Document Zbl 1165.93003

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Boston, MA: Birkh盲user (ISBN 978-0-8176-4494-9/hbk). xiv, 533 p. (2009). </div> <div class="abstract">The monograph consisting of Preface, 15 Chapters, Appendices A–D, References, and Index is the first book that attempts to presents a systematic theory of estimation and control over communication networks. The results can be grouped into 6 topics denoted as (i)-(vi) as follows:<br class="zbmathjax-paragraph">(i) “Estimation and control over limited deterministic channels” (Chaps. 2–5, 13) deals with the connections among observability, stabilizability, and Linear Quadratic (LQ) control via digital channels as well as topological entropy (the metric definition) of the open loop system. Necessary and sufficient conditions (nsc) for observability as well as for stabilizability of a linear plant via a digital channel are proved in Chap. 2. Chap. 3 extends the stabilizability result of Chap. 2 to linear plants with multiple sensors and digital communication channels supposing possible time-varying delays and data losses. In Chap. 4, sufficient conditions for stabilizability and detectability over limited capacity communication channels are derived for a class of nonlinear systems with nonlinearity satisfying a global Lipschitz condition. A design procedure for state estimators and output feedback controllers is given including an illustrative example. Chap. 5 addresses the problem of a robust coder-decoder-estimator design for uncertain systems with the uncertainty satisfying integral quadratic constraint. Chap. 13 considers an optimal coding-decoding strategy for the problem of Linear-Quadratic-Gaussian (LQG) optimal control over a limited capacity channel for a discrete-time plant and a finite time interval.<br class="zbmathjax-paragraph">(ii) “An analog of Shannon information theory: estimation and control over noisy discrete channels” (Chaps. 6–8) considers problems of stabilization and state estimation of unstable linear discrete-time plant via stationary memoryless noisy discrete channels. Chap. 6 presents the result that stabilizability and observability with probability 1 of a linear unstable plant without disturbances is “almost” equivalent to the inequality $H(A)<\varepsilon$, where $H(A)$ is the topological entropy and $\varepsilon$ is the Shannon ordinary capacity. Similar problems are addressed in Chap. 7 supposing the plant affected by disturbances. An “almost” nsc is proved for the existence of a coder-decoder pair bounded with probability 1, i.e., $H(A)<\varepsilon_o$. $\varepsilon_o$ denotes the zero error capacity of the channel. The result of Chap. 6 does dot guarantee robustness against disturbances, while the results of Chap. 7 are conservative. The concept of stabilizability in probability is introduced in Chap. 8 to overcome these shortcomings.<br class="zbmathjax-paragraph">(iii) “Decentralized stabilization via limited capacity communication networks“ (Chap. 9) supposes a general network with arbitrary topology for a discrete-time deterministic linear time-invariant unstable multi-channel system. Nsc for stabilizability are proved in terms of the rate (capacity) domain of the network. The capacity domain describes how much information can be transmitted from an element or set of nodes to another element or set of nodes. Design of the stabilizing control is reduced to construction of the block functions transmitting data at the rates matching the entries of a certain vector.<br class="zbmathjax-paragraph">(iv) “$H_{\infty}$ state estimation via communication channels“ (Chap. 10) considers a continuous-time linear time-invariant system. The goal is to design a coder at the transmitting end of the channel and a decoder-estimator at the receiving end satisfying a standard requirement from $H_{\infty}$ filtering theory. <br class="zbmathjax-paragraph">(v) “Kalman filtering and optimal control via asynchronous channels with irregular delays” (Chaps. 11–12) supposes a discrete-time linear plant with Gaussian disturbances. In Chap. 11, the probability distributions of the channels delays are supposed as known. An analog of the Kalman filter is derived and the LQG problem is solved. In Chap. 12, a finite-horizon LQ problem is solved for discrete-time partially observed systems perturbed by white noises, where the control loop is not perfect and control signals arrive to several actuators via asynchronous communication channels.<br class="zbmathjax-paragraph">(vi) “Kalman filtering with switched sensors“ (Chaps. 14–15) considers plants with multiple sensors communicating to the state estimator via a set of independent channels so that only one sensor can communicate at any time. Thus, the problem reduces to finding a suitable sensor scheduling algorithm. Chap. 14 considers the system with asynchronous communication channels between the sensors and the state estimator, where the algorithm requires solving a set of the Riccati equations and a dynamic programming equation. Chap. 15 deals with the sensor switching problem for uncertain plants with uncertainties satisfying integral quadratic constraints. Suboptimal state estimators are designed using model predictive control approach.