Adaptive fuzzy dynamic surface tracking control for a class of nonlinear systems with unknown distributed time delays and backlash-like hysteresis

Abstract

In this article, an adaptive fuzzy backstepping dynamic surface control approach is developed for a class of nonlinear systems with unknown backlash-like hysteresis and unknown state discrete and distributed time-varying delays. Fuzzy logic systems are used to approximate the unknown nonlinear functions and a fuzzy state observer is designed for estimating the immeasurable states. Then, by combining the backstepping technique and the appropriate Lyapunov-Krasovskii functionals with the dynamic surface control approach, the output-feedback adaptive fuzzy tracking controller is designed. The main advantages of this article are (i) the existence of the state discrete and distributed time-varying delays such that the investigated systems are more general than that of the existing results, (ii) the proposed control scheme can eliminate the problem of "explosion of complexity" inherent in the backstepping design method, and (iii) for the nth nonlinear system, only one fuzzy logic system is used to approximate the unknown continuous time-varying delay functions since all of them are lumped into one unknown nonlinear function, which makes our design scheme easier to be implemented in practical applications. It is proven that the proposed design method is able to guarantee that all the signals in the closed-loop system are bounded and the tracking error can converge to a small neighborhood of origin with an appropriate choice of design parameters. Finally, the simulation results demonstrate the effectiveness of the proposed approach.

Adaptive fuzzy backstepping super‐twisting sliding mode control of nonlinear systems with unknown hysteresis

“…For the hysteresis nonlinear systems, recently, many DSC technique-based adaptive backstepping control schemes without constructing the hysteresis inverse have been reported in the literature [32][33][34]. For instance, in Yue et al [35], an adaptive fuzzy backstepping control scheme was proposed for a class of hysteresis nonlinear systems. Liu et al [36] developed an adaptive backstepping control scheme for the multiple-input-multiple-output (MIMO) hysteresis nonlinear systems.…”

Robust adaptive fuzzy sliding mode controller for nonlinear uncertain hysteretic systems

“…As far as it is known, the foundational work is presented by Su et al (2000). Recently, a considerable attention has been paid to the problem of controlling nonlinear systems with backlash-like hysteresis input, and some interesting results were reported in Su et al (2000, 2003); Ren et al (2009); Xiu-Yu and Yan (2010); Yue et al (2017); Shahnazi et al (2010); Li et al (2012); Chen et al (2016); Wei et al (2017); Wu et al (2017); and Wang et al (2017). By combining the backlash hysteresis model with adaptive control techniques, Su et al (2000, 2003) presented a robust adaptive control algorithm for a class of hysteretic systems with unknown backlash-like nonlinearity.…”

“…The authors of Ren et al (2009) combined the dynamic surface control strategy with neural networks to deal with output tracking control for strict-feedback non-linear systems preceded by backlash hysteresis. This control strategy is extended to uncertain disturbed strict-feedback nonlinear systems preceded by unknown backlash-like hysteresis in Xiu-Yu and Yan (2010), and to nonlinear systems with unknown distributed time delays in Yue et al (2017). In Shahnazi et al (2010) the authors proposed an output feedback controller for uncertain nonlinear hysteretic systems where an observer-based adaptive fuzzy control is used to estimate the system states.…”