Contributed by: A.Zinober@sheffield.ac.uk

        WORKSHOP ON FLATNESS OF NONLINEAR SYSTEMS

Two-day Workshop Meeting : The University of Sheffield

             Date:   25 -- 26 July 1996

FLATNESS OF NONLINEAR SYSTEMS: THEORY AND APPLICATIONS
           (with partial funding from EPSRC, UK)

Organizers: Professor Alan Zinober and Dr Pin Liu

School of Mathematics and Statistics
The University of Sheffield
Sheffield  S10 2TN

A.Zinober@sheffield.ac.uk

An exciting new area of research in control theory with the
possibility of much practical application, is the Differential
Flatness of Nonlinear Control Systems. This is a nonlinear extension
of Kalman's controllability theory arising from new results using a
differential algebraic approach (Fliess and co-workers). A "flat''
control system is linearizable by endogenous feedback. It is known
that controllable linear systems are flat. Non-flat control systems
cannot be controlled by feedback control. Typical non-flat examples
are the ball and beam problem; simple, double and variable length
pendulums;  n-trailer manoeuvering problem. The major property of
differential flatness is that the state and input variables of
nonlinear systems, represented in state-space form, can be expressed
directly in terms of the flat output and a finite number of its
derivatives, without integrating any differential equation. This
property should be extremely useful in the solution of tracking
control problems and other related control problems.

Numerous backstepping and recursive-interlacing methods for
regulating nonlinear systems have been studied since 1991. They have
wide industrial application to robust, adaptive and tracking control
problems including the regulation of Pulse-Width-Modulation (PWM)
DC-to-DC power converters, DC motors, jet engine control, active car
suspensions and flexible robotic problems.

One of the most interesting unsolved questions is: what is the
mathematical relationship between the backstepping approaches
(sometimes combined with sliding mode control) and the resulting
flatness of a system? It has been shown in 1995 by the organizers
that recursive-interlacing control is able to regulate certain
non-flat systems. What is the underlying "flattening'' mechanism?
Furthermore, higher-order sliding mode schemes could possibly be
applied to the control of some non-flat systems. Is there any
underlying relationship between recursive-interlacing and
higher-order sliding mode methods?

The aim of the workshop meeting is to discuss the above fundamental
questions with the European originators of flat systems theory, and
other researchers in sliding mode control, backstepping techniques
and other related areas in nonlinear control systems. It is hoped
that this initial meeting will lead to further collaborative
research which should result in greater theoretical insight, and
also yield practical nonlinear control algorithms for hitherto
problematic industrial problems.

Invited speakers, additional to Sheffield contributors, will
include:

Professors Michel Fliess (CNRS, Paris), Hebertt Sira-Ramirez
(Merida)), Francoise Lamnabhi-Lagarrigue (CNRS, SUPELEC,
Gif-sur-Yvette) and Drs Sarah Spurgeon and Xiao-Yun Lu
(Engineering Department, Leicester University).

On the afternoon of 24th July 1995 we are planning to have
presentations in other areas of nonlinear control theory.

Please send an email to A.Zinober@sheffield.ac.uk to register your
interest in this workshop. Please advise whether you have research
results which may be suitable for presentation.  You will be sent
by email further information about this meeting.