Abstract
A sliding mode adaptive fractional fuzzy control is provided in this article to achieve the trajectory tracking control of uncertain robotic manipulators. By adaptive fractional fuzzy control, we mean that fuzzy parameters are updated through fractional-order adaptation laws. The main idea of this work consists in using fractional input to control complex integer-order nonlinear systems. An adaptive fractional fuzzy control that guarantees tracking errors tend to an arbitrary small region is established. To facilitate the stability analysis, fractional-order integral Lyapunov functions are proposed, and the integer-order Lyapunov stability criterion is used. Finally, simulation results are presented to show the effectiveness of the proposed method.
Highlights
During the past few years, the fractional-order calculus has been extensively studied, which has some special properties, for example, hereditary and memory.[1,2,3,4,5,6] These properties can be well used to describe real-word systems
The fractional-order calculus plays a great role in modeling many actual systems, for example, stochastic diffusion, molecular spectroscopy, control theory, viscoelastic dynamics, quantum mechanics, and many research results can be seen in the previous studies[7,8,9,10,11,12,13,14,15,16] and the references therein
To obtain the trajectory tracking of robotic manipulators, an adaptive fractional fuzzy control (AFFC) method is introduced by combining with an sliding mode control (SMC) algorithm, and the proposed method can guarantee the uniform boundedness of tracking errors
Summary
During the past few years, the fractional-order calculus has been extensively studied, which has some special properties, for example, hereditary and memory.[1,2,3,4,5,6] These properties can be well used to describe real-word systems. The stability analysis of the underlying system under adaptive fuzzy control (AFC) is usually discussed using Lyapunov approaches. Two AFFC approaches were designed for uncertain manipulators by Kumar and Rana[48] and Sharma et al.,[49] respectively, where the control performance was studied only by simulation results.
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