEEE
Trans. on Automatic Control, 43(4):475-482, 1998. [stability] R.A.
Decarlo, M.S. Branicky,
S. Petterson, B. Lennartson.
Perspectives and results on the stability and stabilization of hybrid
systems. Proceedings of the IEEE, 88(7):1069-1082, 2000. [stability] M.
Johansson and A. Rantzer. Computation of piecewise quadratic Lyapunov
function for hybrid systems. IEEE Transactions on Automatic
Control, 43(4):555-559, 1998. [stability] D. Liberzon, A. S. Morse. Basic
problems in stability and design of switched systems. IEEE Control
Systems Magazine, vol. 19, no. 5, pp. 59-70, Oct. 1999. [stability of
switched systems] Daniel Liberzon. Switching in Systems and
Control, Birkhauser, 2003. [stability of
switched systems] A.
Alessandri and P. Coletta.
Switching observers for continuous-time
and discrete-time linear systems. Proceedings of the American Control
Conference Arlington, VA June, 2001. [state observer] A. Balluchi,
L. Benvenuti, M. D. Di Benedetto, A. L. Sangiovanni-Vincentelli. Design of
Observers for Hybrid Systems. In Hybrid Systems: Computation and
Control, Lecture Notes in Computer Science, vol. 2289, Springer-Verlag, 2002. [state observer] Y. Gao, J. Lygeros, M. Quincampoix. On the Reachability Problem for Uncertain Hybrid Systems. IEEE
Transactions on Automatic Control, 52(9): 1572-1586, 2007. [reachability with inputs] J. Lygeros and M. Prandini. Stochastic hybrid systems: a powerful framework for complex, large
scale applications. European Journal of Control, vol. 16(6):583-594, 2010
[stochastic hybrid systems] |