Generation of Limit Cycles in Nonlinear Systems: Machine Leaning Based Type-3 Fuzzy Control

Abstract

A limit cycle is a cyclic path of oscillation on which the states of a nonlinear system settle. A considerable number of practical systems such as robots, converters, and heartbeat require generating the sustainable oscillatory behaviours. The objective is to design a controller to generate limit cycle with specific behaviours. In this paper, a novel fuzzy control (FC) strategy is introduced to create the limit-cycle for nonlinear complex dynamics with unknown uncertainties. The suggested controller benefits from new interval type-3 fuzzy logic, allowing the control synthesis to improve the quality of closed-loop response and robust performance. The adaptively learned backstepping controller based on FC is employed to analyze the convergence and robustness. Various simulations are proposed to ensure the efficiency of the fuzzy-based control law and adaption rules.