A novel algorithm on adaptive backstepping control of fractional order systems

Wei, Yiheng; Chen, Yuquan; Liang, Shu; Wang, Yong

doi:10.1016/j.neucom.2015.03.029

Cited by 148 publications

(86 citation statements)

References 24 publications

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“…We can find that backstepping control approach was proposed in Ref. 44. In this interesting work, the fractional-order system was transferred into some integer-order one, so the stability of the closed system was analyzed by using integer-order Lyapunov stability theorems.…”

Section: (39)mentioning

confidence: 99%

“…Up to now, there were three pioneer works which consider the backstepping control of fractional-order nonlinear systems. [43][44][45] In aforementioned literatures, the integer-order Lyapunov stability theorems were used. So, how to design backstepping control algorithm for fractional-order systems based on fractional-order stability criterion is a challenging work.…”

Section: Introductionmentioning

confidence: 99%

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Adaptive neural network backstepping control for a class of uncertain fractional-order chaotic systems with unknown backlash-like hysteresis

Wu¹,

2016

AIP Advances

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In this paper, we consider the control problem of a class of uncertain fractionalorder chaotic systems preceded by unknown backlash-like hysteresis nonlinearities based on backstepping control algorithm. We model the hysteresis by using a differential equation. Based on the fractional Lyapunov stability criterion and the backstepping algorithm procedures, an adaptive neural network controller is driven. No knowledge of the upper bound of the disturbance and system uncertainty is required in our controller, and the asymptotical convergence of the tracking error can be guaranteed. Finally, we give two simulation examples to confirm our theoretical results. C 2016 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license

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Section: (39)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Adaptive neural network backstepping control for a class of uncertain fractional-order chaotic systems with unknown backlash-like hysteresis

Wu¹,

2016

AIP Advances

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“…The overparametrization and partial overparametrization problems were soon eliminated by elegantly introducing the tuning functions [33,35]. On the other hand, with the aids of this frequency distribute model and the indirect Lyapunov method, the adaptive backstepping control of fractional-order systems were established [37][38][39]. As far as we know, there are few results on the generalization of backstepping into fractional-order systems.…”

Section: Introductionmentioning

confidence: 99%

Mittag-Leffler stabilization of fractional-order nonlinear systems with unknown control coefficients

Wang

2018

Adv Differ Equ

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In this paper, we consider the problem of Mittag-Leffler stabilization of fractional-order nonlinear systems with unknown control coefficients. With the help of backstepping design method, the stabilizing functions and tuning functions are constructed. The controller is designed to ensure that the pseudo-state of the fractional-order nonlinear system converges to the equilibrium. The effectiveness of the proposed method has been verified by some simulation examples.

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“…In the recent research works [6,9], nonlinear fractional-order systems with affine structures have been also investigated. • Nonaffinity: However, there exist several nonlinear nonaffine systems in practice, such as chemical reactors, biochemical processes, some aircraft and pendulum dynamical models, and so on [1,10,12,19,20,23,25,26,44,50,56,58]. Due to the great efforts devoted by researchers, remarkable adaptive control approaches have been developed for non-affine systems [19,44,50,56].…”

Section: Introductionmentioning

confidence: 99%

“…In [10,19,20], it has been shown that the non-affine problem can be traditionally addressed by five approaches, namely: (1) approach based on Taylor series expansion, (2) approach based on implicit function theorem, (3) approach based on the mean value theorem, (4) approach based on differentiating the original system equation, and (5) approach based on a local inversion of the TakagiSugeno (TS) fuzzy affine model. Moreover, the knowledge of the sign of the control gain is required in [20,23] to facilitate the design of the adaptive controls for nonlinear non-affine systems. • Unknown control direction: As stated in [2,8,10,11,40,58,62], there are many systems with unknown control direction such as electrical systems, biochemical and biophysical processes, robotics, to name but a few.…”

Section: Introductionmentioning

confidence: 99%

Observer-based adaptive neural network control for a class of MIMO uncertain nonlinear time-delay non-integer-order systems with asymmetric actuator saturation

Zouari

Boulkroune

Ibeas

et al. 2016

Neural Comput & Applic

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This paper focuses on the adaptive neural output feedback control of a class of uncertain multi-input-multioutput nonlinear time-delay non-integer-order systems with unmeasured states, unknown control direction, and unknown asymmetric saturation actuator. Thus, the mean value theorem and a Gaussian error function-based continuous differentiable model are used in the paper to describe the unknown asymmetric saturation actuator and to get an affine model in which the control input appears in a linear fashion, respectively. The design of the controller follows a number of steps. Firstly, based on the semigroup property of fractional-order derivative, the system is transformed into a normalized fractional-order system by means of a state transformation in order to facilitate the control design. Then, a simple linear state observer is constructed to estimate the unmeasured states of the transformed system. A neural network is incorporated to approximate the unknown nonlinear functions while a Nussbaum function is used to deal with the unknown control direction. In addition, the strictly positive real condition, the Razumikhin Lemma, the frequency-distributed model, and the Lyapunov method are utilized to derive the parameter adaptive laws and to perform the stability proof. The main advantages of this work are that:(1) it can handle systems with constant, time-varying, and distributed time-varying delays, (2) the considered class of systems is relatively large, (3) the number of adjustable parameters is reduced, (4) the tracking errors converge asymptotically to zero and all signals of the closed-loop system are bounded. Finally, some simulation examples are provided to demonstrate the validity and effectiveness of the proposed scheme.

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A novel algorithm on adaptive backstepping control of fractional order systems

Cited by 148 publications

References 24 publications

Adaptive neural network backstepping control for a class of uncertain fractional-order chaotic systems with unknown backlash-like hysteresis

Adaptive neural network backstepping control for a class of uncertain fractional-order chaotic systems with unknown backlash-like hysteresis

Mittag-Leffler stabilization of fractional-order nonlinear systems with unknown control coefficients

Observer-based adaptive neural network control for a class of MIMO uncertain nonlinear time-delay non-integer-order systems with asymmetric actuator saturation

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