Adaptive stabilisation for a class of uncertain coupled parabolic equations. Issue 10 (2nd October 2020)

• Record Type: Journal Article
• Authors: Li, Jian; Liu, Yungang
• Is Part Of: International journal of control. Volume 93:Issue 10(2020)
• Page Start: 2469
• Page End: 2479
• Publication Date: 2020-10-02
• Subjects: Coupled parabolic equation -- uncertain system -- stabilisation -- adaptive control; Automatic control -- Periodicals; Electronic journals; 629.8
• DOI: 10.1080/00207179.2018.1564842
• Languages: English
• ISSNs: 0020-7179

Abstract

ABSTRACT: Adaptive stabilisation is investigated for a class of uncertain coupled parabolic equations in this paper. The presence of unknown coefficients can reduce the rigorousness of system modelling and enlarge the scope of the systems, whereas it could give rise to essential difficulties to control problems. Mainly due to the latter, certain new initiative, such as uncertainty compensation, should be considered to solve the stabilisation problem. For this, by infinite-dimensional backstepping method combining with adaptive compensation technique, an adaptive control scheme is proposed. Then, an adaptive state-feedback controller is constructed which guarantees that all the closed-loop system states are bounded while the original system states converge to zero. A numerical example is provided to validate the effectiveness of the theoretical results.