The aim of this paper is to study the notion of the gradient observability on a subregion w of the evolution domain W and also we consider the case where the subregion of interest is a boundary part of the system evol...The aim of this paper is to study the notion of the gradient observability on a subregion w of the evolution domain W and also we consider the case where the subregion of interest is a boundary part of the system evolution domain for the class of semilinear hyperbolic systems. We show, under some hypotheses, that the flux reconstruction is guaranteed by means of the sectorial approach combined with fixed point techniques. This leads to several interesting results which are performed through numerical examples and simulations.展开更多
The aim of this brief paper is to give several results concerning the regional controllability of distributed systems governed by semi-linear parabolic equations. We concentrate on the determination of a control achie...The aim of this brief paper is to give several results concerning the regional controllability of distributed systems governed by semi-linear parabolic equations. We concentrate on the determination of a control achieving internal and boundary regional controllability. The approach is based on an extension of the Hilbert Uniqueness Method (HUM) and Schauder’s fixed point theorem. We give a numerical example developed in internal and boundary sub region. These numerical illustrations show the efficiency of the approach and lead to conjectures.展开更多
The aim of this work is to study the notion of the gradient observability on a subregion?ω of the evolution domain?Ω for a class of semilinear hyperbolic systems. We show, under some hypothesis, that the gradient re...The aim of this work is to study the notion of the gradient observability on a subregion?ω of the evolution domain?Ω for a class of semilinear hyperbolic systems. We show, under some hypothesis, that the gradient reconstruction is achieved following sectorial approach combined with fixed point techniques. The obtained results lead to an algorithm which can be implemented numerically.展开更多
This paper is focused on studying an important concept of the system analysis, which is the regional enlarged observability or constrained observability of the gradient for distributed parabolic systems evolving in th...This paper is focused on studying an important concept of the system analysis, which is the regional enlarged observability or constrained observability of the gradient for distributed parabolic systems evolving in the spatial domain Ω We will explore an approach based on the Hilbert Uniqueness Method (HUM), which can reconstruct the initial gradient state between two prescribed functions f1 and f2 only in a critical subregion ω of Ω without the knowledge of the state. Finally, the obtained results are illustrated by numerical simulations.展开更多
In this paper, we shall study the stabilization and the robustness of a constrained feedback control for bilinear parabolic systems defined on a Hilbert state space. Then, we shall show that stabilizing such a system ...In this paper, we shall study the stabilization and the robustness of a constrained feedback control for bilinear parabolic systems defined on a Hilbert state space. Then, we shall show that stabilizing such a system reduces stabilization only in its projection on a suitable subspace. For this purpose, a new constrained stabilizing feedback control that allows a polynomial decay estimate of the stabilized state is given. Also, the robustness of the considered control is discussed. An illustrating example and simulations are presented.展开更多
In this paper, we study the notion of the enlarged observability for distributed parabolic systems, where the aim is to reconstruct the initial state between two prescribed profiles P1 and P2 in an internal subregion ...In this paper, we study the notion of the enlarged observability for distributed parabolic systems, where the aim is to reconstruct the initial state between two prescribed profiles P1 and P2 in an internal subregion c0 of the evolution domain f2. We give some definitions and properties of this concept, and then we solve the problem of the reconstruction of initial state using the Hilbert Uniqueness Method （HUM）. This leads to several interesting results which are performed through numerical example and simulations.展开更多
The aim of this paper is to explore the concept of observability with constraints of the gradient for distributed parabolic system evolving in spatial domain Ω, and which the state gradient is to be observed only on ...The aim of this paper is to explore the concept of observability with constraints of the gradient for distributed parabolic system evolving in spatial domain Ω, and which the state gradient is to be observed only on a part of the boundary of the system evolution domain. It consists in the reconstruction of the initial state gradient which must be between two prescribed functions in a subregion Γ of Ω. Two necessary conditions are given. The first is formulated in terms of the subdifferential associated with a minimized functional, and the second uses the Lagrangian multiplier method. Nu-merical illustrations are given to show the efficiency of the second approach and lead to open questions.展开更多
The paper aims to extend the notion of regional observability of the gradient to the semilinear hyperbolic case, in order to reconstruct the gradient of the initial conditions in a subregion w of the domain evolution ...The paper aims to extend the notion of regional observability of the gradient to the semilinear hyperbolic case, in order to reconstruct the gradient of the initial conditions in a subregion w of the domain evolution Ω. We start with an asymptotically linear system, the approach is based on an extension of the Hilbert uniqueness method （HUM） and Schauder＇s fixed point theorem. The analysis leads to an algorithm which is successfully numerically implemented and illustrated with examples and simulations.展开更多
文摘The aim of this paper is to study the notion of the gradient observability on a subregion w of the evolution domain W and also we consider the case where the subregion of interest is a boundary part of the system evolution domain for the class of semilinear hyperbolic systems. We show, under some hypotheses, that the flux reconstruction is guaranteed by means of the sectorial approach combined with fixed point techniques. This leads to several interesting results which are performed through numerical examples and simulations.
