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

Alexey S. Matveev; Anton V. Proskurnikov; Alexander Pogromsky; Emilia Fridman

doi:10.1109/TAC.2019.2894369

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

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

Dynamics and Control

Research output: Contribution to journal › Article › Academic › peer-review

9 Citations (Scopus)

134 Downloads (Pure)

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 language	English
Article number	8620288
Pages (from-to)	4252-4259
Number of pages	8
Journal	IEEE Transactions on Automatic Control
Volume	64
Issue number	10
DOIs	https://doi.org/10.1109/TAC.2019.2894369
Publication status	Published - Oct 2019

Funding

Manuscript received December 26, 2017; revised January 8, 2018 and August 30, 2018; accepted January 12, 2019. Date of publication January 21, 2019; date of current version September 25, 2019. This work was supported in part by the Russian Science Foundation under Project 14-21-00041p (for the work of A. S. Matveev and for the research of Sections II, III-A–III-C, and IV) and under Project 16-19-00057 (for the results of Section III-E that were obtained by A. V. Proskurnikov) and in part by the Russian Foundation for Basic Research under Grant 18-38-20037 (for the results of Section V). The work of A. Pogromsky was supported by the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant 675080 (UCoCoS). The work of E. Fridman was supported by the Israel Science Foundation under Grant 1128/14. Recommended by Associate Editor L. Palopoli. (Corresponding author: Alexander Pogromsky.) A. S. Matveev is with the Department of Mathematics and Mechanics, Saint Petersburg University, Saint Petersburg 198504, Russia, and also with the Faculty of Control Systems and Robotics, Saint Petersburg National Research University of Information Technologies, Mechanics and Optics, Saint Petersburg 197101, Russia (e-mail:, [email protected]).

Keywords

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

Access to Document

10.1109/TAC.2019.2894369

author versionFinal author version , 348 KB

Cite this

@article{e293879251cd4e019385dd1e0ba57746,

title = "Comprehending complexity: data-rate constraints in large-scale networks",

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.",

keywords = "Data-rate estimates, Entropy, Nonlinear systems, Observability, Second Lyapunov method, nonlinear systems, entropy, second Lyapunov method, observability",

author = "Matveev, {Alexey S.} and Proskurnikov, {Anton V.} and Alexander Pogromsky and Emilia Fridman",

year = "2019",

month = oct,

doi = "10.1109/TAC.2019.2894369",

language = "English",

volume = "64",

pages = "4252--4259",

journal = "IEEE Transactions on Automatic Control",

issn = "0018-9286",

publisher = "Institute of Electrical and Electronics Engineers",

number = "10",

}

TY - JOUR

T1 - Comprehending complexity

T2 - data-rate constraints in large-scale networks

AU - Matveev, Alexey S.

AU - Proskurnikov, Anton V.

AU - Pogromsky, Alexander

AU - Fridman, Emilia

PY - 2019/10

Y1 - 2019/10

N2 - 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.

AB - 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.

KW - Data-rate estimates

KW - Entropy

KW - Nonlinear systems

KW - Observability

KW - Second Lyapunov method

KW - nonlinear systems

KW - entropy

KW - second Lyapunov method

KW - observability

UR - http://www.scopus.com/inward/record.url?scp=85075574259&partnerID=8YFLogxK

U2 - 10.1109/TAC.2019.2894369

DO - 10.1109/TAC.2019.2894369

M3 - Article

AN - SCOPUS:85075574259

SN - 0018-9286

VL - 64

SP - 4252

EP - 4259

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

IS - 10

M1 - 8620288

ER -

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

Abstract

Funding

Keywords

Access to Document

Other files and links

Fingerprint

Cite this