Adaptive fuzzy control of a class of nonaffine nonlinear system with input saturation based on passivity theorem

• Published in: ISA transactions 2017-07, Vol.69, p.202-213
• Main Authors: Molavi, Ali, Jalali, Aliakbar, Ghasemi Naraghi, Mahdi
• Format: Article
• Language: English
• Subjects: Adaptive fuzzy; Backstepping; Input saturation; Nonaffine system; Passivity theorem
• ISSN: 0019-0578; 1879-2022
• DOI: 10.1016/j.isatra.2017.03.020

In this paper, based on the passivity theorem, an adaptive fuzzy controller is designed for a class of unknown nonaffine nonlinear systems with arbitrary relative degree and saturation input nonlinearity to track the desired trajectory. The system equations are in normal form and its unforced dynamic may be unstable. As relative degree one is a structural obstacle in system passivation approach, in this paper, backstepping method is used to circumvent this obstacle and passivate the system step by step. Because of the existence of uncertainty and disturbance in the system, exact passivation and reference tracking cannot be tackled, so the approximate passivation or passivation with respect to a set is obtained to hold the tracking error in a neighborhood around zero. Furthermore, in order to overcome the non-smoothness of the saturation input nonlinearity, a parametric smooth nonlinear function with arbitrary approximation error is used to approximate the input saturation. Finally, the simulation results for the theoretical and practical examples are given to validate the proposed controller. •An adaptive fuzzy controller is proposed to passivate an unknown nonlinear nonaffine system with unstable unforced dynamic.•Since the relative degree is n, backstepping method is used to overcome this obstacle to passivation.•Because of the existence of uncertainty and disturbance, passivation with respect to a defined set is obtained.•Non-smoothness of the input saturation nonlinearity is solved by approximating the input saturation with a parametric smooth function.