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

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

VL - 64

SP - 4252

EP - 4259

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

SN - 0018-9286

IS - 10

M1 - 8620288

ER -