Finite Time Fractional-Order Sliding Mode-Based Tracking for a Class of Fractional-Order Nonholonomic Chained System

Abstract

This paper formulates a fractional-order finite time tracking scheme for a perturbed n-dimensional fractional-order extended chained form of nonholonomic system. First, the hierarchical sliding surfaces are properly selected, and then, a novel fractional-order sliding mode methodology is derived mathematically to accomplish the prescribed goal. With the introduction of new virtual controls, the proposed strategy renders finite time tracking of a fractional-order reference model in-spite of various system uncertainties. Further, the closed loop system stability is procured with the proposed method through fractional-Lyapunov and Mittag–Leffler-based stability theorems. It has also been verified analytically that the error dynamics converge to the chosen sliding surfaces in finite time. Finally, two examples including an engineering application of mobile robot are illustrated through matlab simulations to demonstrate the usefulness of the introduced control technique.