Comprehending Complexity: Data-Rate Constraints in Large-Scale Networks
Comprehending Complexity: Data-Rate Constraints in Large-Scale Networks
复制标题
理解复杂性：大规模网络中的数据速率约束
DOI：
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发表时间：
2019
影响因子：
6.8
通讯作者：
E. Fridman
中科院分区：
文献类型：
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作者：
A. Matveev;A. Proskurnikov;A. Pogromsky;E. Fridman
本文关注的是一个离散时间，确定性，并可能大的非线性系统网络产生信息的速率，因此与最小的数据传输速率下，收件人可以保持对网络的当前状态的认识水平。虽然旨在发展易于处理的技术估计这一速度，本文主张直接处理的动力系统作为一组相互作用的子系统的好处。为此，阐述了一种新的估计方法，这是类似的味道的小增益定理的输入输出稳定性。这种方法的实用性证明了严格证明实验发现的现象。当时滞无限增长时，非线性时滞系统的拓扑熵保持有界。这是延长研究的可观测率和附加的建设性上界独立的延迟。结果表明，这些边界是渐近紧的弹跳球动力学的时间延迟模拟。
This paper is concerned with the rate at which a discrete-time, deterministic, and possibly large network of nonlinear systems generates information, and so with the minimum rate of data transfer under which the addressee can maintain the level of awareness about the current state of the network. While being aimed at development of tractable techniques for estimation of this rate, this paper advocates benefits from directly treating the dynamical system as a set of interacting subsystems. To this end, a novel estimation method is elaborated that is alike in flavor to the small gain theorem on input-to-output stability. The utility of this approach is demonstrated by rigorously justifying an experimentally discovered phenomenon. The topological entropy of nonlinear time-delay systems stays bounded as the delay grows without limits. This is extended on the studied observability rates and appended by constructive upper bounds independent of the delay. It is shown that these bounds are asymptotically tight for a time-delay analog of the bouncing ball dynamics.