LEADER 05508nam 22007095 450 001 9910964634203321 005 20250731100459.0 010 $a0-8176-4755-4 024 7 $a10.1007/978-0-8176-4755-1 035 $a(CKB)1000000000777928 035 $a(SSID)ssj0000325405 035 $a(PQKBManifestationID)11243690 035 $a(PQKBTitleCode)TC0000325405 035 $a(PQKBWorkID)10320948 035 $a(PQKB)10693686 035 $a(DE-He213)978-0-8176-4755-1 035 $a(MiAaPQ)EBC3072302 035 $a(PPN)237957108 035 $a(EXLCZ)991000000000777928 100 $a20101013d1997 u| 0 101 0 $aeng 135 $aurcn#|||m|a|a 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aOptimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations /$fby Martino Bardi, Italo Capuzzo-Dolcetta 205 $a1st ed. 1997. 210 1$aBoston, MA :$cBirkhäuser Boston :$cImprint: Birkhäuser,$d1997. 215 $a1 online resource (xvii, 574 pages) $cillustrations 225 1 $aModern Birkhäuser Classics,$x2197-1811 300 $aBibliographic Level Mode of Issuance: Monograph 320 $aIncludes bibliographical references and index. 327 $aOutline of the main ideas on a model problem -- Continuous viscosity solutions of Hamilton-Jacobi equations -- Optimal control problems with continuous value functions: unrestricted state space -- Optimal control problems with continuous value functions: restricted state space -- Discontinuous viscosity solutions and applications -- Approximation and perturbation problems -- Asymptotic problems -- Differential Games. 330 $aThis book is a self-contained account of the theory of viscosity solutions for first-order partial differential equations of Hamilton?Jacobi type and its interplay with Bellman?s dynamic programming approach to optimal control and differential games, as it developed after the beginning of the 1980s with the pioneering work of M. Crandall and P.L. Lions. The book will be of interest to scientists involved in the theory of optimal control of deterministic linear and nonlinear systems. In particular, it will appeal to system theorists wishing to learn about a mathematical theory providing a correct framework for the classical method of dynamic programming as well as mathematicians interested in new methods for first-order nonlinear PDEs. The work may be used by graduate students and researchers in control theory both as an introductory textbook and as an up-to-date reference book. "The exposition is self-contained, clearly written and mathematically precise. The exercises and open problems?will stimulate research in the field. The rich bibliography (over 530 titles) and the historical notes provide a useful guide to the area." ? Mathematical Reviews "With an excellent printing and clear structure (including an extensive subject and symbol registry) the book offers a deep insight into the praxis and theory of optimal control for the mathematically skilled reader. All sections close with suggestions for exercises?Finally, with more than 500 cited references, an overview on the history and the main works of this modern mathematical discipline is given." ? ZAA "The minimal mathematical background...the detailed and clear proofs, the elegant style of presentation, and the sets of proposed exercises at the end of each section recommend this book, in the first place, as a lecture course for graduate students and as a manual for beginners in the field.However, this status is largely extended by the presence of many advanced topics and results by the fairly comprehensive and up-to-date bibliography and, particularly, by the very pertinent historical and bibliographical comments at the end of each chapter. In my opinion, this book is yet another remarkable outcome of the brilliant Italian School of Mathematics." ? Zentralblatt MATH "The book is based on some lecture notes taught by the authors at several universities...and selected parts of it can be used for graduate courses in optimal control. But it can be also used as a reference text for researchers (mathematicians and engineers)...In writing this book, the authors lend a great service to the mathematical community providing an accessible and rigorous treatment of a difficult subject." ? Acta Applicandae Mathematicae. 410 0$aModern Birkhäuser Classics,$x2197-1811 606 $aSystem theory 606 $aControl theory 606 $aMathematical optimization 606 $aDifferential equations 606 $aSystems Theory, Control 606 $aOptimization 606 $aDifferential Equations 615 0$aSystem theory. 615 0$aControl theory. 615 0$aMathematical optimization. 615 0$aDifferential equations. 615 14$aSystems Theory, Control. 615 24$aOptimization. 615 24$aDifferential Equations. 676 $a519 686 $a49L25$2msc 686 $a35F20$2msc 686 $a90D25$2msc 700 $aBardi$b M$g(Martino).$4aut$4http://id.loc.gov/vocabula Mry/relators/aut$062926 702 $aCapuzzo Dolcetta$b I$g(Italo),$f1948-.$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bDLC 801 1$bDLC 801 2$bCaOWtU 906 $aBOOK 912 $a9910964634203321 996 $aOptimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations$9374267 997 $aUNINA