Time-Delayed Feedback Control of a Hydraulic Model Governed by a Diffusive Wave System. (9th March 2020)

• Record Type: Journal Article
• Authors: Chentouf, Boumediène; Smaoui, Nejib
• Other Names: Li Guang Academic Editor.
• Is Part Of: Complexity. Volume 2020(2020)
• Publication Date: 2020-03-09
• Subjects: Chaotic behavior in systems -- Periodicals; Complexity (Philosophy) -- Periodicals; 003
• DOI: 10.1155/2020/4986026
• Languages: English
• ISSNs: 1076-2787

Abstract

Abstract : This paper is concerned with the feedback flow control of an open-channel hydraulic system modeled by a diffusive wave equation with delay. Firstly, we put forward a feedback flow control subject to the action of a constant time delay. Thereafter, we invoke semigroup theory to substantiate that the closed-loop system has a unique solution in an energy space. Subsequently, we deal with the eigenvalue problem of the system. More importantly, exponential decay of solutions of the closed-loop system is derived provided that the feedback gain of the control is bounded. Finally, the theoretical findings are validated via a set of numerical results.