MARC Record from marc_columbia

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008 191102s2003 flu o 000 0 eng d
035 $a(OCoLC)on1124610125
035 $a(NNC)15140238
040 $aEBLCP$beng$epn$cEBLCP$dTYFRS$dOCLCF$dOCLCQ$dK6U$dOCLCO
020 $a9781482264999
020 $a1482264994
020 $a9780429174872$q(electronic bk.)
020 $a042917487X$q(electronic bk.)
035 $a(OCoLC)1124610125
037 $a9780429174872$bTaylor & Francis
050 4 $aQA272.Z39 2002
072 7 $aMAT$x000000$2bisacsh
072 7 $aMAT$x003000$2bisacsh
072 7 $aMAT$x007000$2bisacsh
072 7 $aPBKJ$2bicssc
082 04 $a519.3
049 $aZCUA
100 1 $aZhukovskiĭ, Vladislav Iosifovich.
245 10 $aLyapunov Functions in Differential Games
260 $aBoca Raton :$bCRC Press LLC,$c2003.
300 $a1 online resource (299 pages)
336 $atext$btxt$2rdacontent
337 $acomputer$bc$2rdamedia
338 $aonline resource$bcr$2rdacarrier
490 1 $aStability and Control: Theory, Methods and Applications ;$vv. Vol. 19
588 0 $aPrint version record.
505 0 $aCover; Half Title; Title Page; Copyright Page; Contents; Introduction to the Series; Preface; Notation; 1 General Notions and Examples; 1.0 Introduction; 1.1 Basic Notions of the Theory of Differential Games under Uncertainty; 1.1.1 Aspects of games; 1.1.2 Dynamical aspects; 1.1.3 De principiis non est disputandum; 1.1.4 Economic interpretation of the game; 1.1.5 Content of the theory; 1.2 Game Problems in Economic and Mechanical Systems; 1.2.1 Competition of two economies; 1.2.2 Tracking problems; 1.2.3 Problem of approaching; 1.3 Vector Guarantees; 1.3.1 Ad narrandum, non ad probundum
505 8 $a1.3.2 Formalization of the vector guarantees1.3.3 "Geometric" interpretation of the vector guarantees; 1.3.4 Sufficient conditions; 1.4 The Vector Guarantees May Not Exist; 1.4.1 Statement of the problem; 1.4.2 Lemma for counter-examples; 1.4.3 The Bellman function; 1.4.4 The class of games in which the vector guarantees are absent; 1.5 Converse Problem; 1.5.1 Traditional approach; 1.5.2 Application of dynamical programming; 1.5.3 Comparison with the minimal guarantee; 1.6 The Nash Equilibrium for Uncertainty; 1.6.1 Formalization of the equilibrium; 1.6.2 The sufficient conditions
505 8 $a1.6.3 The coefficient criteria1.6.4 The properties of the ensuring Nash equilibria; Exercises; Comments and References; 2 Objection and Counter-Objection Equilibrium under Uncertainty; 2.0 Introduction; 2.1 Peculiarities of the Nash Equilibrium; 2.1.1 The Nash equilibrium situation; 2.1.2 Properties; 2.1.3 Peculiarities; 2.1.4 The class of games in which the Nash equilibrium is absent; 2.2 Formalization and the Properties of Unimprovable Equilibria; 2.2.1 "Complete" and "incomplete" counter-objections; 2.2.2 Solutions of the multicriteria problem
505 8 $a2.2.3 Formalization of unimprovable equilibria2.2.4 The properties of the unimprovable equilibria; 2.2.5 Existence; 2.3 Comparison with the Nash Equilibrium; 2.3.1 Non-domination and unimprovability; 2.3.2 Class of games, where no Nash equilibrium exists, but the Geoffrione equilibrium of objections and counter-objections exists; 2.3.3 Relationship with the Nash equilibrium; 2.3.4 Examples; 2.4 Formalization of Unimprovable Equilibria in the Differential Game; 2.4.1 Mathematical model of the game; 2.4.2 Analogue of vector saddle point; 2.4.3 Properties; 2.4.4 Stability
505 8 $a2.5 Auxiliary Assertions2.5.1 Coefficient criteria; 2.5.2 Reduction to non-cooperation game; 2.5.3 Properties of matrix linear convolutions; 2.6 Sufficient Conditions for the Analogue of a Saddle Point; 2.6.1 Application of dynamical programming; 2.6.2 Coefficient criteria; 2.6.3 Games with "small" perturbations; 2.7 Unimprovable Guaranteeing Equilibria (Analogue of the Vector Maximin); 2.7.1 Counter-example; 2.7.2 Formalization of unimprovable equilibria; 2.7.3 Properties of USEOC; 2.8 Active Equilibrium under Uncertainty; 2.8.1 Formalization of solution; 2.8.2 Auxiliary assertions
500 $a2.8.3 Construction of the set Zsu
520 $aA major step in differential games is determining an explicit form of the strategies of players who follow a certain optimality principle. To do this, the associated modification of Bellman dynamic programming problems has to be solved; for some differential games this could be Lyapunov functions whose "arsenal" has been supplied by stability theor
650 0 $aDifferential games.
650 0 $aLyapunov functions.
650 6 $aJeux différentiels.
650 6 $aFonctions de Liapounov.
650 7 $aMATHEMATICS$xGeneral.$2bisacsh
650 7 $aMATHEMATICS$xApplied.$2bisacsh
650 7 $aMATHEMATICS$xDifferential Equations.$2bisacsh
650 7 $aDifferential games.$2fast$0(OCoLC)fst00893492
650 7 $aLyapunov functions.$2fast$0(OCoLC)fst01004172
655 0 $aElectronic books.
655 4 $aElectronic books.
776 08 $iPrint version:$aZhukovskiy, Vladislav I.$tLyapunov Functions in Differential Games.$dBoca Raton : CRC Press LLC, ©2003$z9780415273411
830 0 $aStability and control ;$vvolume 19.
856 40 $uhttp://www.columbia.edu/cgi-bin/cul/resolve?clio15140238$zTaylor & Francis eBooks
852 8 $blweb$hEBOOKS