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.
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.