Fuzzy Dynamic Equations, Dynamic Inclusions, and Optimal Control Problems on Time Scales
Springer International Publishing (Verlag)
978-3-030-76134-9 (ISBN)
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.
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.
| Erscheinungsdatum | 17.07.2022 |
|---|---|
| Zusatzinfo | XIII, 882 p. 48 illus., 4 illus. in color. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 1234 g |
| Themenwelt | Mathematik / Informatik ► Informatik ► Theorie / Studium |
| Mathematik / Informatik ► Mathematik ► Analysis | |
| Technik ► Maschinenbau | |
| Schlagworte | adjoint linear dynamics • Alaoglu's theorem • Bang-Bang principle • boundary value problems • Dynamic Programming • Gronwall type inequality • Isaacs equations • Krein-Milman theorem • Lebesgue delta integral • ordinary differential equations with impulses • ordinary differential inclusions • Shift Operators • Sobolev spaces • the Pontryagin maximum principle • weak solutions for dynamic systems |
| ISBN-10 | 3-030-76134-7 / 3030761347 |
| ISBN-13 | 978-3-030-76134-9 / 9783030761349 |
| Zustand | Neuware |
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