國立高雄大學圖資館 |

Language: English

Back

Fuzzy dynamic equations, dynamic inc...

Georgiev, Svetlin G.

Fuzzy dynamic equations, dynamic inclusions, and optimal control problems on time scales

Record Type:	Electronic resources : Monograph/item
Title/Author:	Fuzzy dynamic equations, dynamic inclusions, and optimal control problems on time scalesby Svetlin G. Georgiev.
Author:	Georgiev, Svetlin G.
Published:	Cham :Springer International Publishing :2021.
Description:	xiii, 882 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Dynamics.
Online resource:	https://doi.org/10.1007/978-3-030-76132-5
ISBN:	9783030761325$q(electronic bk.)

Fuzzy dynamic equations, dynamic inclusions, and optimal control problems on time scales
Georgiev, Svetlin G.

Fuzzy dynamic equations, dynamic inclusions, and optimal control problems on time scales[electronic resource] /by Svetlin G. Georgiev. - Cham :Springer International Publishing :2021. - xiii, 882 p. :ill. (some col.), digital ;24 cm.

1. 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.

The 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.

ISBN: 9783030761325$q(electronic bk.)

Standard No.: 10.1007/978-3-030-76132-5doiSubjects--Topical Terms:

189568
Dynamics.

LC Class. No.: QA845 / .G46 2021

Dewey Class. No.: 515.39

Fuzzy dynamic equations, dynamic inclusions, and optimal control problems on time scales
LDR:03071nmm a2200325 a 4500 001 605518
003 DE-He213
005 20210715003942.0
006 m d
007 cr nn 008maaau
008 211201s2021 sz s 0 eng d
020 $a 9783030761325$q(electronic bk.)
020 $a 9783030761318$q(paper)
024 7 $a 10.1007/978-3-030-76132-5 $2 doi
035 $a 978-3-030-76132-5
040 $a GP $c GP
041 0 $a eng
050 4 $a QA845 $b .G46 2021
072 7 $a PBK $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a PBK $2 thema
082 0 4 $a 515.39 $2 23
090 $a QA845 $b .G352 2021
100 1 $a Georgiev, Svetlin G. $3 728094
245 1 0 $a Fuzzy dynamic equations, dynamic inclusions, and optimal control problems on time scales $h [electronic resource] / $c by Svetlin G. Georgiev.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2021.
300 $a xiii, 882 p. : $b ill. (some col.), digital ; $c 24 cm.
505 0 $a 1. 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.
520 $a The 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.
650 0 $a Dynamics. $3 189568
650 0 $a Fuzzy mathematics. $3 243725
650 0 $a Mathematical optimization. $3 183292
650 1 4 $a Analysis. $3 273775
650 2 4 $a Difference and Functional Equations. $3 274826
650 2 4 $a Dynamical Systems and Ergodic Theory. $3 273794
650 2 4 $a Vibration, Dynamical Systems, Control. $3 274667
650 2 4 $a Measure and Integration. $3 273777
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
856 4 0 $u https://doi.org/10.1007/978-3-030-76132-5
950 $a Mathematics and Statistics (SpringerNature-11649)