This paper gives multiswitching synchronisation scheme for a class of fractional-order chaotic systems by combining active and adaptive control theories. Adaptive controllers have been designed by using different laws of switching and fractional-order Lyapunov stability theory. We have also constructed a new fractional-order Duffing system. The fractional-order Duffing system and fractional-order Rabinovich–Fabrikant system have been taken as the drive system and the response system respectively. Applications have been demonstrated. Theoretical analysis and numerical simulations are also given to verify the robustness of the proposed controllers.

中文翻译：

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不同阶次多开关同步的新型分数阶混沌系统

本文结合主动控制理论和自适应控制理论，给出了一类分数阶混沌系统的多开关同步方案。自适应控制器是通过使用不同的开关定律和分数阶李雅普诺夫稳定性理论设计的。我们还构建了一个新的分数阶 Duffing 系统。分数阶 Duffing 系统和分数阶 Rabinovich-Fabrikant 系统分别作为驱动系统和响应系统。已经证明了应用。还给出了理论分析和数值模拟来验证所提出的控制器的鲁棒性。