In this paper, adaptive-sliding mode control method is proposed for synchronisation of two 6D hyper-chaotic systems in the presence of external disturbance and parametric uncertainty and unknown parameters in the slave system. In the first section of this paper, two 6D integer order hyper-chaotic systems in the presence of external disturbance signal, parametric uncertainty and unknown parameters in the slave system are studied. In the second part of this paper, after identifying chaos in fractional order dynamic of the mentioned system, synchronisation of two 6D fractional derivative hyper-chaotic systems in the presence of external disturbance signal, parametric uncertainty and unknown parameters in the slave system is investigated, in which fractional order Riemann-Liouville derivative is used; a new fractional order sliding surface is defined for the hyper-chaotic system to determine the proper active control. Proper adaptive control laws are used to estimate the uncertainty bound, unknown disturbance signal and system parameters. Stability of the closed-loop control system is proved using Lyapunov theory in both modes. Simulation results in MATLAB show the desired application of the proposed controllers in the presence of disturbance and parametric uncertainty.

中文翻译：

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在存在扰动和参数不确定性未知边界的情况下，具有未知参数的 6D 超混沌系统的同步

在本文中，提出了自适应滑模控制方法，用于在存在外部扰动和参数不确定性以及从属系统中的未知参数的情况下同步两个 6D 超混沌系统。本文的第一部分研究了从属系统中存在外部扰动信号、参数不确定性和未知参数的两个6D整数阶超混沌系统。在本文的第二部分，在识别了上述系统的分数阶动力学中的混沌之后，研究了在从系统中存在外部扰动信号、参数不确定性和未知参数的情况下两个 6D 分数阶导数超混沌系统的同步问题，其中使用分数阶 Riemann-Liouville 导数；为超混沌系统定义了一个新的分数阶滑动面，以确定适当的主动控制。适当的自适应控制法则用于估计不确定性界限、未知干扰信号和系统参数。在两种模式下都使用李雅普诺夫理论证明了闭环控制系统的稳定性。MATLAB 中的仿真结果显示了所提出的控制器在存在干扰和参数不确定性的情况下的理想应用。