
Functional Analysis and Linear Control Theory
Description
Alles über E-Books | Antworten auf Fragen rund um E-Books, Kopierschutz und Dateiformate finden Sie in unserem Info- & Hilfebereich.
More details
Other editions
Additional editions
Persons
Content
- Front Cover
- Functional Analysis and Linear Control Theory
- Copyright Page
- Contents
- Preface
- Chapter 1. Preliminaries
- 1.1 Control Theory
- 1.2 Set Theory
- 1.3 Linear Space (Vector Space)
- 1.4 Linear Independence
- 1.5 Maximum and Supremum
- 1.6 Metric and Norm
- 1.7 Sequences and Limit Concepts
- 1.8 Convex Sets
- 1.9 Intervals on a Line
- 1.10 The K Cube
- 1.11 Product Sets and Product Spaces
- 1.12 Direct Sum
- 1.13 Functions and Mappings
- 1.14 Exercises
- Chapter 2. Basic Concepts
- 2.1 Topological Concepts
- 2.2 Compactness
- 2.3 Convergence
- 2.4 Measure Theory
- 2.5 Euclidean Spaces
- 2.6 Sequence Spaces
- 2.7 The Lebesgue Integral
- 2.8 Spaces of Lebesgue Integrable Functions (Lp Spaces)
- 2.9 Inclusion Relations between Sequence Spaces
- 2.10 Inclusion Relations between Function Spaces on a Finite Interval
- 2.11 The Hierarchy of Spaces
- 2.12 Linear Functionals
- 2.13 The Dual Space
- 2.14 The Space of all Bounded Linear Mappings
- 2.15 Exercises
- Chapter 3. Inner Product Spaces and Some of their Properties
- 3.1 Inner Product
- 3.2 Orthogonality
- 3.3 Hilbert Space
- 3.4 The Parallelogram Law
- 3.5 Theorems
- 3.6. Exercises
- Chapter 4. Some Major Theorems of Functional Analysis
- 4.1 Introduction
- 4.2 The Hahn-Banach Theorem and its Geometric Equivalent
- 4.3 Other Theorems Related to Mappings
- 4.4 Hölder's Inequality
- 4.5 Norms on Product Spaces
- 4.6 Exercises
- Chapter 5. Linear Mappings and Reflexive Spaces
- 5.1 Introduction
- 5.2 Mappings of Finite Rank
- 5.3 Mappings of Finite Rank on a Hilbert Space
- 5.4 Reflexive Spaces
- 5.5 Rotund Spaces
- 5.6 Smooth Spaces
- 5.7 Uniform Convexity
- 5.8 Convergence in Norm (Strong Convergence)
- 5.9 Weak Convergence
- 5.10 Weak Compactness
- 5.11 Weak* Convergence and Weak* Compactness
- 5.12 Weak Topologies
- 5.13 Failure of Compactness in Infinite Dimensional Spaces
- 5.14 Convergence of Operators
- 5.15 Weak, Strong and Uniform Continuity
- 5.16 Exercises
- Chapter 6. Axiomatic Representation of Systems
- 6.1 Introduction
- 6.2 The Axioms
- 6.3 Relation between the Axiomatic Representation and the Representation as a Finite Set of Differential Equations
- 6.4 Visualization of the Concepts of this Chapter
- 6.5 System Realization
- 6.6 The Transition Matrix and Some of its Properties
- 6.7 Calculation of the Transition Matrix for Time Invariant Systems
- 6.8 Exercises
- Chapter 7. Stability, Controllability and Observability
- 7.1 Introduction
- 7.2 Stability
- 7.3 Controllability and Observability
- 7.4 Exercises
- Chapter 8. Minimum Norm Control
- 8.1 Introduction
- 8.2 Minimum Norm Problems: Literature
- 8.3 Minimum Norm Problems: Outline of the Approach
- 8.4 Minimum Norm Problem in Hilbert Space: Definition
- 8.5 Minimum Norm Problems in Banach Space
- 8.6 More General Optimization Problems
- 8.7 Minimum Norm Control: Characterization, a Simple Example
- 8.8 Development of Numerical Methods for the Calculation of Minimum Norm Controls
- 8.9 Exercises
- Chapter 9. Minimum Time Control
- 9.1 Preliminaries and Problem Description
- 9.2 The Attainable Set
- 9.3 Existence of a Minimum Time Control
- 9.4 Uniqueness
- 9.5 Characterization
- 9.6 The Pontryagin Maximum Principle
- 9.7 Time Optimal Control
- 9.8 Exercises
- Chapter 10. Distributed Systems
- 10.1 Introduction
- 10.2 Further Theorems From Functional Analysis
- 10.3 Axiomatic Description
- 10.4 Representation of Distributed Systems
- 10.5 Characterization of The Solution of the Equation x =Ax + Bu
- 10.6 Stability
- 10.7 Controllability
- 10.8 Minimum Norm Control
- 10.9 Time-Optimal Control
- 10.10 Optimal Control of a Distributed System: An Example
- 10.11 Approximate Numerical Solution
- 10.12 Exercises
- Glossary of Symbols
- References and Further Reading
- Subject Index
System requirements
File format: PDF
Copy protection: Watermark-DRM (Digital Rights Management)
System requirements:
- Computer (Windows; MacOS X; Linux): Use the free software Adobe Reader, Adobe Digital Editions, or any other PDF viewer of your choice (see eBook Help).
- Tablet/Smartphone (Android; iOS): Install the free app Adobe Digital Editions or another reading app for eBooks, e.g., PocketBook (see eBook Help).
- E-reader: Bookeen, Kobo, Pocketbook, Sony, Tolino and many more (only limited: Kindle).
The file format PDF always displays a book page identically on any hardware. This makes PDF suitable for complex layouts such as those used in textbooks and reference books (images, tables, columns, footnotes). Unfortunately, on the small screens of e-readers or smartphones, PDFs are rather annoying, requiring too much scrolling.
This eBook uses Watermark-DRM, a „soft” copy protection. This means that there are no technical restrictions to prevent illegal distribution. However, there is a personalised watermark embedded in the eBook that can be used to identify the purchaser of the eBook in the event of misuse and to provide evidence for legal purposes.
For more information, see our eBook Help page.