Adaptive output‐feedback control for damped wave equations with unknown damping coefficient and corrupted boundary measurement. (11th August 2020)

• Record Type: Journal Article
• Authors: Xu, Zaihua; Liu, Yungang; Li, Fengzhong; Li, Jian
• Is Part Of: International journal of robust and nonlinear control. Volume 30:Number 16(2020)
• Page Start: 6744
• Page End: 6760
• Publication Date: 2020-08-11
• Subjects: adaptive technique -- corrupted boundary measurement -- output‐feedback control -- unknown damping -- wave equations; Automatic control -- Periodicals; Control theory -- Periodicals; Nonlinear systems -- Periodicals; 629.836
• DOI: 10.1002/rnc.5136
• Languages: English
• ISSNs: 1049-8923

Abstract

Summary: Adaptive output‐feedback control is investigated for a class of uncertain damped wave equations. The remarkable features of the system in question are as follows: (i) Unknown damping is allowed at the boundary; (ii) The boundary measurement is corrupted by an unknown harmonic disturbance. These features make the control problem essentially different from those in the related literature. To solve the problem, a novel adaptive output‐feedback control scheme is established for the system. Specifically, an ingenious observer is first introduced to reconstruct the unmeasured system state in the space domain. Based on this, a certain compensation mechanism is designed for the unknown damping coefficient and output disturbance by adaptive technique based on projection operator. Then, an output‐feedback controller is successfully designed by the backstepping method for ODEs, which guarantees that all states of the resulting closed‐loop system are bounded, and the original system state ultimately converges to an arbitrarily prescribed small neighborhood of the origin. Finally, a simulation example is provided to illustrate the effectiveness of the proposed method.