Regional boundary gradient strategic sensors in Neumann conditions

Regional boundary exponential reduced observability in distributed parameter systems

The aim of this chapter is to introduce the concept of regional boundary exponential reduced observability in connection with the sensors characterizations on a sub-region on boundary of the considered domain boundary. More precisely, we explore the original results devoted to this concept in linear dynamical systems which is generated by a strongly continuous semi-group in Hilbert space of order one. Thus, the existence of sufficient conditions is presented and examined for regional boundary exponential reduced estimator in parabolic infinite dimensional systems. Finally, we apply these resul…

Regional exponential general observability in diffusion problem

The aim of this paper is to extend the concept of regional exponential general observability to the case of Neumann boundary conditions problem in diffusion system. More precisely, for linear distributed parameter diffusion systems, we show that the sensors characterizations allow to reconstruct the regional exponential state in a sub-region of the considered systems domain. Moreover, various interesting results associated with the choice of sensors are given and illustrated in specific situations in order regional exponential general observability notion to be achieved. Finally, we also show …

General Asymptotic Regional Gradient Observer

The main purpose of this paper is to study and characterize the existing of general asymptotic regional gradient observer which observe the current gradient state of the original system in connection with gradient strategic sensors. Thus, we give an approach based to Luenberger observer theory of linear distributed parameter systems which is enabled to determinate asymptotically regional gradient estimator of current gradient system state. More precisely, under which condition the notion of asymptotic regional gradient observability can be achieved. Furthermore, we show that the measurement st…

On the regional gradient observability of time fractional diffusion processes

This paper for the first time addresses the concepts of regional gradient observability for the Riemann-Liouville time fractional order diffusion system in an interested subregion of the whole domain without the knowledge of the initial vector and its gradient. The Riemann-Liouville time fractional order diffusion system which replaces the first order time derivative of normal diffusion system by a Riemann-Liouville time fractional order derivative of order $α\in (0,1]$ is used to well characterize those anomalous sub-diffusion processes. The characterizations of the strategic sensors when the…

带Caputo时间分数阶导数的分数阶微分方程的区域梯度能观性

Regional Gradient Observability for Fractional Differential Equations with Caputo Time-Fractional Derivatives

本文研究含Caputo导数的分数阶次扩散方程的区域梯度能观性，给出相关刻画与基于Hilbert Uniqueness Method的初始梯度恢复方法，数值实验验证了算法在重构误差上的有效性。

Optimal Regional Tracking Control of Time-Fractional Diffusion Systems

In this paper, we aim to explore optimal regional trajectory tracking control problems of the anomalous subdiffusion processes governed by time-fractional diffusion systems under the Neumann boundary conditions. Using eigenvalue theory of the system operator and the semigroup theory, we explore the existence and some estimates of the mild solution to the considered system. An approach on finding solution to the optimal problem that minimizes the regional trajectory tracking error and the corresponding control cost over a finite space and time domain is then explored via the Hilbert uniqueness …

Riemann-Liouville分数阶半线性方程的边界可控性

Boundary Controllability of Riemann-Liouville Fractional Semilinear Equations

本文研究带Neumann边界条件的Riemann-Liouville分数阶半线性次扩散系统的边界区域可控性，利用半群理论、分数阶Hilbert唯一性方法和Schauder不动点定理给出充分条件，并通过数值模拟验证了方法的有效性。