异构分数阶混沌系统的自适应有限时间投影同步控制

Adaptive Finite-time Projective Synchronization Control for Non-identical Fractional-order Chaotic Systems

  • 摘要: 针对存在未知参数的分数阶混沌系统,探讨两个异构分数阶混沌系统的自适应同步控制问题。首先通过引入分数阶算子Dp-q改进传统整数投影同步控制器以适应分数阶系统的特性,实现异构分数阶混沌系统的同步。其次,设计合适的自适应律在线估计和补偿系统中的未知参数,实现对未知参数异构分数阶混沌系统的鲁棒同步控制。基于Lyapunov稳定性理论和有限时间稳定性理论,推导实现分数阶混沌系统有限时间同步的充分条件,并给出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近稳定。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: This paper addresses the adaptive synchronization control problem for non-identical fractional-order chaotic systems with unknown parameters. Firstly, by introducing the fractional-order operator Dpq, the traditional integer-order projection synchronization controller is improved to achieve synchronization between the non-identical fractional order systems. Secondly, an appropriate adaptive law is developed to estimate and compensate for the unknown parameters in real time, thereby realizing robust synchronization control for fractional-order chaotic systems with parameter uncertainties. Rigorous proofs based on Lyapunov stability theory and finite-time stability theory establish the global asymptotic stability of the closed-loop system, while sufficient conditions for finite-time synchronization are derived, providing an upper bound on the settling time that explicitly depends on the system’s initial conditions. The proposed adaptive fractional projection control strategy guarantees the boundedness of synchronization errors and their convergence within a finite time. Numerical simulations demonstrate the effectiveness of the proposed synchronization scheme and its practical applicability in secure communication.

     

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