Adaptive hybrid complex projective combination–combination synchronization in non-identical hyperchaotic complex systems

Khan, Ayub; Nigar, Uzma

doi:10.1007/s40435-019-00584-z

Cited by 13 publications

(11 citation statements)

References 44 publications

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“…The construction of adaptive controller and parameter estimation correction law is shown in Eq.8 and Eq.9 [11]:…”

Section: Lemma 1: If There Exists a Differentiable Positive Definite ...mentioning

confidence: 99%

Finite-time Synchronization of the 4-D Hyper-chaotic Chen-Qi-like System

Wang

2023

J. Phys.: Conf. Ser.

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For Chen-Qi-like four-dimensional hyper-chaotic system, controllers designed with Lyapunov stability theory to achieve synchronous/anti- synchronous control of chaos are found that sometimes synchronization errors do not decrease to zero in finite time. To solve it, a new controller and parameter estimation law are proposed to achieve finite-time synchronization. The stability analysis of the closed-loop dynamics is derived and the effectiveness of the theoretical results is testified. Taking the parameters L=2, μ=0.5, the state time history diagram and the synchronous error curve are investigated via numerical simulation, which show that the synchronization errors are zero in finite time while two systems in chaotic motion, but synchronization error of the state with cubic nonlinearity is not zero in finite time while two systems in periodic motion; Adjust L=200,μ=0.5, numerical simulation again, then all the errors are zero in finite time. Thus the effectiveness is verified.

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“…The construction of adaptive controller and parameter estimation correction law is shown in Eq.8 and Eq.9 [11]:…”

Section: Lemma 1: If There Exists a Differentiable Positive Definite ...mentioning

confidence: 99%

Finite-time Synchronization of the 4-D Hyper-chaotic Chen-Qi-like System

Wang

2023

J. Phys.: Conf. Ser.

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“…Reference 17 developed a combination‐combination synchronization scheme for a kind of 4‐D autonomous hyperchaotic system. Reference 18 coped with the CS problem for the complex chaotic systems by designing an adaptive control proposal. More recently, finite‐time stability theory has been applied to the stabilization of different systems, such as the event‐triggered control of nonlinear Markov jump singularly perturbed models, 19 the event‐triggered control of semi‐Markovian switching cyber‐physical systems, 20 the input‐output stabilization of nonlinear hidden semi‐Markov switching systems 21 .…”

Section: Introductionmentioning

confidence: 99%

Fixed time function combination synchronization of perturbed chaotic systems via adaptive control

Su,

Luo

2024

Adaptive Control & Signal

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SummaryThe concerns of this article is to investigate the fixed time function combination synchronization (FCS) among three different chaotic systems with disturbances. First, a new stability theorem is presented by virtue of the integral inequality technique and a more accurate upper estimation of the convergence time is given. Next, the fixed time FCS problem is considered for the perturbed chaotic systems in which the scaling functions are generated by the bounded dynamical systems. Besides, the synchronization time is related to the control parameters rather than the initial values. The time upper bound can be calculated out by the simple formula, which is the function of control parameters. Finally, a simulation example is provided to illustrate the correctness of the derived criteria.

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“…Since Runzi et al [28] revealed the combination synchronization scheme, the synchronization of multi-drive and multi-response systems, multi-drive and single-response systems, single-drive and multi-response systems are suggested. Later, some new synchronization schemes appeared and have been developed by leaps and bounds, such as the combination-combination synchronization [29][30][31][32], compound synchronization [33][34][35] and double compound synchronization [36,37], etc. It will be a major breakthrough in chaos synchronization.…”

Section: Introductionmentioning

confidence: 99%

The Multi-Switching Sliding Mode Combination Synchronization of Fractional Order Non-Identical Chaotic System with Stochastic Disturbances and Unknown Parameters

Pan

Wang

2022

Fractal Fract

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This paper deals with the issue of the multi-switching sliding mode combination synchronization (MSSMCS) of fractional order (FO) chaotic systems with different structures and unknown parameters under double stochastic disturbances (SD) utilizing the multi-switching synchronization method. The stochastic disturbances are considered as nonlinear uncertainties and external disturbances. Our theoretical part considers that the drive-response systems have the same or different dimensions. Firstly, a FO sliding surface is established in terms of the fractional calculus. Secondly, depending on the FO Lyapunov stability theory and the sliding mode control technique, the multi-switching adaptive controllers (MSAC) and some suitable multi-switching adaptive updating laws (MSAUL) are designed. They can ensure that the state variables of the drive systems are synchronized with the different state variables of the response systems. Simultaneously, the unknown parameters are assessed, and the upper bound values of stochastic disturbances are examined. Selecting the suitable scale matrices, the multi-switching projection synchronization, multi-switching complete synchronization, and multi-switching anti-synchronization will become special cases of MSSMCS. Finally, examples are displayed to certify the usefulness and validity of the scheme via MATLAB.

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Adaptive hybrid complex projective combination–combination synchronization in non-identical hyperchaotic complex systems

Cited by 13 publications

References 44 publications

Finite-time Synchronization of the 4-D Hyper-chaotic Chen-Qi-like System

Finite-time Synchronization of the 4-D Hyper-chaotic Chen-Qi-like System

Fixed time function combination synchronization of perturbed chaotic systems via adaptive control

The Multi-Switching Sliding Mode Combination Synchronization of Fractional Order Non-Identical Chaotic System with Stochastic Disturbances and Unknown Parameters

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