未知参数的异构分数阶混沌系统的自适应有限时间同步控制及其在在保密通信的应用

Adaptive Finite-time synchronization of non-identical fractional-order chaotic systems with unknown parameters and its application in secure communication

  • 摘要: 针对存在未知参数的分数阶混沌系统,本文探讨了两个异构分数阶混沌系统的自适应同步控制问题。本文首先通过引入分数阶算子对传统投影同步控制器进行了改进,以适应分数阶系统的特性;其次,设计了合适的自适应律来在线估计和补偿系统中的未知参数,从而实现了对异构分数阶混沌系统的鲁棒同步控制。同时,基于Lyapunov稳定性理论和有限时间稳定性理论,本文推导了实现分数阶混沌系统有限时间同步的充分条件,并首次给出了与系统初始条件密切相关的稳定时间上限,严格证明了系统的全局渐进稳定。所提出的自适应分数投影控制策略确保了同步误差的有界性及其在有限时间内的收敛稳定性。仿真实验进一步验证了该同步方案的有效性和在保密通信领域的实际可行性。

     

    Abstract: For fractional-order chaotic systems with unknown parameters, this paper investigates the adaptive synchronization control problem of two non-identical fractional-order chaotic systems. Firstly, by introducing fractional-order operators into the synchronization controller, an improved projective synchronization scheme is proposed. Secondly, appropriate adaptive laws are designed to handle the unknown parameters in the system, making it adaptable to the design of synchronization controllers for non-identical fractional-order chaotic systems with unknown parameters. Meanwhile, based on Lyapunov stability theory and finite-time stability theory, sufficient conditions for achieving finite-time synchronization of fractional-order chaotic systems are derived, an upper bound of the settling time related to the system’s initial conditions is obtained, and the stability of the system is proven. The developed adaptive fractional projective control strategy ensures the boundedness of all synchronization errors and their stability within a finite time. Simulation results demonstrate the effectiveness of the proposed synchronization scheme and its feasibility for application in secure communication.

     

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