A. El Jai

Regional controllability of distributed parameter systems

The purpose of this paper is to show how one can achieve regional controllability for distributed systems. First, we give a definition and some properties of this new concept, then we concentrate on the determination of a control achieving regional controllability with minimum energy. A direct method is developed and is illustrated by a hyperbolic system with point control and a parabolic system with zone control. We also give an important remark that converts the problem into a constrained optimization one.

Cellular automata modelling and spreadability

The purpose of this paper is to give an alternative modelling approach to spatiotemporal systems which is more satisfactory from an implementation point of view: a discrete approach based on cellular automata. Moreover, we concentrate on geographic spread phenomenon which occurs in various fields ranging from ecology and biology to medical science and species abundance. Spreadability concept and spray control [1,2] has been much less studied in continuous systems because of the difficulties in partial differential equations modelling approach. We recall the main features of spreadability as developed in [1] and show that they may be described and implemented very simply by cellular automata approach. Various examples illustrate the developed results.

Regional observability of distributed systems

The aim of this paper is to develop the concept of regional observability for distributed systems. This original concept is closer to practical considerations since it only requires the observation of the state on a given subregion. We show by means of an example that it is a weaker concept and we describe two approaches. The first one is state space based and can be easily implemented for numerical simulations. Then a second approach leads to the estimation of the state on the considered subregion with a zero residual state.

Distributed systems analysis via sensors and actuators

Abstract The purpose of this paper is to give some results related to the link between actuator and sensor structures and systems analysis. Abstract concepts of actuators and sensors are introduced and applied to the controllability and observability of systems described by partial differential equations. The developed results are illustrated by many examples of specific geometries and systems.

Spreadable distributed systems

We present in this paper an original concept in the theory of dynamical distributed systems. The motivation is based on spreading phenomena which generally arise in biogeographical processes (forests, populations, pollution,...). Our objective is to provide a mathematical description and characterization of this concept. The notion of spray control will be introduced and applied to linear distributed systems by solving quadratic equations in Hilbert spaces.

Regional observability and sensor structures

Abstract In various distributed systems we are interested in the knowledge of the state of a given sub-region. The aim of this paper is to introduce the concept of regionally strategic sensors for a class of distributed parameter systems. This emphasizes the spatial structure and location of the sensors in order that regional observability can be achieved. For different geometrical situations we give the characterization of regional strategic sensors. We also give the dual results for the characterizations of regional strategic actuators.

LUCAS: an original tool for landscape modelling ☆

Abstract The aim of this paper is to present an original modelling tool for biogeographical systems. This software named LUCAS (LUcifer Cellular Automata Simulator) has been developed within the European programme LUCIFER (Land Use Change Interactions with Fire in MeditERrranean landscapes). LUCAS constitutes general software, based on coupling local dynamics described by a set of nonlinear ordinary differential equations with a cellular automaton spatial model. Various parameters related to the system considered can be chosen by the user. Numerous possibilities of LUCAS are illustrated through a real application regarding the catchment of a Polish river.

Sensors and regional boundary state reconstruction of parabolic systems

The aim of this paper is to explore the concept of observability in the case where the state is to be observed only on a part of the boundary. The developed approach takes into account the structure of the sensors; the case of pointwise, zone and boundary sensors are considered.

Spreadability of transport systems

The spreadability concept of distributed parameter systems was essentially motivated by environment systems and various environment systems are governed by transport equations. The aim of this paper is to study the spreadability of systems modelled by transport equations. We shall be concerned by linear autonomous systems as well as nonlinear systems. For those systems we give characterisation results for spreadability.

New approach of spreadability

In this paper, we present a new approach of spreadability (A-spreadability) which generalizes that introduced by El Jai and Kassara [1,2] in 1994. This approach explores a more general mathematical framework for distributed parameter systems. The control which makes a system, A-spreadable (A-spray control) is also introduced and characterized in the case of linear systems.