scholarly journals On Regional Boundary Gradient Strategic Sensors In Diffusion Systems

2021 ◽  
Vol 20 ◽  
pp. 66-78
Author(s):  
Raheam Al-Saphory ◽  
Ahlam Y Al-Shaya
Keyword(s):  
Hilbert Space ◽  
Differential Equations ◽  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
Parabolic Differential Equations ◽  
Continuous Type ◽  
Diffusion Systems ◽  
Regional Boundary ◽  
Boundary Gradient

This paper is aimed at investigating and introducing the main results regarding the concept of Regional Boundary Gradient Strategic Sensors (RBGS-sensors  the in Diffusion Distributed Parameter Systems (DDP-Systems  . Hence, such a method is characterized by Parabolic Differential Equations (PDEs  in which the behavior of the dynamic is created by a Semigroup ( of Strongly Continuous type (SCSG  in a Hilbert Space (HS) . Additionally , the grantee conditions which ensure the description for such sensors are given respectively to together with the Regional Boundary Gradient Observability (RBG-Observability  can be studied and achieved . Finally , the results gotten are applied to different situations with altered sensors positions are undertaken and examined.

scholarly journals Regional Boundary Gradient Detectability in Distributed Parameter Systems

2018 ◽  
Vol 14 (2) ◽  
pp. 7818-7833 ◽  
Author(s):  
Raheam Al Saphory ◽  
Mrooj Al Bayati
Keyword(s):  
Hilbert Space ◽  
Domain Boundary ◽  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
System State ◽  
Infinite Dimensional ◽  
Infinite Dimensional Systems ◽  
Unknown System ◽  
Regional Boundary ◽  
Boundary Gradient

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.

scholarly journals On some stochastic parabolic differential equations in a Hilbert space

2005 ◽  
Vol 2005 (2) ◽  
pp. 167-173 ◽  
Author(s):  
Khairia El-Said El-Nadi
Keyword(s):  
Hilbert Space ◽  
Partial Differential Equations ◽  
Differential Operator ◽  
Differential Equations ◽  
Partial Differential Operator ◽  
Parabolic Differential Equations ◽  
Partial Differential ◽  
Mixed Problems ◽  
Uniqueness Of The Solution ◽  
Weiner Process

We consider some stochastic difference partial differential equations of the form du(x,t,c)=L(x,t,D)u(x,t,c)dt+M(x,t,D)u(x,t−a,c)dw(t), where L(x,t,D) is a linear uniformly elliptic partial differential operator of the second order, M(x,t,D) is a linear partial differential operator of the first order, and w(t) is a Weiner process. The existence and uniqueness of the solution of suitable mixed problems are studied for the considered equation. Some properties are also studied. A more general stochastic problem is considered in a Hilbert space and the results concerning stochastic partial differential equations are obtained as applications.

Transient Response of Distributed Parameter Systems

1997 ◽  
Author(s):  
Jianping Zhou ◽  
Zhigang Feng
Keyword(s):  
Differential Equations ◽  
Transient Response ◽  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
Algebraic Equations ◽  
Equilibrium Equations ◽  
One Dimensional ◽  
Linear Algebraic Equations ◽  
Global Equilibrium ◽  
Distributed Transfer Function

Abstract A semi-analytic method is presented for the analysis of transient response of distributed parameter systems which are consist of one dimensional subsystems. The system is first divided into one dimensional sub-systems. Within each subsystem, replacing differentials on time t by finite difference, the governing partial differential equations are reduced to difference-differential equations. The solution of derived ordinary differential equations is obtained in an exact and closed form by distributed transfer function method and represented in nodal displacement parameters. Assemling global equilibrium equations at each nodes according to displacement continuity and force equilibrium requirements gives simutaneous linear algebraic equations. Numerical results are illustrated and compared with that of finite element method.

On the Exponential Stability of the Singular Distributed Parameter Systems

2015 ◽  
Vol 719-720 ◽  
pp. 496-503
Author(s):  
Zhao Qiang Ge
Keyword(s):  
Hilbert Space ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Distributed Parameter Systems ◽  
Necessary And Sufficient Conditions ◽  
Distributed Parameter ◽  
Necessary And Sufficient

Exponential stability for the singular distributed parameter systems is discussed in the light of the theory of GE0-semigroup in Hilbert space. The necessary and sufficient conditions concerning the exponential stability are given.

An Efficient Computational Procedure for the Optimization of a Class of Distributed Parameter Systems

1969 ◽  
Vol 91 (2) ◽  
pp. 190-194 ◽  
Author(s):  
D. A. Wismer
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Broad Class ◽  
Distributed Parameter Systems ◽  
Parabolic Partial Differential Equation ◽  
Distributed Parameter ◽  
Total System ◽  
Partial Differential

The optimal control problem for a broad class of distributed parameter systems defined by vector parabolic partial differential equations is considered. The problem is solved by discretizing the spatial domain and then treating the (large) resultant set of ordinary differential equations as a set of independent subsystems. The subsystems are determined by decomposition of the total system into lower-dimensional problems and the necessary conditions for optimality of the overall system are then satisfied by an iterative procedure. With this treatment, the optimal control problem can be solved for larger systems (or finer spatial discretizations) than would otherwise be feasible. An example is given for a system described by a nonlinear parabolic partial differential equation in one space dimension.

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