用于控制高维开放环境系统的区域混沌同步
Regional Chaos Synchronization towards controlling high-dimensional open environmental systems
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中文总结 AI 辅助
针对传统混沌同步无法控制高维开放环境系统的问题，提出区域混沌同步方法，通过选择仅在目标区域有差异的目标轨迹减少外部误差注入，实现目标区域状态与目标轨迹同步，为天气控制等提供新框架。
中文摘要 AI 辅助
尽管控制混沌可被视为混沌同步的一种形式，但传统混沌同步并未提供控制高维开放混沌系统（如天气）的实用框架。在高维开放环境系统中，根本不可能使驱动系统与响应系统之间的差异在整个域内渐近趋近于零。本文提出区域混沌同步，替代传统全局混沌同步，该方法仅利用位于目标区域内的执行器，使仅在小目标区域内的状态变量与目标轨迹同步。理论分析与数值实验表明，区域混沌同步的性能会因控制器无意修改的外部区域注入的误差而大幅下降；即使执行器规格相同，区域混沌同步的性能在不同轨迹间也存在差异，而传统全局混沌同步不存在此情况。合适的目标轨迹仅在目标区域内与自然轨迹有显著差异，这种目标轨迹的选择可最小化外部区域的误差注入，从而实现成功的区域混沌同步。本文还探讨了该新框架对天气控制等现实控制问题的意义。
英文摘要
Although controlling chaos can be regarded as a form of chaos synchronization, conventional chaos synchronization does not provide a practical framework for controlling high-dimensional open chaotic systems, such as weather. In high-dimensional open environmental systems, it is simply impossible to make the difference between drive and response systems asymptotically approach zero over the entire domain. Instead of conventional global chaos synchronization, here I define regional chaos synchronization, in which state variables within only a small target region are synchronized with a target trajectory using actuators located in the target region. Theoretical considerations and numerical experiments show that the performance of regional chaos synchronization is substantially degraded by the injection of errors from exterior regions that the controller is not intended to modify. Even under the same actuator specifications, the performances of regional chaos synchronization differ among trajectories, which is not the case of conventional global chaos synchronization. An appropriate target trajectory differs substantially from the natural trajectory only in the target region. This choice of target trajectories can minimize the injection of errors from exterior regions and thereby enable successful regional chaos synchronization. The implications of this new framework for realistic control problems such as weather control are discussed.
