Fixed-time tracking control for fractional-order uncertain parametric nonlinear systems with input delay: A command filter-based neuroadaptive control method

Abstract

This paper discusses the fixed-time tracking control (FTTC) problem of fractional-order nonlinear systems (FONSs) subject to uncertain dynamics, parametric nonlinearities and input delay. An radial basis function neural network (RBFNN) is applied to tackle uncertain nonlinearities and input delay nonlinearity in the backstepping control (BC) process, with the vectors of weight and basis function being reconstructed accordingly. Meanwhile, adaptive control laws are designed to enable online updating of the new weight and approximation error. Moreover, a nonlinear fractional-order command filter (FOCF) is utilized to circumvent the “complexity explosion” issue caused by BC method, and compensation control strategies are presented to compensate for filtering errors. By introducing the FOCF, BC method and fixed-time (FT) control theory, a neuroadaptive FTTC strategy with command filter (CF) is ultimately proposed. This strategy ensures that the tracking error converges to a small neighborhood of zero in a fixed time, while maintaining the boundedness of all signals in the closed-loop system. Eventually, the validity of the developed control strategy is testified through three aspects.