Abstract
This paper examines approximation-based fixed-time adaptive tracking control for a class of uncertain nonlinear pure-feedback systems. Novel virtual and actual controllers are designed that resolve the meaninglessness of virtual and actual controllers at the origin and in the negative domain, and the sufficient condition for the system to have semiglobal fixed-time stability is also provided. Radial basis function neural networks are introduced to approximate unknown functions for solving the fixed-time control problem of unknown nonlinear pure-feedback systems, and the mean value theorem is used to solve the problem of nonaffine structure in nonlinear pure-feedback systems. The controllers designed in this paper ensure that all signals in the closed-loop system are semiglobally uniform and ultimately bounded in a fixed time. Two simulation results show that appropriate design parameters can limit the tracking error within a region of the origin in a fixed time.
Highlights
Nonlinear pure-feedback systems [1, 2] are more common than general strict feedback nonlinear systems or nonlinear systems with input affine structure
A finite-time control system ensures that a nonlinear system converges in a finite time, but the convergence time is related to the initial state of the system
In [35], a fixed-time control with generalized directional topology was proposed for nonlinear multiagent systems; in [36], a prescribed performance fixed-time recurrent neural network control was proposed for a class of uncertain nonlinear systems; in [37], a fast fixed-time nonsingular terminal sliding mode control was proposed to solve the problem of chaos suppression of power systems; and in [38], a fixedtime observer was proposed to detect distributed faults of nonlinear multiagent systems
Summary
Nonlinear pure-feedback systems [1, 2] are more common than general strict feedback nonlinear systems or nonlinear systems with input affine structure. The fixed-time control problem is solved based on nonlinear pure-feedback systems, and the sufficient condition and design steps for semiglobal fixed-time stability are provided. (1) e fixed-time control algorithm proposed in [35,36,37,38,39,40] does not solve the problem of the nonaffine structure of the control input u(t). Is paper applies fixed-time control theory in nonlinear pure-feedback systems to solve this problem. (3) An RBF neural network control algorithm is introduced to approximate the unknown functions fi(·) to overcome the difficulty of modeling accurately and solving the problem of interference in nonlinear pure-feedback systems.
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