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

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Svetlin G. Georgiev

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

Svetlin G. Georgiev

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English

Springer Nature Switzerland AG
15 July 2021

Differential calculus & equations; Integral calculus & equations; Non-linear science; Dynamics & vibration

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.

By: Svetlin G. Georgiev
Imprint: Springer Nature Switzerland AG
Country of Publication: Switzerland
Edition: 2021 ed.
Dimensions: Height: 235mm, Width: 155mm,
Weight: 1.502kg
ISBN: 9783030761318
ISBN 10: 3030761312
Pages: 882
Publication Date: 15 July 2021
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

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.