Synchronization of incommensurate fractional order system

Martínez-Guerra, Rafael; Pérez-Pinacho, Claudia A.; Gómez-Cortés, Gian Carlo; Cruz-Victoria, Juan C.

doi:10.1016/j.amc.2015.03.121

Cited by 6 publications

(3 citation statements)

References 8 publications

(10 reference statements)

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“…This completes the proof. (18) to faster attenuate the energy of Lyapunov function V and achieve better control performance.…”

Section: Sliding Manifold Designmentioning

confidence: 99%

“…In [17], the authors discuss the problem of tracking and stabilization of a class of chained fractionalorder nonlinear systems via SMC with a single input. SMC is used to realize the stabilization and synchronization of fractional chaotic systems [18][19][20][21]. For instance, in [22], SMC with an adaptive reaching law is presented to control a class of fractional chaotic systems, including fractional Lure systems, fractional Lorenz systems, and so on.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Sliding Mode Control for a Class of Nonlinear Fractional Order Systems with a Fractional Fixed-Time Reaching Law

et al. 2022

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In this paper, the sliding-mode control method was used to control a class of general nonlinear fractional-order systems which covers a wide class of chaotic systems. A novel sliding manifold with an additional nonlinear part which achieved better control performance was designed. Furthermore, a novel fixed-time reaching law with a fractional adaptive gain is proposed, where the reaching time to the sliding manifold is determined by the first positive zero of a Mittag–Leffler function and is independent of initial conditions. We have provided some instructions on tuning the parameters of the proposed reaching law to avoid exacerbating the chattering phenomenon. Finally, simulation examples are presented to validate all results.

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“…This completes the proof. (18) to faster attenuate the energy of Lyapunov function V and achieve better control performance.…”

Section: Sliding Manifold Designmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Sliding Mode Control for a Class of Nonlinear Fractional Order Systems with a Fractional Fixed-Time Reaching Law

et al. 2022

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“…Additionally, synchronization of fractional‐order chaotic systems is also a field of active research. And a variety of synchronization approaches have been proposed for the fractional‐order chaotic systems that include complete synchronization, antisynchronization, phase and antiphase synchronization, impulsive synchronization, lag synchronization, and projective synchronization, just to enumerate a few examples.…”

Section: Introductionmentioning

confidence: 99%

Synchronization and antisynchronization of N‐coupled fractional‐order complex chaotic systems with ring connection

Jiang

Zhang

2018

Math Methods in App Sciences

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This paper is devoted to investigate synchronization and antisynchronization of N‐coupled general fractional‐order complex chaotic systems described by a unified mathematical expression with ring connection. By means of the direct design method, the appropriate controllers are designed to transform the fractional‐order error dynamical system into a nonlinear system with antisymmetric structure. Thus, by using the recently established result for the Caputo fractional derivative of a quadratic function and a fractional‐order extension of the Lyapunov direct method, several stability criteria are derived to ensure the occurrence of synchronization and antisynchronization among N‐coupled fractional‐order complex chaotic systems. Moreover, numerical simulations are performed to illustrate the effectiveness of the proposed design.

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State estimation-based parameter identification for a class of nonlinear fractional-order systems

Oliva-Gonzalez,

Martínez-Guerra

2024

Nonlinear Dyn

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Parametric identification is an important part of system theory since knowledge of the parameters allows the analysis and control of the system. The aim of this paper is to propose a novel robust (against measurement noise) parameter identification method for a class of nonlinear fractional-order systems. In order to solve the parametric identification we carry out this problem to a state estimation problem, we introduce a Fractional Algebraic Identifiability (FAI) property which allows to represent the system parameters as a function of the inputs and outputs of the system, this parameter identification method provides an on-line identification process (while the system is operating), we also propose a fractional-order differentiator which allows to reduce the effect of measurement noise as well as to provide the estimation of a fractional-order derivative of the system output. Moreover, we use the Mittag–Leffler boundedness to demonstrate the convergence of this method, a different approach for this stability analysis method is given in this paper. Finally, we illustrate the accuracy and robustness of our proposed method by means of the parametric identification of two nonlinear fractional-order systems: a time-varying nonlinear fractional-order system and a nonlinear fractional-order mathematical model of a simple pendulum.

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Synchronization of incommensurate fractional order system

Cited by 6 publications

References 8 publications

Sliding Mode Control for a Class of Nonlinear Fractional Order Systems with a Fractional Fixed-Time Reaching Law

Sliding Mode Control for a Class of Nonlinear Fractional Order Systems with a Fractional Fixed-Time Reaching Law

Synchronization and antisynchronization of N‐coupled fractional‐order complex chaotic systems with ring connection

State estimation-based parameter identification for a class of nonlinear fractional-order systems

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