Fuzzy Dynamic Equations, Dynamic Inclusions, and Optimal Control Problems on Time Scales / by Svetlin G. Georgiev.

Format:

Book

Author/Creator:

Georgiev, Svetlin, author.

Series:

Mathematics and Statistics Series

Language:

English

Subjects (All):

Mathematical analysis.

Difference equations.

Functional equations.

Dynamics.

Multibody systems.

Vibration.

Mechanics, Applied.

Measure theory.

Analysis.

Difference and Functional Equations.

Dynamical Systems.

Multibody Systems and Mechanical Vibrations.

Measure and Integration.

Local Subjects:

Analysis.

Difference and Functional Equations.

Dynamical Systems.

Multibody Systems and Mechanical Vibrations.

Measure and Integration.

Physical Description:

1 online resource (882 pages)

Edition:

1st ed. 2021.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2021.

Summary:

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.

Contents:

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.

Notes:

Includes bibliographical references and index.

ISBN:

3-030-76132-0

OCLC:

1260340798