Adaptive generation of limit cycles in a class of nonlinear systems with unknown parameters and dead-zone nonlinearity

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 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.