This paper presents a method to deal with an extension of regional gradient observability developed for parabolic system [1,2] to hyperbolic one. This concerns the reconstruction of the state gradient only on a subregion of the system domain. Then necessary conditions for sensors structure are established in order to obtain regional gradient observability. An approach is developed which allows the reconstruction of the system state gradient on a given subregion. The obtained results are illustrated by numerical examples and simulations
The purpose of this paper is to introduce the notion of regional boundary asymptotic gradient reduced order observer (Γ*AGRO-observer) in distributed parameter systems. More precisely, we explore and discuss the existing of this approach in which estimates a considered sub-region Γ* for the considered domain boundary. Thus, we show that the approach is enables to build the unknown part of the state gradient when the output function gives part of information about the region state. Furthermore, the characterization of this notion depend on regional boundary gradient strategic sensors (RBG-strategic sensors) concept in order that regional boundary asymptotic gradient reduced order observability (Γ*AGRO-observability) to be achieved and analyzed. Finally, an application is presented to various situations of strategic sensors for internal case.
The goal of this work is demonstrating, through the gradient observation of a of type linear ( -systems), the possibility for reducing the effect of any disturbances (pollution, radiation, infection, etc.) asymptotically, by a suitable choice of related actuators of these systems. Thus, a class of ( -system) was developed based on finite time ( -system). Furthermore, definitions and some properties of this concept -system and asymptotically gradient controllable system ( -controllable) were stated and studied. More precisely, asymptotically gradient efficient actuators ensuring the weak asymptotically gradient compensation system ( -system) of known or unknown disturbances are examined. Consequently, under convenient hypothesis, the existence and the uniqueness of the control of type optimal, guaranteeing the asymptotically gradient compensation system ( -system), are shown and proven. Finally, an approach that leads to a Mathematical approximation algorithm is explored.
In this paper we interest to the regional gradient remediability or compensation problem with minimum energy. That is, when a system is subjected to disturbances, then one of the objectives becomes to find the optimal control which compensates regionally the effect of the disturbances of the system, with respect to the regional gradient observation. Therefore, we show how to find the optimal control ensuring the effect compensation of any known or unknown disturbance distributed only on a subregion of the geometrical evolution domain, with respect to the observation of the gradient on any given subregion of the evolution domain and this in finite time. Under convenient hypothesis, the minimum energy problem is studied using an extension of the Hilbert Uniqueness Method (HUM). Approximations, numerical simulations, appropriate algorithm, and illustrative examples are also presented.
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