School of Automation, Guangdong Polytechnic Normal University, Guangzhou, China.
Guangzhou Key Laboratory of Intelligent Building Equipment Information Integration and Control, Guangzhou, China.
PLoS One. 2022 Mar 23;17(3):e0263007. doi: 10.1371/journal.pone.0263007. eCollection 2022.
This paper focuses on the finite-time generalized synchronization problem of non-identical fractional order chaotic (or hyper-chaotic) systems by a designing adaptive sliding mode controller and its application to secure communication. The effects of both disturbances and model uncertainties are taken into account. A novel fractional order integral sliding mode surface is designed and its stability to the origin is proved in a given finite time. By the aid of the fractional Lyapunov stability theory, a robust controller with adaptive update laws is proposed and its finite-time stability for generalized synchronization between two non-identical fractional-order chaotic systems in the presence of model uncertainties and external disturbances is derived. Numerical simulations are provided to demonstrate the effectiveness and robustness of the presented approach. All simulation results obtained are in good agreement with the theoretical analysis. According to the proposed generalized finite-time synchronization criterion, a novel speech cryptosystem is proposed to send or share voice messages privately via secure channel. Security and performance analyses are given to show the practical effect of the proposed theories.
本文主要研究非一致分数阶混沌（或超混沌）系统的有限时间广义同步问题，设计自适应滑模控制器并将其应用于安全通信。考虑了干扰和模型不确定性的影响。设计了一种新颖的分数阶积分滑模面，并证明了其在给定有限时间内的原点稳定性。借助分数阶 Lyapunov 稳定性理论，提出了一种具有自适应更新律的鲁棒控制器，并推导了在存在模型不确定性和外部干扰的情况下，两个非一致分数阶混沌系统之间的广义同步的有限时间稳定性。数值模拟验证了所提出方法的有效性和鲁棒性。所有得到的仿真结果都与理论分析一致。根据所提出的广义有限时间同步准则，提出了一种新的语音加密系统，通过安全通道发送或共享私人语音消息。给出了安全性和性能分析，以显示所提出理论的实际效果。
