基于牵制协议的异质网络拟同步分析

Quasi-synchronization in heterogeneous networks based on pinning control protocol

本文主要考虑一类异质谐振子系统的有界同步(或拟同步)问题。对于一般的异质谐振子系统,考虑了具有异质非线性扰动的情形,即每个谐振子的非线性扰动也是异质的。引入了一个领导者,基于牵制控制算法,设计了一个分布式同步协议。构造了一个Lyapunov函数,通过运用稳定性理论和线性矩阵不等式方法证明了异质谐振子系统在一定条件下可以实现拟同步,即每个跟随者谐振子的状态与领导者谐振子状态的差最终趋于有界的范围,给出了实现拟同步的充分性判据。同时,给出了拟同步误差上界的估计。最后,通过数值仿真验证了理论结果的有效性。

This paper mainly investigates the bounded synchronization(or quasi-synchronization) problem of heterogeneous harmonic oscillators. For a general heterogeneous harmonic oscillator system, heterogeneous nonlinear perturbations are considered for each harmonic oscillator. A leader is introduced to design a distributed synchronization protocol based on the pinning control algorithm. A Lyapunov function is constructed. By applying the stability theory and the linear matrix inequality method, it is proved that the heterogeneous harmonic oscillator systems can reach quasi-synchronization, that is, the errors between each follower harmonic oscillator and the leader harmonic oscillator tend to a bounded range. The sufficient criterion for achieving quasi-synchronization is derived. Furthermore, the upper bound of quasi-synchronization errors is estimated. Finally, numerical simulations are provided to verify the effectiveness of the theoretical results.