Comprehending complexity

Data-rate constraints in large-scale networks

Journal article (2019)

Authors

Alexey S. Matveev ITMO University, St. Petersburg State University

A.V. Proskurnikov Team Tamas Keviczky - Mechanical, Maritime and Materials Engineering , Russian Academy of Sciences

A. Pogromsky ITMO University, Eindhoven University of Technology

Emilia Fridman Tel Aviv University

Research Group

Team Tamas Keviczky (Mechanical, Maritime and Materials Engineering) (TU Delft)

Entropy Observability Nonlinear systems Second Lyapunov method Data-rate estimates

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Published Date

2019

Language

English

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Faculty

Mechanical, Maritime and Materials Engineering

Department

Delft Center for Systems and Control

Research Group

Team Tamas Keviczky

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.

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