DISC Course
on
Modeling and Control of Hybrid Systems
November 10, 17, 24 and December 1, 2008
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. In practice a hybrid system arises,
e.g., when continuous physical processes are controlled via embedded
software that intrinsically has a finite number of states only (such
as on/off control).
Objectives of the course
This course will offer a brief overview of the field of hybrid
systems ranging from modeling, over analysis and simulation, to
verification and control.
We will particularly focus on modeling, analysis,
and control of tractable classes of hybrid systems.
Date and location
The course will be take place on Mondays
November 10, 17, 24 and December 1, 2008
from 10.15 to 12.30
at
Regardz La Vie Utrecht,
Lange Viestraat 351,
3511 BK Utrecht,
The Netherlands,
phone: 030-2340088, URL:
http://www.regardz.nl
(in Dutch).
Click here for travel
directions (in Dutch).
Lecture notes
The pdf file of the Lecture Notes for the course will be
communicated to the registrered participants of the course via email.
Slides
Homework assignments
- Homework for Chapters 1-2 (November 10):
pdf
- Homework for Chapters 3-4 (November 17):
pdf
Notes:
- The Matlab software (using yalmip/sedumi solvers as in the
MPT toolbox
developed at the ETH in Zürich)
needed for solving LMIs during
this DISC course can be downloaded here
(14 MB). There is also a short manual with instructions on how to
install the software and further starters.
- To get an impression of the basic function of the toolbox you can run
"yalmipdemo" and use option 1 (basic functions in the toolbox) and option 4
related to setting up LMIs for the stability analysis/construction of
Lyapunov functions. This might help quite a lot for solving the LMIs that you
are supposed to do as homework.
- Moreover, the m files
Example1_2007.m
and
Example2_2007.m
can be used as starting points.
The first example shows how to find a quadratic Lyapunov function for a linear
system (satisfying a Lyapunov inequality) and also shows how you can set up an
optimization problem with LMI constraints (optimizing over gamma in this
case).
The second example constructs a continuous PWQ Lyapunov function for a
PWL system (explanations on this technique follow on November 24).
- Homework for Chapters 4-5 (November 24):
pdf
Note:
- This 3rd homework onsists of
4
problems. It is sufficient (in order to get the full score) to solve 3
out of the 4 problems. You can pick whatever 3 problems you like to
solve. If you solve all 4 problems you can even obtain bonus points that
will increase your final grade!
- Homework for Chapters 6-7 (December 1):
pdf
Note:
-
If you have/install the tomlab cplex toolbox, you may want to use the
following MIQP tomlab cplex wrapper function: miqp_solve_tomlab_cplex.m
Evaluation
Your final grade for this DISC course consists in the average
of your grades for the homeworks (1 homework for each lecture).
You can obtain a bonus point if you detect a sufficient amount
of errors in the lecture notes and report them to the lecturers.
The final grades will be communicated by the end of January 2009.
Registration
To register for the course please
contact
Ms A. van Regteren.
Lecturers
This page is maintained by Bart De Schutter.
Last update: November 27, 2008.