Hyperchaos control of the hyperchaotic Chen system by optimal control design

Effati, Sohrab; Nik, Hassan Saberi; Jajarmi, Amin

doi:10.1007/s11071-013-0804-0

Cited by 55 publications

(28 citation statements)

References 31 publications

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“…Therefore, the design and implementation of chaotic generators that could synchronize has become one of the most followed research avenues. To obtain higher security, the adoption of hyperchaotic systems [Barboza, 2007;Effati et al, 2013;Matsumoto et al, 1986;Rössler, 1979;Tamasevicius et al, 1997] characterized by two or more positive Lyapunov exponents seems to be more advantageous than the use of chaotic systems with only one positive Lyapunov exponent.…”

Section: Introductionmentioning

confidence: 99%

Coexistence of Chaos with Hyperchaos, Period-3 Doubling Bifurcation, and Transient Chaos in the Hyperchaotic Oscillator with Gyrators

Kengne

2015

Int. J. Bifurcation Chaos

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In this paper, the dynamics of the paradigmatic hyperchaotic oscillator with gyrators introduced by Tamasevicius and co-workers (referred to as the TCMNL oscillator hereafter) is considered. This well known hyperchaotic oscillator with active RC realization of inductors is suitable for integrated circuit implementation. Unlike previous literature based on piecewise-linear approximation methods, I derive a new (smooth) mathematical model based on the Shockley diode equation to explore the dynamics of the oscillator. Various tools for detecting chaos including bifurcation diagrams, Lyapunov exponents, frequency spectra, phase portraits and Poincaré sections are exploited to establish the connection between the system parameters and various complex dynamic regimes (e.g. hyperchaos, period-3 doubling bifurcation, coexistence of attractors, transient chaos) of the hyperchaotic oscillator. One of the most interesting and striking features of this oscillator discovered/revealed in this work is the coexistence of a hyperchaotic attractor with a chaotic one over a broad range of system parameters. This phenomenon was not reported previously and therefore represents a meaningful contribution to the understanding of the behavior of nonlinear dynamical systems in general. A close agreement is observed between theoretical and experimental analyses.

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Section: Introductionmentioning

confidence: 99%

Coexistence of Chaos with Hyperchaos, Period-3 Doubling Bifurcation, and Transient Chaos in the Hyperchaotic Oscillator with Gyrators

Kengne

2015

Int. J. Bifurcation Chaos

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“…According to [44], C derivative of order α of the function t γ is equal to: (38) using the above formula, C 0 D α t h i (t) can be calculated for t ≤ T as follows:…”

Section: Fractional Derivative Of the Proposed Terminal Functionmentioning

confidence: 99%

“…Unfortunately, these works also suffer from all the abovementioned problems. Effati et al in [38] have utilized the optimal control technique for the finite-time chaos synchronization. The main feature of this work is that the synchronization time can be set in advance.…”

mentioning

confidence: 99%

A novel continuous time-varying sliding mode controller for robustly synchronizing non-identical fractional-order chaotic systems precisely at any arbitrary pre-specified time

Khanzadeh

Pourgholi

2016

Nonlinear Dyn

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In this paper, attempts are made to design a novel time-varying switching surface in sliding mode control which enables us to synchronize two fractional chaotic systems precisely at any arbitrary pre-specified time. For both Caputo (C) and Riemann-Liuville (RL) derivatives, control laws based on Lyapunov stability theorem are derived. The proposed method is completely robust against existence of uncertainties and exogenous disturbances due to eliminating the reaching phase. Since the sign function is replaced by fractional RL integral of the sign function, the chattering is removed. The simulation results in different scenarios are reported to show the effectiveness of the proposed method.

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“…Several control methods are applied to chaotic systems, such as adaptive [9], optimal [10] and fuzzy [11] control Among the aforementioned control methods, some must use high gain in designing parameters; while others need Lipschitz conditions for nonlinear terms to be satisfied. Several control methods are applied to chaotic systems, such as adaptive [9], optimal [10] and fuzzy [11] control Among the aforementioned control methods, some must use high gain in designing parameters; while others need Lipschitz conditions for nonlinear terms to be satisfied.…”

Section: Introductionmentioning

confidence: 99%

Sum‐of‐Squares‐Based Finite‐Time Adaptive Sliding Mode Control of Uncertain Polynomial Systems With Input Nonlinearities

Mardani¹,

Vafamand²,

Zeini³

et al. 2017

Asian Journal of Control

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This paper proposes a novel adaptive sliding mode control (ASMC) for a class of polynomial systems comprising uncertain terms and input nonlinearities. In this approach, a new polynomial sliding surface is proposed and designed based on the sum-of-squares (SOS) decomposition. In the proposed method, an adaptive control law is derived such that the finite-time reachability of the state trajectories in the presence of input nonlinearity and uncertainties is guaranteed. To do this, it is assumed that the uncertain terms are bounded and the input nonlinearities belong to sectors with positive slope parameters. However, the bound of the uncertain terms is unknown and adaptation law is proposed to effectively estimate the uncertainty bounds. Furthermore, based on a novel polynomial Lyapunov function, the finite-time convergence of the sliding surface to a pre-chosen small neighborhood of the origin is guaranteed. To eliminate the time derivatives of the polynomial terms in the stability analysis conditions, the SOS variables of the Lyapunov matrix are optimally selected. In order to show the merits and the robust performance of the proposed controller, chaotic Chen system is provided. Numerical simulation results demonstrate chattering reduction in the proposed approach and the high accuracy in estimating the unknown parameters.

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Hyperchaos control of the hyperchaotic Chen system by optimal control design

Cited by 55 publications

References 31 publications

Coexistence of Chaos with Hyperchaos, Period-3 Doubling Bifurcation, and Transient Chaos in the Hyperchaotic Oscillator with Gyrators

Coexistence of Chaos with Hyperchaos, Period-3 Doubling Bifurcation, and Transient Chaos in the Hyperchaotic Oscillator with Gyrators

A novel continuous time-varying sliding mode controller for robustly synchronizing non-identical fractional-order chaotic systems precisely at any arbitrary pre-specified time

Sum‐of‐Squares‐Based Finite‐Time Adaptive Sliding Mode Control of Uncertain Polynomial Systems With Input Nonlinearities

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