Adaptive generation of limit cycles in a class of nonlinear systems with unknown parameters and dead-zone nonlinearity. Issue 15 (17th November 2020)

• Record Type: Journal Article
• Authors: Binazadeh, T.; Hakimi, A. R.
• Is Part Of: International journal of systems science. Volume 51:Issue 15(2020)
• Page Start: 3134
• Page End: 3145
• Publication Date: 2020-11-17
• Subjects: Nonlinear systems -- limit cycle control -- adaptive control -- dead-zone nonlinearity -- unknown parameters; System analysis -- Periodicals; 003.3
• DOI: 10.1080/00207721.2020.1808733
• Languages: English
• ISSNs: 0020-7721

Abstract

Abstract : This paper presents a new method to design an adaptive controller for generating stable limit cycles in a class of nonlinear systems subject to unknown dead-zone nonlinearity and unknown parameters. In this regard, the set stabilisation-based approach is utilised and the proper Lyapunov function is taken concerning the geometric shape of the desired limit cycle. Firstly, the state feedback control is designed to create the desired limit cycle in the second-order subsystem and then, extended to the arbitrary n order system through the adaptive backstepping technique. Besides, the explosion of a complex problem, which happens during the backstepping implementation in high-order systems, is handled. In the final stage, the boundedness of all the closed-loop signals is guaranteed via Lyapunov analysis. The effectiveness of the proposed control algorithm is demonstrated by a simulation example.