Abstract
In this paper, the problem of robust control of nonlinear fractional-order systems in the presence of uncertainties and external disturbance is investigated. Fuzzy logic systems are used for estimating the unknown nonlinear functions. Based on the fractional Lyapunov direct method and some proposed Lemmas, an adaptive fuzzy controller is designed. The proposed method can guarantee all the signals in the closed-loop systems remain bounded and the tracking errors converge to an arbitrary small region of the origin. Lastly, an illustrative example is given to demonstrate the effectiveness of the proposed results.
Highlights
During the past two decades, fractional-order dynamic systems have received lots of attention due to their broad range of application in dielectric polarization, viscoelastic systems, electromagnetic waves, chaotic systems and so on [1]
Fuzzy logic systems are used for estimating the unknown nonlinear functions
The proposed method can guarantee all the signals in the closed-loop systems remain bounded and the tracking errors converge to an arbitrary small region of the origin
Summary
During the past two decades, fractional-order dynamic systems have received lots of attention due to their broad range of application in dielectric polarization, viscoelastic systems, electromagnetic waves, chaotic systems and so on [1]. In [11], a finite-time control method is introduced for control of a class of non-autonomous fractional-order nonlinear systems in the presence of uncertainties and external noises. Some authors have proposed Lyapunov functions to prove the stability of fractional-order nonlinear systems, for example, a new property for Caputo fractional derivative which allows to find a simple Lyapunov candidate function for many fractional-order systems is presented in [15] Either they have neglected the consideration of the effects of both system uncertainties and external noises, or they have not applied the fractional Lyapunov stability theory to guarantee the stability of the overall system. An adaptive fuzzy control method for fractional-order nonlinear systems in the presence of model uncertainty and external noises is proposed. To update the fuzzy parameter. (3) A direct Lyapunov function method is proposed to analyze the stability of the fractional-order systems
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