Mini-course Technical Program:

System Theory on the Eve of the 21st Century

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.
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

Shankar Sastry and Joćo P. Hespanha - University of California, Berkeley

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:
  1. Intelligent Vehicle Highway Systems (IVHS)
  2. Air Traffic Management Systems (ATMS)
  3. 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:
  1. Rapid prototyping of real time control laws: a hybrid systems design and simulation environment.
  2. Mode Switching and envelope protection.
  3. Vision based control for navigation.
  4. 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

Alberto Isidori - University of Rome

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

Roger Brockett - Harvard University

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

A. Stephen Morse - Yale University

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
U.C. Berkeley - Dept. EECS, 275M Cory Hall #1770, Berkeley, CA 94720-1770.

Last update on 4/4/99.