Adaptive terminal sliding mode control subject to input nonlinearity for synchronization of chaotic gyros

Chao, Yang; Ou, Chung-Ming

doi:10.1016/j.cnsns.2012.07.012

Cited by 45 publications

(35 citation statements)

References 29 publications

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“…The traditional works on the synchronization of nonlinear systems with slope-restricted input nonlinearity [9,17,19,21,22] do not consider the input time-delays, which are unavoidable in many practical systems due to distant position of an actuator from the control system unit. Ignoring the input nonlinearity or the input delay for derivation of a synchronization control strategy either causes performance degradation of an overall closed-loop system or even leads to noncoherent behaviors of two nonlinear systems.…”

Section: Remarkmentioning

confidence: 99%

“…Incorporation of slope-restricted nonlinearities is important in studying synchronization controller synthesis for nonlinear systems under uncertain inputs [16][17][18][19][20][21][22]. Sliding mode control strategies for nonlinear gyroscopes and unified second order complex oscillatory systems with input nonlinearities are explored in [16] and [17].…”

Section: Introductionmentioning

confidence: 99%

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Synchronization of nonlinear master–slave systems under input delay and slope‐restricted input nonlinearity

2015

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This article addresses the synchronization of nonlinear master-slave systems under input time-delay and sloperestricted input nonlinearity. The input nonlinearity is transformed into linear time-varying parameters belonging to a known range. Using the linear parameter varying (LPV) approach, applying the information of delay range, using the triple-integral-based Lyapunov-Krasovskii functional and utilizing the bounds on nonlinear dynamics of the nonlinear systems, nonlinear matrix inequalities for designing a simple delay-range-dependent state feedback control for synchronization of the drive and response systems is derived. The proposed controller synthesis condition is transformed into an equivalent but relatively simple criterion that can be solved through a recursive linear matrix inequality based approach by application of cone complementary linearization algorithm. In contrast to the conventional adaptive approaches, the proposed approach is simple in design and implementation and is capable to synchronize nonlinear oscillators under input delays in addition to the slope-restricted nonlinearity. Further, time-delays are treated using an advanced delay-range-dependent approach, which is adequate to synchronize nonlinear systems with either higher or lower delays. Furthermore, the resultant approach is applicable to the input nonlinearity, without using any adaptation law, owing to the utilization of LPV approach. A numerical example is worked out, demonstrating effectiveness of the proposed methodology in synchronization of two chaotic gyro systems.

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Section: Remarkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Synchronization of nonlinear master–slave systems under input delay and slope‐restricted input nonlinearity

2015

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“…Chen et al [14,15] researched the synchronization of fractional-order chaotic neural networks. With the development of sliding mode control (SMC) technique, SMC approach has became a universal method to realize the stabilization or synchronization of chaotic systems [16][17][18][19][20]. It is well known that the system on the sliding manifold has desired properties such as good stability, disturbance rejection ability, and tracking capability.…”

Section: Introductionmentioning

confidence: 99%

Robust Control of a Class of Uncertain Fractional-Order Chaotic Systems with Input Nonlinearity via an Adaptive Sliding Mode Technique

Tian

Fei

2014

Entropy

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Abstract:In this paper, the problem of stabilizing a class of fractional-order chaotic systems with sector and dead-zone nonlinear inputs is investigated. The effects of model uncertainties and external disturbances are fully taken into account. Moreover, the bounds of both model uncertainties and external disturbances are assumed to be unknown in advance. To deal with the system's nonlinear items and unknown bounded uncertainties, an adaptive fractional-order sliding mode (AFSM) controller is designed. Then, Lyapunov's stability theory is used to prove the stability of the designed control scheme. Finally, two simulation examples are given to verify the effectiveness and robustness of the proposed control approach.

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“…Many methods have been proposed to synchronize chaotic systems including active control [6], back-stepping control [7], linear feedback control [8], adaptive control theory [9], sliding mode control [10,11], and fuzzy control [12]. For example, Bhalekar and Daftardar-Gejji [13] used active control for the problem of synchronization of fractional-order Liu system with fractional-order Lorenz system.…”

Section: Introductionmentioning

confidence: 99%

Active Sliding Mode for Synchronization of a Wide Class of Four-Dimensional Fractional-Order Chaotic Systems

Wang

Yuangui

Xue

et al. 2014

ISRN Applied Mathematics

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We focus on the synchronization of a wide class of four-dimensional (4-D) chaotic systems. Firstly, based on the stability theory in fractional-order calculus and sliding mode control, a new method is derived to make the synchronization of a wide class of fractional-order chaotic systems. Furthermore, the method guarantees the synchronization between an integer-order system and a fraction-order system and the synchronization between two fractional-order chaotic systems with different orders. Finally, three examples are presented to illustrate the effectiveness of the proposed scheme and simulation results are given to demonstrate the effectiveness of the proposed method.

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Adaptive terminal sliding mode control subject to input nonlinearity for synchronization of chaotic gyros

Cited by 45 publications

References 29 publications

Synchronization of nonlinear master–slave systems under input delay and slope‐restricted input nonlinearity

Synchronization of nonlinear master–slave systems under input delay and slope‐restricted input nonlinearity

Robust Control of a Class of Uncertain Fractional-Order Chaotic Systems with Input Nonlinearity via an Adaptive Sliding Mode Technique

Active Sliding Mode for Synchronization of a Wide Class of Four-Dimensional Fractional-Order Chaotic Systems

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