Adaptive output-feedback stabilisation for wave equations with dynamic boundary condition and corrupted boundary measurement. Issue 10 (3rd October 2021)

• Record Type: Journal Article
• Authors: Xu, Zaihua; Liu, Yungang; Li, Jian; Li, Fengzhong
• Is Part Of: International journal of control. Volume 94:Issue 10(2021)
• Page Start: 2669
• Page End: 2678
• Publication Date: 2021-10-03
• Subjects: Wave equations -- dynamic boundary condition -- output disturbance -- adaptive stabilisation -- backstepping method; Automatic control -- Periodicals; Electronic journals; 629.8
• DOI: 10.1080/00207179.2020.1730007
• Languages: English
• ISSNs: 0020-7179

Abstract

Abstract : This paper is devoted to the output-feedback stabilisation for a class of wave equations. Remarkably, only one boundary measurement corrupted by disturbance is available for feedback, and the boundary condition at the control end is dynamic, rather than static. This renders the control problem more challenging than those in the related literature, largely because certain reconstruction and compensation mechanisms respectively for the state and disturbance are necessary but difficult to integrate with the control design for dynamic boundary condition. For this, a powerful adaptive output-feedback stabilising scheme is proposed. Specifically, a delicate observer is constructed for the state in the space domain, with which a dynamic estimate for the disturbance is incorporated. Then, a desired output-feedback controller is designed by backstepping method, which renders the states of the original system and observer to converge to zero, while the estimate of the unknown disturbance converges to its true value.