Regionally Gradient Efficient actuators and Sensors

In this paper, we introduce and characterize the notions of regional gradient remediability and regionally gradient efficient actuators. We study their relationship with regional gradient controllability and sensors. As an application, we consider the case where the domain is one and two dimension. nbs

Regional Boundary Gradient Detectability in Distributed Parameter Systems

The aim of this paper is study and explore the notion of  the regional boundary gradient detectability in connection with the choice of strategic gradient sensors on sub-region of the considered system domain boundary. More precisely, the principal reason behind introducing this notion is that the possibility to design a dynamic system (may be called regional boundary gradient observer) which enable to estimate the unknown system state gradient. Then for linear infinite dimensional systems in a Hilbert space,  we give various new results related with different measurements. In addition, we provided a description of the regional boundary exponential gradient strategic sensors for completion the regional boundary exponential gradient observability and regional boundary exponential gradient detectability. Finally, we present and illustrate the some applications of sensors structures which relate by regional boundary exponential gradient detectability in diffusion distributed parameter systems

REGIONAL GRADIENT STRATEGIC SENSORS CHARACTERIZATIONS

In the present paper, the characterizations of regional gradient strategic sensors notions have been given for different cases of regional gradient observability. The results obtained are applied to two dimensional linear infinite distributed system in Hilbert space where the dynamic is governed by strongly continuous semi-group. Various cases of regional strategic sensors are considered and analyzed in connection with regional gradient strategic sensors concepts. Also, we show that there is a various sensors which are not gradient strategic in usual sense for the considered systems, but may be regionally gradient strategic of this system

Regional Boundary Asymptotic Gradient Full-Order Observer in Distributed Parabolic Systems

The purpose of this paper is to explore the concept of the regional boundary asymptotic gradient full order observer (RBAGFO-observer) in connection with the characterizations of sensors structures. Then, we present various results related to different types of measurements, domains and boundary conditions for distributed parameter systems (DPSS) in parabolic systems problem.  The considered approach of this work is derived from Luenberger observer theory which is enable to estimate asymptotically the state gradient of the original system on a sub-region of the domain boundary  in order that the RBAGFO-observability notion to be achieved. We also show that there exists a dynamical system for the considered system is not BAGFO-observer in the usual sense, but it may be regional RBAGFO-observer

REGIONAL EXPONENTIAL GENERAL OBSERVABILITY IN DISTRIBUTED PARAMETER SYSTEMS

The purpose of this paper is to explore the concept of regional exponential general observability for a class of distributed parameter systems, in connection with the regional strategic sensors. Then, we give characterization of the strategic sensors in order that exponential regional general observability can be achieved. Furthermore, we apply these results to one and two dimensional systems, and various cases of sensors are considered and discussed. We also show that there exists a dynamical system for diffusion system is not exponentially general observable in the usual sense, but it may be regionally exponentially general observable