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Entropy
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Entropy in Networked Control
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Entropy in Networked Control

A special issue of Entropy (ISSN 1099-4300).

Deadline for manuscript submissions: closed (15 January 2019) | Viewed by 23588

Special Issue Editor

Dr. Christoph Kawan

E-Mail Website
Guest Editor
Fakultät für Informatik und Mathematik, Universität Passau, Innstraße 33, 94032 Passau, Germany
Interests: networked control; control under communication constraints; ergodic theory of nonautonomous dynamical systems; hyperbolic theory of dynamical and control systems

Special Issue Information

Dear Colleagues,

Networked control systems are spatially-distributed systems in which the communication between sensors, controllers, and actuators is accomplished through a shared digital communication network. Examples can be found, e.g., in vehicle tracking, underwater communications, remote surgery, and space exploration. In the simplest model, the communication network is displayed as a rate-limited digital channel over which state information acquired by sensors is transmitted to a controller. The most fundamental problem in this context is to determine the smallest information rate above which a specified control objective can be achieved.

For linear systems, the data-rate theorem characterizes this infimal rate for various forms of stabilization as the sum of the open-loop unstable modes, or equivalently, as the entropy of the uncontrolled system. For nonlinear systems, dynamical entropy concepts also play a fundamental role in describing the data-rate limits for stabilization, estimation and related objectives. While such characterizations are mostly restricted to deterministic models, information-theoretic entropy concepts naturally show up in stochastic models which incorporate noise in different system components.

This Special Issue features research involving information-theoretic and/or dynamical concepts of entropy in the context of control under communication constraints. In addition, contributions related to the classical data-rate theorem are welcome.

Dr. Christoph Kawan
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Networked control
  • Control under communication constraints
  • Control over digital channels
  • Data-rate theorems
  • Feedback entropy
  • Invariance entropy
  • Estimation entropy

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Published Papers (5 papers)

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Research

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3 pages, 184 KiB  
Article
Editorial: Entropy in Networked Control
by Christoph Kawan
Entropy 2019, 21(4), 392; https://doi.org/10.3390/e21040392 - 11 Apr 2019
Cited by 2 | Viewed by 2292
Abstract
This is an editorial article summarizing the scope and contents of the Special Issue Entropy in Networked Control. Full article
(This article belongs to the Special Issue Entropy in Networked Control)
29 pages, 1022 KiB  
Article
Data-Rate Constrained Observers of Nonlinear Systems
by Quentin Voortman, Alexander Yu. Pogromsky, Alexey S. Matveev and Henk Nijmeijer
Entropy 2019, 21(3), 282; https://doi.org/10.3390/e21030282 - 14 Mar 2019
Cited by 11 | Viewed by 2764
Abstract
In this paper, the design of a data-rate constrained observer for a dynamical system is presented. This observer is designed to function both in discrete time and continuous time. The system is connected to a remote location via a communication channel which can [...] Read more.
In this paper, the design of a data-rate constrained observer for a dynamical system is presented. This observer is designed to function both in discrete time and continuous time. The system is connected to a remote location via a communication channel which can transmit limited amounts of data per unit of time. The objective of the observer is to provide estimates of the state at the remote location through messages that are sent via the channel. The observer is designed such that it is robust toward losses in the communication channel. Upper bounds on the required communication rate to implement the observer are provided in terms of the upper box dimension of the state space and an upper bound on the largest singular value of the system’s Jacobian. Results that provide an analytical bound on the required minimum communication rate are then presented. These bounds are obtained by using the Lyapunov dimension of the dynamical system rather than the upper box dimension in the rate. The observer is tested through simulations for the Lozi map and the Lorenz system. For the Lozi map, the Lyapunov dimension is computed. For both systems, the theoretical bounds on the communication rate are compared to the simulated rates. Full article
(This article belongs to the Special Issue Entropy in Networked Control)
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14 pages, 307 KiB  
Article
On the Relation between Topological Entropy and Restoration Entropy
by Christoph Kawan
Entropy 2019, 21(1), 7; https://doi.org/10.3390/e21010007 - 23 Dec 2018
Cited by 5 | Viewed by 3138
Abstract
In the context of state estimation under communication constraints, several notions of dynamical entropy play a fundamental role, among them: topological entropy and restoration entropy. In this paper, we present a theorem that demonstrates that for most dynamical systems, restoration entropy strictly exceeds [...] Read more.
In the context of state estimation under communication constraints, several notions of dynamical entropy play a fundamental role, among them: topological entropy and restoration entropy. In this paper, we present a theorem that demonstrates that for most dynamical systems, restoration entropy strictly exceeds topological entropy. This implies that robust estimation policies in general require a higher rate of data transmission than non-robust ones. The proof of our theorem is quite short, but uses sophisticated tools from the theory of smooth dynamical systems. Full article
(This article belongs to the Special Issue Entropy in Networked Control)

Review

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29 pages, 579 KiB  
Review
An Overview on Denial-of-Service Attacks in Control Systems: Attack Models and Security Analyses
by Ahmet Cetinkaya, Hideaki Ishii and Tomohisa Hayakawa
Entropy 2019, 21(2), 210; https://doi.org/10.3390/e21020210 - 22 Feb 2019
Cited by 115 | Viewed by 9614
Abstract
In this paper, we provide an overview of recent research efforts on networked control systems under denial-of-service attacks. Our goal is to discuss the utility of different attack modeling and analysis techniques proposed in the literature for addressing feedback control, state estimation, and [...] Read more.
In this paper, we provide an overview of recent research efforts on networked control systems under denial-of-service attacks. Our goal is to discuss the utility of different attack modeling and analysis techniques proposed in the literature for addressing feedback control, state estimation, and multi-agent consensus problems in the face of jamming attacks in wireless channels and malicious packet drops in multi-hop networks. We discuss several modeling approaches that are employed for capturing the uncertainty in denial-of-service attack strategies. We give an outlook on deterministic constraint-based modeling ideas, game-theoretic and optimization-based techniques and probabilistic modeling approaches. A special emphasis is placed on tail-probability based failure models, which have been recently used for describing jamming attacks that affect signal to interference-plus-noise ratios of wireless channels as well as transmission failures on multi-hop networks due to packet-dropping attacks and non-malicious issues. We explain the use of attack models in the security analysis of networked systems. In addition to the modeling and analysis problems, a discussion is provided also on the recent developments concerning the design of attack-resilient control and communication protocols. Full article
(This article belongs to the Special Issue Entropy in Networked Control)
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Other

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11 pages, 261 KiB  
Discussion
Category Theory for Autonomous and Networked Dynamical Systems
by Jean-Charles Delvenne
Entropy 2019, 21(3), 302; https://doi.org/10.3390/e21030302 - 20 Mar 2019
Cited by 8 | Viewed by 5083
Abstract
In this discussion paper we argue that category theory may play a useful role in formulating, and perhaps proving, results in ergodic theory, topogical dynamics and open systems theory (control theory). As examples, we show how to characterize Kolmogorov–Sinai, Shannon entropy and topological [...] Read more.
In this discussion paper we argue that category theory may play a useful role in formulating, and perhaps proving, results in ergodic theory, topogical dynamics and open systems theory (control theory). As examples, we show how to characterize Kolmogorov–Sinai, Shannon entropy and topological entropy as the unique functors to the nonnegative reals satisfying some natural conditions. We also provide a purely categorical proof of the existence of the maximal equicontinuous factor in topological dynamics. We then show how to define open systems (that can interact with their environment), interconnect them, and define control problems for them in a unified way. Full article
(This article belongs to the Special Issue Entropy in Networked Control)
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