Research Interests of Samira EL YACOUBI
My
research fields are mainly focused on Modelling, Analysis, Control and
Simulation of spatiotemporal Systems modelled by Partial Differential Equations
and Cellular Automata models, with various applications in environmental, biological
or engineering systems.
Analysis
and Control of Distributed Parameter Systems:
Systems theory concerns the study of abstract
properties and techniques for analysing the systems behaviour taking into
account observation and control. Spatiotemporal systems, studied in terms
of inputs (controls) and outputs (observations), called distributed parameter
systems are traditionally modelled by partial differential equations. The area
of distributed parameter systems concerns the investigation of the control law,
stability and structures optimization of the systems. These notions that are
relatively simple and well developed for
lumped models become very hard when the space variable is added.
An extensive study of distributed
parameter systems via sensors and actuators have been done by A. El Jai and A.
J. Pritchard. Various developments have concerned the optimization of
input-output structures regarding the spatial support, the distribution
function and the number of actuators and sensors for hyperbolic and parabolic
systems. My contribution in this filed has concerned the minimization of
the number of actuators in parabolic systems and the relations between
actuators structures and final-constraint minimum energy problem.
In the last
decade, concentrating on geographic spread phenomenon which occurs in various
fields ranging from ecology and biology to medical science and species
abundance, the spreadability concept has been introduced and studied
in terms of continuous PDE’s. The idea is related to the fact that
the subdomains where the state of a distributed system is enforced to
obey a spatial property are no decreasing. Several developments have been
done in the field in collaboration with A. El Jai. We have also shown that it is
possible to make spreadable a system described by PDE’s, by means of
appropriate controls. The notion of spray controls was then developed.
Cellular Automata in
systems theory:
Cellular Automata (CA) are a class of spatially and
temporally discrete mathematical systems characterized by local interactions.
Even if the interaction is based on simple local rules, the resulting
structures from the CA evolution may be extremely complex.
CA were first introduced by Stanislaw Ulam and John von
Neumann in the late 1940s as formal models of self-reproducing organisms. Since
their conception, CA have been used to model spatial dynamics across the
spectrum of applied science and a wide literature has been devoted to the area
including applications to physics (fluid dynamics, reaction-diffusion,
solidification of crystals, interfacial diffusion fronts), environmental
processes (population genetics, interrelations between preys and predators in
ecosystems, plant growth, propagation of infectious diseases, the effects of
fire and dispersal on spatial patterns in forests) or engineering (geographical
information systems, routing traffic in an urban area, image processing,
cryptography, ). More recently, with the emergence of powerful massively
parallel architectures, a lively interest in CA models and their extensions has
been observed particularly for inhomogeneous environments and complex
dynamics. CA models have been extensively used as a modelling tool
to approximate nonlinear discrete and continuous dynamical systems. We proposed
to introduce control and observation in CA in an appropriate way to make them
more useful in systems theory.
The study of analysis
and control aspects by means of CA models which range from the inverse problems
category needs the use of no conventional optimization methods since the
considered cost functions are not continuous and mostly of gradient zero
wherever they are defined. In this context, global random search methods are
more appropriate, particularly, the heuristics of evolutionary algorithms which
have received in the last two decades increasing attention regarding their
potential as optimization tools for engineering problems.
As an extension of Cellular Automata for fluid dynamics, we have used Lattice Boltzmann models in the
framework of the FNS project “Modelling
and control of water flow in open-channels by a lattice Boltzmann method” as an alternative to the conventional shallow
water equation based on nonlinear PDEs. This job has been done in collaboration with
Pr. Bastien Chopard and our joined PhD student Olivier Marcou. Thanks to our collaboration with the LCIS-Valence, the model validation used an
experimental micro Canal at ESISAR high school.
Modelling and Simulation of spatiotemporal systems by means of Cellular
Automata.
Modelling using CA has the advantage of being conceptually easier than
PDE and evolution of such systems is easily implemented on computer avoiding rounding
or approximation errors. I have successfully used CA to model and simulate a
large range of applications including spatial spread of epidemics, regulation
of irrigation canals, ocean acidification, and forest fire spread and so on. Among
these studies, some have been carried out within the framework of collaborative
projects (LUCIFER, MedSea, FNS, OMS). Some emergent spatial properties have been
highlighted using concepts of systems
analysis. With the introduction of control in CA models, the notion of spray and
protector controls have been studied in relation with spreadability and
vulnerability concepts, respectively.
