Course:
Randomized
Algorithms for Analysis and Control of Uncertain Systems
Lecturer: Roberto Tempo
IEIIT-CNR
Politecnico di Torino, Italy
at the:
Dept. Ing. de Sistemas y Automatica
Escuela Superior de Ingenieros, Univ.
March 14-18
Registration: e-mail to Eduardo F. Camacho (eduardo@esi.us.es )
The course is funded by the Spanish Ministry of Education and no fees
will be charged. The number of places is limited and a first in first served
system
will be used
Timetable:
Monday 14th
Tuesday 15th
Wednesday 16th
Thursday 17th
Summary
This course
concentrates on nonstandard tools for control of uncertain systems with main
emphasis on the interplay of probability and robustness. The objective is to
combine hard bounds, which are frequently used in classical robust control,
with probabilistic information which is often neglected in this context. The
main advantage is to provide additional insight to the control engineer. This
insight may be very useful in analyzing and designing complex control systems
in the presence of uncertainty. The interplay of probability and robustness
also leads to innovative concepts such as the probabilistic robustness margin
and the probability degradation function. The algorithms obtained are low
complexity (polynomial-time) and are associated to robustness bounds which are
generally less conservative than the classical ones, obviously at the expense
of a small risk expressed in probability. These algorithms are usually called
"randomized algorithms."
In the first part of the course, we concentrate on analysis and, in particular,
we address the issue of finite sample size. Subsequently, we present results
for sample generation in various norm-bounded sets of interest in robust
control. These results are based on methods of statistical analysis and of the
theory of random matrices. The construction of specific randomized algorithms
concludes this part of the course. In the second part, we study probabilistic robust
design of uncertain systems. We show how this problem can be formulated in the
context of classical optimal control and then we discuss how randomization and
stochastic gradient methods can be successfully used. We also consider
extensions of this approach to linear parameter-varying systems. Other topics
that will be addressed is the design of randomized algorithms for model
predictive control and for robust fault-tolerant
control.
The course will end with a description of a number of open problems which may
be important to consider in the near future.
The course is focused on the exposition of the theoretical developments as well
as on simulations showing the efficacy of these techniques.
Main list of topics
- Preliminaries and
Motivations for a Probabilistic Approach
- Uncertain Systems
- The Interplay of Probability and Robustness
- Randomized Algorithms
- Sample Size Bounds and Statistical Learning Theory
- Sample Generation Theory
- Probabilistic Robust Design with Linear Quadratic Regulators
- Probabilistic Design for Linear Parameter-Varying Systems
- Randomized Algorithms for Model Predictive Control
- Applications (robustness of high-speed networks, stability of quantized
sampled-data systems, performance of flexible structures)
- Discussion of Open Research Problems
Slides download