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Fuzzy Dynamic Equations, Dynamic Inclusions, and Optimal Control Problems on Time Scales

Autor Svetlin G. Georgiev
en Limba Engleză Paperback – 15 iul 2022
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.
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Specificații

ISBN-13: 9783030761349
ISBN-10: 3030761347
Ilustrații: XIII, 882 p. 48 illus., 4 illus. in color.
Dimensiuni: 155 x 235 mm
Greutate: 1.23 kg
Ediția:1st ed. 2021
Editura: Springer International Publishing
Colecția Springer
Locul publicării:Cham, Switzerland

Cuprins

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.

Textul de pe ultima copertă

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.

Caracteristici

Presents a systematic account of new developments in the theory of dynamic equations
Illustrates a number of practical problems
Contains over 50 pages of useful appendices