Mini-course Technical Program:
June 28th - July 3rd, 1999
Monastery of Arrįbida, Arrįbida,
PORTUGAL
Monday (June 28th)
4:30PM-5:20PM Introduction
A Portuguese Multidisciplinary Research Experience
driven by a Systems and Control perspective
Joćo Sentieiro
- Instituto Superior Técnico
In this talk I will describe the research and development activities that
are currently being pursued at the Institute for Systems and Robotics (ISR-Lisbon
Pole). Special emphasis will be placed on explaining how a common systems
and control background of the researchers involved was instrumental
in setting-up an innovative multidisciplinary research program. For
the different areas of application in which ISR researchers are involved
I will identify the related systems and control problems that warrant further
research.
5:30PM-7:30PM Lecture
Tuesday (June 29th)
The Behavioral Approach to Systems Modeling and Control
Jan Willems
- University of Groningen
The aim of these lectures is to introduce some of the main features of
the behavioral approach as a mathematical framework for discussing systems
and control. Three main aspects of this vantage point are:
(i) the behavior as the basic mathematical concept
that a model specifies
(ii) the role of latent variables in first principles modeling
(iii) interconnection as the main aspect of control
10:00AM-11:25AM The Logic of Modeling, Controllability and
Observability
In this first lecture we will explain some essential features of the behavioral
approach as a logic of modeling dynamical phenomena. We will view
a model as an exclusion law, and explain behavioral equations in this setting.
Next, we will turn to the distinction between manifest and latent variables
and introduce the elimination problem in the context of systems described
by differential equations. We will illustrate how all this fits modeling
interconnected systems by tearing and zooming. Finally, we will translate
all this into a formal mathematical framework.
We will subsequently turn to linear dynamical systems. We will
introduce the concept of controllability in the behavioral setting and
contrast it with the classical state space oriented version of controllability.
The notion of observability deals with systems with latent variables and
has to do with the possibility of deducing the behavior of the latent variables
from the behavior of the manifest ones. Tests for controllability
and observability in terms of the system parameters will be derived.
11:40AM-1:00PM Control as Interconnection
The second lecture will be dedicated to questions of automatic control.
We will view control as interconnection and contrast this point of view
with the usual feedback processor structure used in intelligent control.
We will subsequently study a number of control problems, notably stabilization,
linear-quadratic, and H-infinity control. The algorithms which emerge
in this setting are more akin to spectral factorization and the Riccati
equation can be viewed as a special case. Our basic purpose, however,
is to set up algorithms which pass immediately from the plant specification
to the controller specification.
References:
J.C. Willems, "Paradigms and puzzles in the theory of dynamical systems",
IEEE Transactions on Automatic Control, Volume 36, pages 259-294,
1991.
J.C. Willems, "On interconnections, control, and feedback", IEEE Transactions
on Automatic Control, Volume 42, pages 326-339, 1997.
Algorithms for the Design of Networks of Unmanned
Aerial Vehicles
At Berkeley we have been interested in design schemes for network of
complex networks of semi-autonomous agents. These networks are characterized
by interaction between discrete decision making and continuous control.
The control of such systems is often frequently organized in hierarchical
fashion to obtain a logarithmic decrease in complexity associated with
the design, We have used as examples three classes of systems to motivate
the design approach:
-
Intelligent Vehicle Highway Systems (IVHS)
-
Air Traffic Management Systems (ATMS)
-
Unmanned Aerial Vehicles
Over the last five years or so, a group of us have developed a set of design
approaches which are aimed at designing control schemes which are live,
deadlock free, and "safe". Our design methodology is to be considered an
alternative to the verification based approaches to hybrid control systems
design, and is an interesting blend of game theoretic ideas, fault handling
in a probabilistic framework, mathematical and temporal logic and planning
ideas from robotics. In these talks, we will focus on design problems
involved in coordinating groups of Unmanned Aerial Vehicles (UAVs). Problems
to be addressed include:
-
Rapid prototyping of real time control laws: a hybrid systems design and
simulation environment.
-
Mode Switching and envelope protection.
-
Vision based control for navigation.
-
Mission planning for multi-UAV missions.
The work is joint with Datta Godbole, Hyoun Jin Kim, John Koo, John Lygeros,
Omid Shakernia, David Shim, and Claire Tomlin.
4:30PM-5:55PM Lecture 1
6:10PM-7:30PM Lecture 2
Wednesday (June 30th)
Constructive Nonlinear Control
Petar
Kokotovic - University of California, Santa Barbara
A tutorial presentation will be given of analytical tools and procedures
for systematic feedback design of several classes of nonlinear systems.
The emphasis will be on designs which achieve large regions of stability
in the presence of strong nonlinearities, disturbances and unknown parameters.
Some of the basic design tools are passivation and inverse optimality,
combined with Lyapunov and input-to-state stability. Passivation designs
are expanded into recursive procedures -- backstepping and forwarding.
For systems with unknown parameters adaptive versions of these procedures
are developed.
For systems with bounded disturbances, a design is presented which is
locally optimal in the H-infinity sense, while globally it possesses an
inverse optimal property. Illustrative application examples include
designs for axial compressors and diesel engines.
