Document Zbl 0731.49001

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East European Series</a> 44. Dordrecht etc.: Kluwer Academic Publishers; Warszawa: PWN-Polish Scientific Publishers (ISBN 0-7923-0675-9). xix, 240 p. (1991). </div> <div class="abstract">This book is devoted to the analysis and optimal control of dynamical systems described by functional-differential equations. This type of mathematical models arises whenever the past exerts a significant influence upon the future behaviour of the system. The optimal control problem for this class of systems leads to functional-differential inclusions and, in particular, to neutral functional-differential inclusions. The main body of the book deals with the latter type of problems and is based on recently published monographs on the subject of functional-differential inclusions [see <span class="zbmathjax-textit">J. P. Aubin</span> and <span class="zbmathjax-textit">A. Cellina</span>, “Differential inclusions” (1984; <a href="/0538.34007">Zbl 0538.34007</a>); <span class="zbmathjax-textit">M. C. Castaing</span> and <span class="zbmathjax-textit">M. Valadier</span>, “Convex analysis and measurable multifunctions”, Lect. Notes Math. 580 (1977; <a href="/0346.46038">Zbl 0346.46038</a>); <span class="zbmathjax-textit">A. F. Filippov</span>, “Differential equations with discontinuous right hand sides” (Russian) (1985; <a href="/0571.34001">Zbl 0571.34001</a>) (for the 1988 English ed. see <a href="/0664.34001">Zbl 0664.34001</a>); <span class="zbmathjax-textit">T. Parthasarathy</span>, “Selection theorems and their applications” (1972; <a href="/0239.54011">Zbl 0239.54011</a>); <span class="zbmathjax-textit">A. A. Tolstogonov</span>, “Differential inclusions in a Banach space” (Russian) (1986; <a href="/0689.34014">Zbl 0689.34014</a>)]. <br class="zbmathjax-paragraph">The book is divided into five chapters. Chapter I repeats basic notations and theorems of topology, functional analysis and vector measure. Chapter II covers the fundamental theory of set-valued functions. Chapter III presents the properties of subtrajectory and trajectory integrals of these functions depending on parameters. Chapters IV and V deal with neutral functional-differential inclusions and their applications in optimal control theory. <br class="zbmathjax-paragraph">This book is written on a high mathematical level. It is intended for students and professionals in mathematics and specialists in optimal control theory. It is too theoretical for engineers.<div class="reviewer"> Reviewer: <a href="/authors/?q=rv%3A4960">D.Franke (Hamburg)</a></div> <div class="clearfix"></div></div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A46933">Cited in <strong>201</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td class="mono"> 49J24 </td> <td class="space"> Optimal control problems with differential inclusions (existence) (MSC2000) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A49-02" title="MSC2020">49-02</a> </td> <td class="space"> Research exposition (monographs, survey articles) pertaining to calculus of variations and optimal control </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Afunctional-differential+equations">functional-differential equations</a>; <a href="/?q=ut%3Afunctional-differential+inclusions">functional-differential inclusions</a>; <a href="/?q=ut%3Aset-valued+functions">set-valued functions</a>; <a href="/?q=ut%3Asubtrajectory">subtrajectory</a>; <a href="/?q=ut%3Atrajectory+integrals">trajectory integrals</a></div><div class="keywords"> <h3>Citations:</h3><a href="/0538.34007">Zbl 0538.34007</a>; <a href="/0346.46038">Zbl 0346.46038</a>; <a href="/0571.34001">Zbl 0571.34001</a>; <a href="/0664.34001">Zbl 0664.34001</a>; <a href="/0239.54011">Zbl 0239.54011</a>; <a href="/0689.34014">Zbl 0689.34014</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 0731.49001" data-ciurl="/ci/00046933" data-biburl="/bibtex/00046933.bib" data-amsurl="/amsrefs/00046933.bib" data-xmlurl="/xml/00046933.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/00046933.pdf" title="Zbl 0731.49001 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 = ""; </script> <script src="/static/scripts.js?v=20240926"> </script> <script src="https://static.zbmath.org/contrib/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ "HTML-CSS": { preferredFont: "TeX", availableFonts: [ "STIX", "TeX" ], linebreaks: { automatic: true }, EqnChunk: (MathJax.Hub.Browser.isMobile ? 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