<br class="zbmathjax-paragraph">This essentially self-contained monograph presents basic links among mathematical control theory, Shannon information theory, and entropy theory of dynamical systems. The results fundamentally contribute to a more comprehensive understanding of networked control systems. The book is an excellent up-to-date resource of working knowledge with long-term evidence in the field. The text can serve also as a useful reference book about this challenging research topic. The monograph is intended for researchers, practitioners, postgraduate students, and all professionals working in the areas of control engineering, communications, information theory, signal processing, and applied mathematics interested in the emerging subject of networked control systems.<div class="reviewer"> Reviewer: <a href="/authors/?q=rv%3A2187">Lubom铆r Bakule (Praha)</a></div> <div class="clearfix"></div></div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A5485979">Cited in <strong>52</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A93-02" title="MSC2020">93-02</a> </td> <td class="space"> Research exposition (monographs, survey articles) pertaining to systems and control theory </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93B50" title="MSC2020">93B50</a> </td> <td class="space"> Synthesis problems </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93B52" title="MSC2020">93B52</a> </td> <td class="space"> Feedback control </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93C05" title="MSC2020">93C05</a> </td> <td class="space"> Linear systems in control theory </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93C10" title="MSC2020">93C10</a> </td> <td class="space"> Nonlinear systems in control theory </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93E10" title="MSC2020">93E10</a> </td> <td class="space"> Estimation and detection in stochastic control theory </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A94A15" title="MSC2020">94A15</a> </td> <td class="space"> Information theory (general) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A90B10" title="MSC2020">90B10</a> </td> <td class="space"> Deterministic network models in operations research </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A68M10" title="MSC2020">68M10</a> </td> <td class="space"> Network design and communication in computer systems </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A90B18" title="MSC2020">90B18</a> </td> <td class="space"> Communication networks in operations research </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Anetworked+control+systems">networked control systems</a>; <a href="/?q=ut%3Atopological+entropy">topological entropy</a>; <a href="/?q=ut%3Adecentralized+stabilization">decentralized stabilization</a>; <a href="/?q=ut%3AKalman+filtering">Kalman filtering</a>; <a href="/?q=ut%3Aswitched+sensors">switched sensors</a>; <a href="/?q=ut%3AShannon+information+theory">Shannon information theory</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1165.93003" data-ciurl="/ci/05485979" data-biburl="/bibtex/05485979.bib" data-amsurl="/amsrefs/05485979.bib" data-xmlurl="/xml/05485979.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/05485979.pdf" title="Zbl 1165.93003 as PDF">Review PDF</a> </div> <div class="fulltexts"> </div> <div class="sfx" style="float: right;"> </div> </div> </article> </div></div> </div> </div> <div class="clearfix"></div> </div> </div> <div id="foot"><div class="copyright"> © 2025 <a target="fiz" href="https://www.fiz-karlsruhe.de/en">FIZ Karlsruhe GmbH</a> <a href="/privacy-policy/">Privacy Policy</a> <a href="/legal-notices/">Legal Notices</a> <a href="/terms-conditions/">Terms & Conditions</a> <div class="info"> <ul class="nav"> <li class="mastodon"> <a href="https://mathstodon.xyz/@zbMATH" target="_blank" class="no-new-tab-icon"> <img src="/static/mastodon.png" title="zbMATH at Mathstodon (opens in new tab)" alt="Mastodon logo"> </a> </li> </ul> </div> </div> <div class="clearfix" style="height: 0px;"></div> </div> </div> <script src="https://static.zbmath.org/contrib/jquery/1.9.1/jquery.min.js"></script> <script src="https://static.zbmath.org/contrib/jquery-caret/1.5.2/jquery.caret.min.js"></script> <script src="/static/js/jquery-ui-1.10.1.custom.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap/v3.3.7zb1/js/bootstrap.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.js"></script> <script src="https://static.zbmath.org/contrib/retina/unknown/retina.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/js/bootstrap-select.min.js"></script> <script> var SCRIPT_ROOT = ""; 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