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 |
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Article number | 8620288 |
Pages (from-to) | 4252-4259 |
Number of pages | 8 |
Journal | IEEE Transactions on Automatic Control |
Volume | 64 |
Issue number | 10 |
DOIs | |
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