Application in the Optimal Control Problems
Buch, Englisch, 208 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 464 g
ISBN: 978-1-394-19097-3
Verlag: Wiley
Interval Analysis
An innovative and unique application of interval analysis to optimal control problems
In Interval Analysis: Application in the Optimal Control Problems, celebrated researcher and engineer Dr. Navid Razmjooy delivers an expert discussion of the uncertainties in the analysis of optimal control problems. In the book, Dr. Razmjooy uses an open-ended approach to solving optimal control problems with indefinite intervals. Utilizing an extended, Runge-Kutta method, the author demonstrates how to accelerate its speed with the piecewise function.
You’ll find recursive methods used to achieve more compact answers, as well as how to solve optimal control problems using the interval Chebyshev’s function. The book also contains: - A thorough introduction to common errors and mistakes, generating uncertainties in physical models
- Comprehensive explorations of the literature on the subject, including Hukurara’s derivatives
- Practical discussions of the interval analysis and its variants, including the classical (Minkowski) methods
- Complete treatments of existing control methods, including classic, conventional advanced, and robust control.
Perfect for master’s and PhD students working on system uncertainties, Interval Analysis: Application in the Optimal Control Problems will also benefit researchers working in laboratories, universities, and research centers.
Autoren/Hrsg.
Fachgebiete
- Technische Wissenschaften Energietechnik | Elektrotechnik Elektrotechnik
- Technische Wissenschaften Elektronik | Nachrichtentechnik Elektronik Sensorik
- Technische Wissenschaften Elektronik | Nachrichtentechnik Nachrichten- und Kommunikationstechnik Regelungstechnik
- Technische Wissenschaften Maschinenbau | Werkstoffkunde Produktionstechnik Zuverlässigkeitstechnik
Weitere Infos & Material
About the Author viii
1 Preface and Overview 1
Chapter 1: Preface and Overview 1
Chapter 2: Introduction 2
Chapter 3: Literature Review 2
Chapter 4: Introduction to Interval Analysis and Solving the Problems with Interval Uncertainties 2
Chapter 5: Stability and Controllability Based on Interval Analysis 3
Chapter 6: Optimal Control of the Systems with Interval Uncertainties 3
Chapter 7: Conclusions 3
2 Introduction 5
2.1 Background 5
2.2 Relationship Between Error and Uncertainty 7
2.3 Expert Perspectives on Interval Analysis 8
2.4 Precision Analysis of Interval-Based Models (Self-Validated Numeric) 10
2.5 Concepts of the Ordinary and Interval-based Optimal Control 11
2.6 Orthogonal Spectral Methods 13
2.7 Desired Confidence Interval 13
2.8 Conclusions 14
3 Literature Review 17
4 Introduction to Interval Analysis and Solving the Problems with Interval Uncertainties 29
4.1 Introduction 29
4.2 Introduction to IA 30
4.3 The Algebra of Interval Sets 31
4.3.1 Classic Interval Algebra (Minkowski Method) 31
4.3.2 Mathematical Norm and Distance in the IA 33
4.3.3 Kaucher Extended Interval Analysis 33
4.3.4 Modal Interval Analysis 34
4.3.5 Hukuhara Difference Method 35
4.4 Interval Representations 36
4.5 Interval Complex Integers 39
4.6 Interval Vector and Matrix 41
4.6.1 Vector and Matrix IA 41
4.6.2 Interval Vector Norm 42
4.6.3 Interval Matrix Analysis 42
4.6.3.1 Conceptional Example: Wrapping Effect 43
4.6.4 Interval Matrices Norm 44
4.6.5 Interval Determination of a Matrix 45
4.6.6 The Inverse of a Regular Interval Matrix 45
4.6.7 Eigenvalues and Eigenvectors of an Interval Matrix 45
4.7 Solving Linear Systems with Interval Parameters 46
4.8 Interval Functions 46
4.8.1 Overestimated Interval Function 46
