Theses
Control
and observation of systems with variable delays - Theory and applications
Alexandre Seuret
(PhD defended Oct. 4th, 2006), Contact: as389
"AT" leicester.ac.uk
This work deals with the control and the observation
of linear or nonlinear systems with time-varying delays, as well as
some related experimentations: sampling, networked control systems and
control with visual feedback. For such so-called "hereditary"
systems, the behavior depends not only on current information but also
depends on past times. The first chapter deals with the presentation
of the context and of theoretical grounds of this work. The second chapter
concerns the problem of exponential stability and stabilization of systems
with time-varying delays. Here, the speed performance is then taken
into account in the control design. The third chapter generalizes these
results to disturbed systems the behavior of which do not amount to
the linear and time invariant models. We consider in particular two
practical problems: uncertainties due to parameter variations and saturated
control inputs. In the fourth chapter, we focuss on continuous systems
subject to sampled-data control. An input-delay approach is proposed
which allows one to apply classical in "continuous-time" results.
The fifth chapter is devoted to the observation of delay systems. The
worked-out results hold for systems with known delays (which case often
appears in the literature), as well as for unknown delays (which is
a sensitive and less explored case) The last chapter presents some applicative
problems where the theoretical results find their justification. We
specially focuss on remote control trough an internet network and on
a visual feedback control of mechanical benchmark.
Modelling
and identification of aircraft behaviours in turbulent flight using
time delay models
Francois Veysset
(PhD defended Nov. 17th, 2006), Contact: francois.veysset
"AT" onera.fr
This study relates to the mathematical
representation of the behaviour of the aircraft in atmospheric turbulence
as well as the identification of the dynamics induced by the gust. The
approach falls under a prospect for identification from tests carried
out in the Flight Analysis Laboratory of the DCSD of ONERA in Lille.
To achieve this, the plane is considered into various elements which
consist in the fuselage, the wing and the tail. The obtained model incorporates
unsteady effects, modelled via Küssner functions, and clearly clarified
delays. Results in simulation confronting our model with recent work
on modelling highlight the fact that these phenomena have to be taken
into account in the modelling. The comparison with experimental data
shows that the tendencies observed during the tests are confirmed for
our model. The algebraic identification method initiated by Fliess and
Sira-Ramirez in 2003 was extended to time delay systems. This technique
based on the distributional framework allows to identify some delays
and parameters of our model.
Definitions
and analysis of stabilities for nonlinear time-delay systems
Nima Yeganefar
(PhD defended Nov. 24th, 2006), Contact: nimnima
"AT" gmail.com
Currently at ATER in Ecole Centrale
de Lille
The focus of this work is the notion
of stability for nonlinear time-delay systems using the Lyapunov time-domain
approach. Five different chapters are devoted to stability properties.
After a general introduction, the second chapter proposes an unconventional
approach --- based on Lyapunov-Krasovskii functionals --- to the problem
of input-output stability. The descriptor form is used to guaranty this
stability by solving linear matricial inequalities (LMI). The next chapter,
finite-time stability, is, as far we know, the first work on this topic
for time-delay systems. Specifically several results are given for the
stabilization problem on linear systems with delayed input. The first
examples of finite-time stable delayed systems are also given. The fourth
chapter is devoted to the input-to-state stability, which is generalized
to the delay case. Sufficient conditions are given to check this stability
using Lyapunov-Krasovskii methodology. The interest of the study based
on perturbation problems is highlighted and some interesting perspectives
for further research are given. The last part of the work is devoted
to the study of practical stability used in solving the so-called chattering
problem in sliding mode control. As the control is rapidly switching,
chattering may appear on the state space --- for instance in practical
applications when the control dynamics can no longer be neglected. The
chattering problem is carefully analyzed and many simulations are given
to demonstrate the advantages of the proposed solution.
Methodology
for the analysis and the control of time-delay systems
Michael Di Loreto,
IRCCyN, UMR CNRS 6597, Nantes, France, Contact: michael.di-loreto"AT"
insa-lyon.fr
Currently at Insa-Lyon, LAI
69621, Villeurbanne, France
This thesis deals with methodologies
for the analysis and the control of linear time-delay systems. The first
is the geometric approach. The linear time-delay systems can be modelled
by a quadruple of matrices with entries over a ring. Then the geometric
approach makes it possible to analyze a system with the properties of
the modules over a ring. In this part, we develop a well argued analysis
of invariance concepts for application in system control. Some logical
relationships among various classes of controlled and conditioned invariant
modules are established. The second approach is based on algebraic concepts.
In this approach, the use of pseudo-polynomials, which are operators
with a finite number of derivatives, pointwise and distributed delays,
is fundamental. More precisely, the ring of proper and stable fractions
of pseudo-polynomials is used in the stabilization problem. The solution
gives us a parameterization of all stabilizing controllers and closed-loop
transfer matrices. Then, various control problems are addressed, like
the disturbance rejection, the disturbance attenuation, the exact or
approximated model matching, or the optimal l1 control. Finally, the
last approach is about numerical calculus. In this part, the interval
analysis is used to solve hard numerical problems, like the robust stability,
the stabilization, or the verification of a gauge for performances and
robustness.
Habilitation
thesis, French "Habilitation à diriger des recherches",
University of Lille 1, 3 October 2006.
Contribution
to the Identification of Delay Systems
Lotfi Belkoura,
Associate Professor at the University of Lille, Contact: Lotfi.Belkoura
"AT" univ-lille1.fr
In the first part of this thesis,
parameter identifiability is studied for a class of finite and infinite
dimensional systems described by convolution equations. The notion of
sufficiently rich input which enforces identifiability is also addressed
and the results are obtained assuming knowledge of solutions on a bounded
time interval. The second part deals with on-line identification of
delay systems. It is based on new non-asymptotic algebraic estimation
techniques. A concrete case-study and an application to transmission
delays are discussed. Several successful numerical simulations are provided
even with noisy data.
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