论文标题
基于奇异的扰动分析在异质非线性系统的有名网络中的动态共识分析
Singular-Perturbations-Based Analysis of Dynamic Consensus in Directed Networks of Heterogeneous Nonlinear Systems
论文作者
论文摘要
我们分析了网络的异质非线性系统，具有扩散耦合并在通用静态有向图上互连。由于网络的构成性，总的来说，完全同步是不可能的，但是出现了出现的动态。这可能是在两个时间尺度中演变的两个动态系统的特征。第一个“慢”对应于同步歧管上网络的动力学。第二个“快速”对应于同步误差。我们提出了一个框架，以根据缓慢动力学的行为来分析新兴动态。首先，我们给出条件，如果缓慢的动力学接收到全球渐近稳定的平衡，则网络系统也是如此。其次，我们给出条件，如果缓慢的动力学接收渐近稳定的轨道和一个不稳定的平衡点，则存在一个唯一的周期性轨道，几乎是渐近稳定的。因此，紧急行为是明确的，系统渐近地在频率上同步，并且在极限上随着耦合强度的增长，新兴的动力学接近慢系统的动力学。我们的分析是使用奇异扰动理论建立的。在这方面，我们对不变套件的稳定性和限制周期的稳定性做出了贡献。
We analyze networked heterogeneous nonlinear systems, with diffusive coupling and interconnected over a generic static directed graph. Due to the network's hetereogeneity, complete synchronization is impossible, in general, but an emergent dynamics arises. This may be characterized by two dynamical systems evolving in two time-scales. The first, "slow", corresponds to the dynamics of the network on the synchronization manifold. The second, "fast", corresponds to that of the synchronization errors. We present a framework to analyse the emergent dynamics based on the behavior of the slow dynamics. Firstly, we give conditions under which if the slow dynamics admits a globally asymptotically stable equilibrium, so does the networked systems. Secondly, we give conditions under which, if the slow dynamics admits an asymptotically stable orbit and a single unstable equilibrium point, there exists a unique periodic orbit that is almost-globally asymptotically stable. The emergent behavior is thus clear, the systems asymptotically synchronize in frequency and, in the limit, as the coupling strength grows, the emergent dynamics approaches that of the slow system. Our analysis is established using singular-perturbations theory. In that regard, we contribute with original statements on stability of disconnected invariant sets and limit cycles.
