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Time-Delayed Feedback Control of a Hydraulic Model Governed by a Diffusive Wave System

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  • Boumediène Chentouf
  • Nejib Smaoui

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.

Suggested Citation

  • Boumediène Chentouf & Nejib Smaoui, 2020. "Time-Delayed Feedback Control of a Hydraulic Model Governed by a Diffusive Wave System," Complexity, Hindawi, vol. 2020, pages 1-15, March.
    • Handle: RePEc:hin:complx:4986026
    DOI: 10.1155/2020/4986026
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