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Georgiev 205 $a1st ed. 2021. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2021. 215 $a1 online resource (882 pages) 225 1 $aMathematics and Statistics Series 311 08$a3-030-76131-2 320 $aIncludes bibliographical references and index. 327 $a1. Calculus of Fuzzy Functions -- 2. First Order Fuzzy Dynamic Equations -- 3. Second Order Fuzzy Dynamic Equations -- 4. Functional Fuzzy Dynamic Equations -- 5. Impulsive Fuzzy Dynamic Equations -- 6. The Lebesgue Integration. Lp Spaces. Sobolev spaces -- 7. First Order Dynamic Inclusions -- 8. Second Order Dynamic Inclusions -- 9. Boundary Value Problems for First Order Impulsive Dynamic Inclusions -- 10. Controllability, Bang-Bang Principle -- 11. Linear Time-Optimal Control -- 12. The Pontryagin Maximum Principle -- 13. Dynamic Programming -- 14. Weak Solutions and Optimal Control Problems for Some Classes Linear First Order Dynamic Systems -- 15. Nonlinear Dynamic Equations and Optimal Control Problems -- 16 Nonlinear Integro-Dynamic Equations and Optimal Control Problems -- Appendix: Fuzzy Sets -- Appendix: Set-Valued Maps -- Appendix: Alaoglu's Theorem. Krein-Milman Theorem -- Appendix: Mazur's Theorem -- Index. 330 $aThe theory of dynamic equations has many interesting applications in control theory, mathematical economics, mathematical biology, engineering and technology. In some cases, there exists uncertainty, ambiguity, or vague factors in such problems, and fuzzy theory and interval analysis are powerful tools for modeling these equations on time scales. The aim of this book is to present a systematic account of recent developments; describe the current state of the useful theory; show the essential unity achieved in the theory fuzzy dynamic equations, dynamic inclusions and optimal control problems on time scales; and initiate several new extensions to other types of fuzzy dynamic systems and dynamic inclusions. The material is presented in a highly readable, mathematically solid format. Many practical problems are illustrated, displaying a wide variety of solution techniques. The book is primarily intended for senior undergraduate students and beginning graduate students of engineering and science courses. Students in mathematical and physical sciences will find many sections of direct relevance. 410 0$aMathematics and Statistics Series 606 $aMathematical analysis 606 $aDifference equations 606 $aFunctional equations 606 $aDynamics 606 $aMultibody systems 606 $aVibration 606 $aMechanics, Applied 606 $aMeasure theory 606 $aAnalysis 606 $aDifference and Functional Equations 606 $aDynamical Systems 606 $aMultibody Systems and Mechanical Vibrations 606 $aMeasure and Integration 615 0$aMathematical analysis. 615 0$aDifference equations. 615 0$aFunctional equations. 615 0$aDynamics. 615 0$aMultibody systems. 615 0$aVibration. 615 0$aMechanics, Applied. 615 0$aMeasure theory. 615 14$aAnalysis. 615 24$aDifference and Functional Equations. 615 24$aDynamical Systems. 615 24$aMultibody Systems and Mechanical Vibrations. 615 24$aMeasure and Integration. 676 $a531.11 700 $aGeorgiev$b Svetlin$01218802 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910492146703321 996 $aFuzzy dynamic equations, dynamic inclusions, and optimal control problems on time scales$92818446 997 $aUNINA