参数未知的复混沌系统错位复修正函数投影同步

Misalignment complex correction function projection synchronization of complex chaotic systems with unknown parameters

摘要:

为解决参数未知的复混沌系统在复杂状态变量无法分离情况下的同步控制问题,提出了错位复修正函数投影同步(misalignment complex correction function projection synchronization,MCCFPS)控制方案。首先,设计一种自适应跟踪控制器,使其能够适应任意有界复混沌系统之间的差异。该控制器通过动态控制强度和收敛因子增强自适应能力并调节收敛速度,通过Lyapunov理论证明该控制器的收敛性,从而为控制方案的可靠性提供理论支持。然后,对两个异构的复混沌系统进行动力学模型分析,计算并比较混沌系统和复混沌系统时间序列的模糊熵,验证复混沌系统的复杂度更高,从而突显其同步控制在保密通信应用中的优越性,并进一步设计其MCCFPS同步方案。最后,通过数值仿真验证MCCFPS方案的有效性。结果表明:该方案能够成功实现复混沌系统的同步控制,并具有良好的同步效果和控制性能。总体来说,相较于传统的混沌系统,研究引入复变量,并采用更复杂的MCCFPS同步控制方案,直接在复域中实现混沌同步,有效提高了系统的安全性。研究结果为复系统同步控制问题提供了新的思路和途径,具有重要的应用价值。

Abstract:

To address the problem of synchronizing chaotic systems with unknown parameters and complex state variables that cannot be separated, a misalignment complex correction function projection synchronization (MCCFPS) control scheme is proposed. First, an adaptive tracking controller is designed to accommodate the differences between any bounded complex chaotic systems. This controller enhances adaptive capability and adjusts convergence speed through dynamic control strength and convergence factors, and proves the convergence of the controller through Lyapunov theory, providing theoretical support for the reliability of the control scheme. Subsequently, the dynamic models of two heterogeneous complex chaotic systems are analyzed. Fuzzy entropy of the time series of chaotic and complex chaotic systems is calculated and compared to validate that complex chaotic systems have higher complexity. This highlights the superiority of their synchronization control in secure communication applications. The MCCFPS synchronization scheme is further designed. Finally, the effectiveness of the MCCFPS scheme is verified through numerical simulations. The results demonstrate that the scheme successfully achieves synchronization control of complex chaotic systems, exhibiting good synchronization effects and control performance. Overall, compared to traditional chaotic systems, this study introduces complex variables and adopts a more sophisticated synchronization control scheme, MCCFPS, to directly achieve chaotic synchronization in the complex domain, effectively enhancing system security. This research provides new ideas and approaches to the synchronization control problem of complex systems, holding significant practical value.