Regional gradient controllability of sub-diffusion processes

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:440

Article

Ge, Fudong¹  Chen, YangQuan²  Kou, Chunhai³ 

[1] Donghua Univ, Coll Informat Sci & Technol, Shanghai 201620, Peoples R China

[2] Univ Calif, Mechatron Embedded Syst & Automat Lab, Merced, CA 95343 USA

[3] Donghua Univ, Dept Appl Math, Shanghai 201620, Peoples R China

关键词: Regional gradient controllability;    Minimum energy;    Fractional order;    Sub-diffusion process;    Strategic actuators;   

DOI  :  10.1016/j.jmaa.2016.03.051

来源: Elsevier

【 摘 要 】

By sub-diffusion systems we mean to replace the first order time derivative of normal diffusion system with a Riemann-Liouville time fractional derivative of order alpha is an element of (0,1). In this paper, we first introduce a new definition of regional gradient controllability for the sub-diffusion system with the control inputs appearing in the differential equations as distributed inputs, which recovers the usual definition of regional gradient controllability as a -> 1. The sufficient and necessary conditions on actuators to achieve the gradient controllability in a given subregion of the whole domain are presented. An approach to guarantee the regional gradient controllability of the problems studied within the considered subregion using minimum energy control effort is presented. Several examples are presented in the end to illustrate the effectiveness of our results, where zone actuators, pointwise actuators or filament actuators are respectively considered. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free