Comprehending complexity: data-rate constraints in large-scale networks

Alexey S. Matveev, Anton V. Proskurnikov, Alexander Pogromsky (Corresponding author), Emilia Fridman

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Abstract

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.

Original languageEnglish
Article number8620288
Pages (from-to)4252-4259
Number of pages8
JournalIEEE Transactions on Automatic Control
Volume64
Issue number10
DOIs
Publication statusPublished - Oct 2019

Keywords

  • Data-rate estimates
  • Entropy
  • Nonlinear systems
  • Observability
  • Second Lyapunov method
  • nonlinear systems
  • entropy
  • second Lyapunov method
  • observability

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