Adaptive Neural Indirect Inverse Control for a Class of Fractional-Order Hysteretic Nonlinear Time-Delay Systems and Its Application

Motivated by wide utilizations of the smart material actuator-based motion control systems in soft robotics, this article proposes a neural adaptive fractional-order backstepping indirect inverse control (NAFBIIC) scheme for a class of fractional-order hysteretic nonlinear time-delay systems with the following features: 1) The effective control for the fractional-order hysteretic nonlinear system without constructing the direct hysteresis inverse model is realized. Then, the hysteresis indirect inverse compensator for fractional-order hysteretic nonlinear systems is designed. This makes the construction of the direct hysteresis inverse model to be not required any more and the hysteresis in the fractional-order nonlinear systems is effectively mitigated. 2) The time-delay functions are approximated by combining the finite covering lemma with neural networks, which leads to the abandonment of the traditional Lyapunov–Krasoviskii functions when dealing with time-delay functions. 3) The fractional-order model of piezoelectric positioning stage is proposed, and the motion control experiments are implemented to show the effectiveness of the proposed fractional-order indirect inverse control scheme.