文摘The aim of this brief paper is to give several results concerning the regional controllability of distributed systems governed by semi-linear parabolic equations. We concentrate on the determination of a control achieving internal and boundary regional controllability. The approach is based on an extension of the Hilbert Uniqueness Method (HUM) and Schauder’s fixed point theorem. We give a numerical example developed in internal and boundary sub region. These numerical illustrations show the efficiency of the approach and lead to conjectures.
文摘The aim of this work is to study the notion of the gradient observability on a subregion?ω of the evolution domain?Ω for a class of semilinear hyperbolic systems. We show, under some hypothesis, that the gradient reconstruction is achieved following sectorial approach combined with fixed point techniques. The obtained results lead to an algorithm which can be implemented numerically.
文摘This paper is focused on studying an important concept of the system analysis, which is the regional enlarged observability or constrained observability of the gradient for distributed parabolic systems evolving in the spatial domain Ω We will explore an approach based on the Hilbert Uniqueness Method (HUM), which can reconstruct the initial gradient state between two prescribed functions f1 and f2 only in a critical subregion ω of Ω without the knowledge of the state. Finally, the obtained results are illustrated by numerical simulations.
文摘In this paper, we shall study the stabilization and the robustness of a constrained feedback control for bilinear parabolic systems defined on a Hilbert state space. Then, we shall show that stabilizing such a system reduces stabilization only in its projection on a suitable subspace. For this purpose, a new constrained stabilizing feedback control that allows a polynomial decay estimate of the stabilized state is given. Also, the robustness of the considered control is discussed. An illustrating example and simulations are presented.
文摘In this paper, we study the notion of the enlarged observability for distributed parabolic systems, where the aim is to reconstruct the initial state between two prescribed profiles P1 and P2 in an internal subregion c0 of the evolution domain f2. We give some definitions and properties of this concept, and then we solve the problem of the reconstruction of initial state using the Hilbert Uniqueness Method （HUM）. This leads to several interesting results which are performed through numerical example and simulations.
文摘The aim of this paper is to explore the concept of observability with constraints of the gradient for distributed parabolic system evolving in spatial domain Ω, and which the state gradient is to be observed only on a part of the boundary of the system evolution domain. It consists in the reconstruction of the initial state gradient which must be between two prescribed functions in a subregion Γ of Ω. Two necessary conditions are given. The first is formulated in terms of the subdifferential associated with a minimized functional, and the second uses the Lagrangian multiplier method. Nu-merical illustrations are given to show the efficiency of the second approach and lead to open questions.
文摘The paper aims to extend the notion of regional observability of the gradient to the semilinear hyperbolic case, in order to reconstruct the gradient of the initial conditions in a subregion w of the domain evolution Ω. We start with an asymptotically linear system, the approach is based on an extension of the Hilbert uniqueness method （HUM） and Schauder＇s fixed point theorem. The analysis leads to an algorithm which is successfully numerically implemented and illustrated with examples and simulations.
