Synchronization of nonlinear chaotic electromechanical gyrostat systems with uncertainties

Aghababa, Mohammad Pourmahmood; Aghababa, Hasan Pourmahmood

doi:10.1007/s11071-011-0181-5

Cited by 51 publications

(25 citation statements)

References 19 publications

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“…To achieve asymptotic stability of the error dynamics (4), let us introduce the following assumptions and a lemma. Assumption 1 [20]. …”

Section: ( )mentioning

confidence: 99%

“…Chaos Synchronization is one of the critical issues and has received a considerable interest among researchers in nonlinear sciences for more than two decades [6,7] after the exceptional work of Pecorra and Carroll [5]. Until now, certain linear and nonlinear techniques have been proposed and applied successfully to achieve control and synchronization of chaotic systems [8][9][10][11][12][13][14][15][16][17][18][19][20]. Notable among those, ACTs is one of the effectual techniques for stabilizing and synchronizing chaotic systems [11][12][13][14].…”

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confidence: 99%

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Chaos Control and Synchronization of a Novel Chaotic System Based upon Adaptive Control Algorithm

Ahmad

Saaban²,

Ibrahim³

et al. 2014

International Journal of Advances in Telecommunications, Electrotechnics, Signals and Systems

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Abstract-Controlling chaos is stabilizing one of the unstable periodic orbits either to its equilibrium point or to a stable periodic orbit by means of an appropriate continuous signal injected to the system. On the other hand, chaos synchronization refers to a procedure where two chaotic oscillators (either identical or nonidentical) adjust a given property of their motion to a common behavior. This research paper concerns itself with the Adaptive control and synchronization of a new chaotic system with unknown parameters. Based on the Lyapunov direct method (LDM), the Adaptive control techniques (ACTs) are designed in such a way that the trajectory of the new chaotic system is globally stabilized to one of its equilibrium points of the uncontrolled system. Moreover, the Adaptive control law is also applied to achieve the synchronization state of two identical systems and two different chaotic systems with fully unknown parameters. The parameters identification, chaos control and synchronization of the chaotic system have been carried out simultaneously by the Adaptive controller. All simulation results are carried out to corroborate the effectiveness and the robustness of the proposed methodology and possible feasibility for synchronizing two chaotic systems by using Mathematica 9.

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“…To achieve asymptotic stability of the error dynamics (4), let us introduce the following assumptions and a lemma. Assumption 1 [20]. …”

Section: ( )mentioning

confidence: 99%

mentioning

confidence: 99%

Chaos Control and Synchronization of a Novel Chaotic System Based upon Adaptive Control Algorithm

Ahmad

Saaban²,

Ibrahim³

et al. 2014

International Journal of Advances in Telecommunications, Electrotechnics, Signals and Systems

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“…Furthermore, the finite-time control strategies have demonstrated better robustness and disturbance rejection properties. In the works [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30], we have proposed finitetime controllers for chaos control/synchronization of chaotic systems.…”

Section: Introductionmentioning

confidence: 99%

A fractional sliding mode for finite-time control scheme with application to stabilization of electrostatic and electromechanical transducers

Aghababa

2015

Applied Mathematical Modelling

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Please cite this article as: M.P. Aghababa, A fractional sliding mode for finite-time control scheme with application to stabilization of electrostatic and electromechanical transducers, Appl. Math. Modelling (2015), doi: http:// dx. AbstractChaos suppression of non-autonomous uncertain chaotic systems is a very important and attractive topic in the field of physics and engineering. On the other hand, the use of fractional calculus in both research and practice has become as an increasing and interesting issue in recent years. In this paper, we introduce a novel fractional control method for chaos control of integer-order non-autonomous chaotic systems. It is assumed that the system is disturbed by some model uncertainties and external noises. A novel fractional nonsingular terminal sliding manifold which is appropriate for integerorder systems is proposed. Then, on the basis of fractional Lyapunov stability theorem, a suitable robust sliding mode control law is designed to force the state trajectories of the system into the sliding manifold. It is proved that both the sliding mode and reaching phase are realized in a given finite time.Finally, the proposed method is applied for stabilization of chaotic electrostatic and electromechanical transducers.

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“…Many techniques have been devised for controlling chaos via, for example, nonlinear and robust control, sliding mode control, adaptive control, partial control, control by weak signals, and finite time control ( [9][10][11][12][13][14][15][16] and the references therein). In these approaches, the unstable periodic orbits are determined and a control signal is then generated which will stabilize the chaotic system to an equilibrium, locally or globally.…”

Section: Introductionmentioning

confidence: 99%

Taming Chaos by Linear Regulation with Bound Estimation

Wang

Chen

2015

Journal of Applied Mathematics

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Chaos control has become an important area of research and consequently many approaches have been proposed to control chaos. This paper proposes a linear regulation method. Different from the existing approaches is that it can provide region of attraction while estimating the bounding behaviour of the norm of the states. The proposed method also possesses design flexibility and can be easily used to cater for special requirement such that control signal should be generated via single input, single state, static feedback and so forth. The applications to the Tigan system, the Genesio chaotic system, the novel chaotic system, and the Lorenz chaotic system justify the above claims.

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Synchronization of nonlinear chaotic electromechanical gyrostat systems with uncertainties

Cited by 51 publications

References 19 publications

Chaos Control and Synchronization of a Novel Chaotic System Based upon Adaptive Control Algorithm

Chaos Control and Synchronization of a Novel Chaotic System Based upon Adaptive Control Algorithm

A fractional sliding mode for finite-time control scheme with application to stabilization of electrostatic and electromechanical transducers

Taming Chaos by Linear Regulation with Bound Estimation

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