Abdelhaq El Jai

Regional Controllability with Cellular Automata Models

In relation with spatio-temporal systems theory some regional analysis aspects were recently developed [6, 24] and well studied in continuous systems described by partial differential equations. The purpose of this paper is to give a comparative study of the regional controllability by means of cellular automata models. We show through various examples how the main features of regional controllability may be simply described and implemented by cellular automata approach. To solve this problem, we propose one of the most efficient evolutionary techniques based on genetic algorithms.

Regional Observation and Sensors

Regional Observation and Sensors The purpose of this short paper is to provide original results related to the choice of the number of sensors and their supports for general distributed parameter systems. We introduce the notion of extended sensors and we show that the observation error decreases when the support of a sensor is widened. We also show that the observation error decreases when the number of sensors increases.

How to Compensate a Spreading Disturbance for a Class of Nonlinear Systems

How to Compensate a Spreading Disturbance for a Class of Nonlinear Systems We consider a system which is assumed to be affected by an expanding disturbance which occurs at the initial time. The compensation of the disturbance is accomplished by extending the concept of remediability to a class of nonlinear systems. The results are implemented and illustrated with a nonlinear distributed model.

Weak and exact domination in distributed systems

Weak and exact domination in distributed systems In this work, we introduce and examine the notion of domination for a class of linear distributed systems. This consists in studying the possibility to make a comparison between input or output operators. We give the main algebraic properties of such relations, as well as characterizations of exact and weak domination. We also study the case of actuators, and various situations are examined. Applications and illustrative examples are also given. By duality, we extend this study to observed systems. We obtain similar results and properties, and the case of sensors is equally examined.

Input and output parameters domination in infinite dimensional systems

This work concerns the systems analysis of a class of distributed parameter systems, and more precisely the notions of weak and exact domination. We introduce and we study these concepts for controlled and observed systems. This consists to study the possibility of comparison of systems and input-output parameters. We give the main characterization results and properties of the notion of domination for control operators and then for observation operators. We show that there is a duality between these two cases. We also examine the case of actuators and sensors. Various other situations and extensions are considered, applications are also given. The relationship between the domination and other concepts as controllability, observability and compensation are examined.