时滞网络周期事件触发的有限时间同步控制

Finite-Time Synchronization Control of Delayed Networks via Periodic Event Triggering

摘要: 研究时变耦合时滞网络在周期事件触发牵制控制下的有限时间实用同步。采用有界时间基、平滑反馈及正性离散内部变量，建立误差包络和有限进入时间上界，并以保持值估计降低保守性。进一步构造Lorenz参考域上的显式平方和证书，给出可认证的局部同步配置。标量认证算例在RMS容差0.04下的统一时间上界为1.796 s，满足4 s期限；动态触发较静态减少85.4%的局部更新。原Lorenz仿真基准中，五种机制按相同搜索预算和共同窗口容差比较：0.01容差下，缩放动态较调参后的缩放静态少更新30.9%，但不优于全部未缩放及参考方案。冻结参数后的10组独立初值中，两种静态机制持续达标率为100%，三种动态机制均为90%。理论认证与仿真配置分别说明；结论为有限时间实用同步，不是有限时间精确同步。

Abstract: Practical finite-time synchronization of networks with time-varying coupling delays is studied under periodic event-triggered pinning control. Bounded time-base feedback and a positivity-preserving discrete internal variable yield an error envelope and a finite entry-time bound. A held-value estimate reduces conservatism. An explicit sum-of-squares certificate on an invariant Lorenz reference domain further yields a certified local synchronization configuration. For the scalar certified example, the uniform bound is 1.796 s at an RMS tolerance of 0.04, meeting the 4 s deadline; dynamic triggering reduces local updates by 85.4% relative to static triggering. The original Lorenz simulation benchmark compares five mechanisms with equal search budgets and common window tolerances. At a tolerance of 0.01, scaled dynamic triggering uses 30.9% fewer updates than tuned scaled static triggering, but does not outperform all unscaled and reference schemes. With parameters frozen, both static mechanisms maintain the tolerance in all ten held-out trials, while each dynamic mechanism succeeds in nine, revealing a trade-off between updates and post-deadline accuracy. The certified and simulation configurations are distinguished explicitly. The conclusions concern practical, not exact, finite-time synchronization.