Sliding mode control of a class of fractional chaotic systems in the presence of parameter perturbations

Xu, Yong; Wang, Hua; Liu, Di; Huang, Hui

doi:10.1177/1077546313486283

Cited by 45 publications

(21 citation statements)

References 31 publications

(26 reference statements)

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“…In most of the considered research, the boundaries of the perturbations are directly employed in the design of the TSMC law [22,23]. To estimate the disturbances, various design procedures based on the disturbance observer have been planned in the recent years [24].…”

Section: Literature Reviewmentioning

confidence: 99%

Nonsingular fast terminal sliding-mode stabilizer for a class of uncertain nonlinear systems based on disturbance observer

Mobayen

Tchier

2017

Scientia Iranica

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Abstract. This paper investigates a novel nonsingular fast terminal sliding-mode control method for the stabilization of the uncertain time-varying and nonlinear thirdorder systems. The designed disturbance observer satis es the nite-time convergence of the disturbance approximation error and the suggested nite-time stabilizer assures the presence of the switching behavior around the switching curve in the nite time. Furthermore, this approach can overcome the singularity problem of the fast terminal sliding-mode control technique. Moreover, knowledge about the upper bounds of the disturbances is not required and the chattering problem is eliminated. Usefulness and e ectiveness of the o ered procedure are con rmed by numerical simulation results.

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Section: Literature Reviewmentioning

confidence: 99%

Nonsingular fast terminal sliding-mode stabilizer for a class of uncertain nonlinear systems based on disturbance observer

Mobayen

Tchier

2017

Scientia Iranica

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“…Studies on chaos synchronization for the fractional order systems are just beginning to attract some attention due to its potential applications in secure communication and control processing. There are many different methods and strategies of fractional order continuous and discrete chaos synchronization have been developed such as activation feedback method, linear and nonlinear feedback synchronization [3,4,8,13,20,25,29], sliding mode control [12,16,22,23,30,34], adaptive control [1,2,5,9,14,21,33], and projective synchronization [10,17,24]. To the best of our knowledge, most of research efforts mentioned above have concentrated on studying the synchronization of fractional order chaotic systems whose models are identical, different.…”

Section: Introductionmentioning

confidence: 99%

Projective reduce order synchronization of fractional order chaotic systems with unknown parameters

Al-Sawalha¹

2017

J. Nonlinear Sci. Appl.

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This paper, mainly concerns the adaptive projective reduce order synchronization behavior of uncertain chaotic system. By Lyapunov stability theory, the adaptive control law and the parameter update law are derived to make the states of two chaotic and hyperchaotic systems asymptotically synchronized up to a desired identical and different scaling matrix. Numerical simulation results show that the proposed method is effective, convenient, and also faster for projective dual synchronization of chaotic and hyperchaotic systems.

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“…[11][12][13][14] In the work of Karimipour et al, 15 stabilization of the unstable periodic orbits of uncertain time-delayed chaotic systems with uncertain dynamics and input nonlinearity was handled. However, most of the previous literatures either have not attended for robust operation against system uncertainties and external perturbations or have assumed that the dynamics of the chaotic system is fully known.…”

Section: Introductionmentioning

confidence: 99%

Adaptive control of complex systems with unknown dynamics and input constraint: Applied to a chaotic elastic beam

Aghababa

2017

Adaptive Control & Signal

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Owing to the limitations of system identification and modeling techniques, there is usually some unknown dynamics in the mathematical models of the complex systems. In addition, external perturbations can affect the chaotic systems' responses and may destroy the desired control purpose. Consideration of such uncertain dynamics and external fluctuations in control applications is important in research and practice. On the other hand, because of the limited operation of control actuators, most of the practical implementations of control systems are forced with some input constraints. Therefore, this paper investigates the control problem of uncertain autonomous and/or nonautonomous complex chaotic systems in the presence of input saturation. The upper bounds of the unknown dynamics, modeling uncertainties, external perturbations, and the parameters of the saturation function are assumed to be unknown in advance. To make a fast control response, an adaptive nonsingular terminal variable structure controller is proposed to assure the finite-time stability of the equilibrium states. Rigorous stability analysis is performed to prove the correct performance of the designed control algorithm. Numerical simulations on the unified system and a chaotic elastic beam model are developed to demonstrate the usefulness of the introduced adaptive control strategy. It is worth to notice that the derived adaptive nonsmooth sliding mode approach is general and it can be easily adopted for controlling of a wide class of uncertain MIMO nonlinear systems. KEYWORDSadaptive variable structure control, complex system, finite settling time, input constraint, nonautonomous system Int J Adapt Control Signal Process. 2018;32:213-228. wileyonlinelibrary.com/journal/acs 214 AGHABABAperformance of the overall closed-loop system and even can destabilize the process. For example, consider mechanical system intrinsic stresses concentrated by a chaotic motion. Such condition not only can result in strain fractures of the system's mechanical parts but also can decrease machine power, engender noise and disturbance, and enlarge friction. Generally speaking, any form of unwanted oscillation may yield to machine performance degradation, more energy spending, noise generation, reliability, and efficiency decrease, damaging mechanical parts of the system and human discomfort. 2 Therefore, to avoid terrible failures of components and materials of the system, to reduce the lifetime of the machine, to modify the oscillation such that the system state is conveyed in a suitable level, and to avoid human injuries, some alternative control mechanisms should be adopted to compensate and suppress unnecessary chaotic behaviors.Up to now, a wide variety of control algorithms, such as adaptive control, 3 sliding mode control, 4 robust control, 5 fuzzy logic method, 6 fault tolerant control, 7 impulsive control, 8 backstepping design, 9 and neural networks, 10 have been addressed for chaos control and synchronization. However, most of the previous literatures either h...

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Sliding mode control of a class of fractional chaotic systems in the presence of parameter perturbations

Cited by 45 publications

References 31 publications

Nonsingular fast terminal sliding-mode stabilizer for a class of uncertain nonlinear systems based on disturbance observer

Nonsingular fast terminal sliding-mode stabilizer for a class of uncertain nonlinear systems based on disturbance observer

Projective reduce order synchronization of fractional order chaotic systems with unknown parameters

Adaptive control of complex systems with unknown dynamics and input constraint: Applied to a chaotic elastic beam

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