10:00AM-11:25AM Lecture 1
11:40AM- 1:00PM Lecture 2
Topics in Nonlinear Control
4:30PM-5:55PM Regulation and Tracking in Nonlinear
Systems
The problem of controlling the output of a system so as to achieve asymptotic
tracking of prescribed trajectories and/or asymptotic rejection of undesired
disturbances is a central problem in control theory. A classical
setup in which the problem was posed and successfully addressed -- in the
context of linear, time-invariant and finite dimensional systems
-- is the one in which the exogenous inputs, namely commands and disturbances,
may range over the set of all possible trajectories of a given autonomous
linear system, commonly known as the exosystem. Recently,
this approach was successfully extended also to nonlinear systems.
The purpose of this lecture is to review some relevant features of the
theory of output regulation for nonlinear systems as well as to outline
the major problems on which the research is presently progressing.
6:10PM-7:30PM Stabilization via Output Feedback of Uncertain
Nonlinear Systems
One of the basic fundamental issues in control theory is the ability to
design a feedback law to the purpose of robustly stabilizing a system,
in the presence of structured uncertainties, such as parameter variations,
and/or unstructured uncertainties, such as unmodeled dynamics. In
this lecture, we describe a new approach for constructing (robust) stabilizers
via output feedback, which do not necessarily appeal to the principle of
"composing a state feedback with (direct or indirect) estimates of the
state". In particular, we describe a recursive stabilization scheme,
which essentially -- at each stage -- only uses "small-gain" and/or "high-gain"
arguments to determine the values of certain design parameters. For
convenience, this method is described first in the case of linear systems,
when it is always applicable under no extra hypothesis other than the obvious
one of "stabilizability by output feedback", and then in the case of nonlinear
systems.
Thursday (July 1st)
A Geometric Approach to Nonlinear Control
Over the last ten years the use of differential geometry to study nonlinear
control problems has assumed increasing importance. This is due,
in part to the realization that there are a large number of practical problems
in mechanics and electrical machine theory that can be effectively treated
only in this way. In this lecture I will explain this theory placing
an emphasis on solved problems and intuition. Some applications to
pattern generation in biology will be included.
10:00AM-11:25AM Lecture 1
11:40AM- 1:00PM Lecture 2
Control Using Logic and Switching
By a logic-based switching controller is meant a controller whose subsystems
include not only familiar analog dynamical components, but event-driven
logics and switches as well. The overall models of systems composed
of such logics together with the processes they are intended to control,
are concrete examples of what might are sometimes called "hybrid dynamical
systems.'' In these two lectures descriptions will be given of a number
of different classes of hybrid systems of this type -- each consists of
a continuous-time process to be controlled, a family of fixed-gain
or variable-gain candidate controllers, and an "event-driven switching
logic.'' Each switching logic is a simple, easy to implement strategy
capable of determining in real time which candidate controller should
be put in feedback with a process in order to accomplish a desired task.
Logic-based switching can be found, for example, in flight control, in
commercial aircraft engine control, in chemical process control,
in various automobile systems, and in many other physical device endowed
with some form of intelligence. Major reasons for introducing
logic and switching are to deal with changes in operating conditions, with
uncertainty, with unforeseen events or to avoid performing difficult tasks
{e.g., precise equipment calibration} which might otherwise
be necessary were one to consider only conventional controls.
These lectures will focus mainly on logic-based switching controls intended
to deal with uncertainty or unpredictable changes in process dynamics.
Illustrations will be given of many of the concepts discussed
using simulations and experimental results.
10:00AM-11:25AM Lecture 1
11:40AM- 1:00PM Lecture 2
Friday (July 2nd)
Challenging Problems in Ocean Robotics
António Pascoal - Instituto Superior Técnico
Worldwide, there is currently great interest in the development of robotic
ocean vehicles for the exploration and exploitation of the oceans. The
design and operation of such vehicles pose considerable challenges to system
theoreticians, who must strive to develop efficient methods for plant
design to minimize energy expenditure, as well as sophisticated algorithms
for navigation, guidance, and control for increased vehicle performance
and reliability. In this talk I will address some interesting problems
in system theory that arise in the design of ocean robotic vehicles, describe
their solutions, and bring up related theoretical problems that warrant
further investigation. In the first part of the talk I will focus on the
problems of trajectory tracking, path following, and vehicle stabilization
to a point in 3-D space with a desired orientation. The mathematical tools
used borrow from Lyapunov-based design techniques and from the theory of
hybrid systems. Applications in the control of underactuated vehicle are
discussed in detail. The second part will address the important problem
of combined plant/controller optimization by resorting to the theory of
Linear Matrix Inequalities. Finally, the last part of the talk will tackle
the problem of nonlinear navigation systems using the theory of polytopic
systems. Throughout the presentation I will use concrete examples from
the area of ocean robotics to better illustrate the problems described.
The topics addressed are the subject of on-going research by the group
of Dynamical Systems and Ocean Robotics of the Institute for Systems and
Robotics of Lisbon, Portugal.
10:00AM-12:30AM Lecture
12:45AM- 1:00PM Conclusion
For more information please contact:
Joćo
P. Hespanha - hespanha at usc.edu
U.C. Berkeley - Dept. EECS, 275M Cory Hall #1770, Berkeley, CA 94720-1770.
Last update on 4/4/99.