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

Alexey S. Matveev, Anton V. Proskurnikov, Alexander Pogromsky*, Emilia Fridman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


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
Issue number10
StatePublished - Oct 2019


FundersFunder number
Horizon 2020 Framework Programme
H2020 Marie Skłodowska-Curie Actions675080
Russian Foundation for Basic Research18-38-20037
Israel Science Foundation1128/14
Russian Science FoundationIII-A–III-C, 14-21-00041p, 16-19-00057
Horizon 2020


    • Data-rate estimates
    • Entropy
    • Nonlinear systems
    • Observability
    • Second Lyapunov method


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