Adaptive Fuzzy Control for Nonlinear Fractional-Order Uncertain Systems with Unknown Uncertainties and External Disturbance

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.

[1]  Guanrong Chen,et al.  A note on the fractional-order Chen system , 2006 .

[2]  Jun-Guo Lu,et al.  Stability Analysis of a Class of Nonlinear Fractional-Order Systems , 2008, IEEE Transactions on Circuits and Systems II: Express Briefs.

[3]  James Lam,et al.  Non-existence of finite-time stable equilibria in fractional-order nonlinear systems , 2014, Autom..

[4]  Alain Oustaloup,et al.  A Lyapunov approach to the stability of fractional differential equations , 2009, Signal Process..

[5]  M. P. Aghababa.  Finite-time chaos control and synchronization of fractional-order nonautonomous chaotic (hyperchaotic) systems using fractional nonsingular terminal sliding mode technique , 2012 .

[6]  Changpin Li,et al.  Stability Analysis of Fractional Differential Systems with Order Lying in (1, 2) , 2011 .

[7]  Ravi P. Agarwal,et al.  Stability analysis of fractional differential system with Riemann-Liouville derivative , 2010, Math. Comput. Model..

[8]  Manuel A. Duarte-Mermoud,et al.  Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems , 2015, Commun. Nonlinear Sci. Numer. Simul..

[9]  Yangquan Chen,et al.  Computers and Mathematics with Applications Stability of Fractional-order Nonlinear Dynamic Systems: Lyapunov Direct Method and Generalized Mittag–leffler Stability , 2022 .

[10]  Mohammad Pourmahmood Aghababa,et al.  Design of a chatter-free terminal sliding mode controller for nonlinear fractional-order dynamical systems , 2013, Int. J. Control.

[11]  Weihua Deng,et al.  Smoothness and stability of the solutions for nonlinear fractional differential equations , 2010 .

[12]  Jun-Guo Lu,et al.  Robust Stability and Stabilization of Fractional-Order Interval Systems with the Fractional Order $\alpha$: The $0≪\alpha≪1$ Case , 2010, IEEE Transactions on Automatic Control.

[13]  Manuel A. Duarte-Mermoud,et al.  Lyapunov functions for fractional order systems , 2014, Commun. Nonlinear Sci. Numer. Simul..

[14]  Mathieu Moze,et al.  Pseudo state feedback stabilization of commensurate fractional order systems , 2009, 2009 European Control Conference (ECC).

[15]  Liping Chen,et al.  Stability and Stabilization of a Class of Nonlinear Fractional-Order Systems With Caputo Derivative , 2012, IEEE Transactions on Circuits and Systems II: Express Briefs.

[16]  Z. Ge,et al.  Chaos, control and synchronization of a fractional order rotational mechanical system with a centrifugal governor , 2007 .

[17]  Igor Podlubny,et al.  Mittag-Leffler stability of fractional order nonlinear dynamic systems , 2009, Autom..