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E-grāmata: Surveys in Differential-Algebraic Equations III

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Surveys in Differential-Algebraic Equations IIIPalielināt
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The present volume comprises survey articles on various fields of Differential-Algebraic Equations (DAEs), which have widespread applications in controlled dynamical systems, especially in mechanical and electrical engineering and a strong relation to (ordinary) differential equations. The individual chapters provide reviews, presentations of the current state of research and new concepts in- Flexibility of DAE formulations- Reachability analysis and deterministic global optimization- Numerical linear algebra methods- Boundary value problemsThe results are presented in an accessible style, making this book suitable not only for active researchers but also for graduate students (with a good knowledge of the basic principles of DAEs) for self-study.

1 The Flexibility of DAE Formulations (Stephen L. Campbell).- 2 Reachability Analysis and Deterministic Global Optimization of DAE Models (Joseph K. Scott and Paul I. Barton).- 3 Numerical Linear Algebra Methods for Linear Differential-Algebraic Equations (Peter Benner, Philip Losse, Volker Mehrmann and Matthias Voigt).- 4 Boundary Value Problems for Differential-Algebraic Equations (René Lamour, Roswitha März and Ewa Weinmüller).
The Flexibility of DAE Formulations
1(60)
Stephen L. Campbell
1 Introduction
2 Observer Design
2(21)
2.1 Nonlinear Observers
4(12)
2.2 Estimation of Disturbances
16(7)
3 Optimization by Direct Transcription
23(16)
3.1 Virtual Index
25(10)
3.2 Differential Algebraic Inequalities
35(4)
4 Delayed DAEs
39(15)
4.1 Direct Transcription Algorithm
40(4)
4.2 DAEs and Delays
44(10)
5 Conclusion
54(7)
References
55(6)
Reachability Analysis and Deterministic Global Optimization of DAE Models
61(56)
Joseph K. Scott
Paul I. Barton
1 Introduction
62(4)
2 Problem Formulation
66(5)
2.1 Notation
66(1)
2.2 Semi-explicit Index-One DAEs
67(1)
2.3 Reachable Set Enclosures
68(1)
2.4 Global Dynamic Optimization
69(2)
3 Factorable Functions, Interval Arithmetic, and McCormick Relaxations
71(6)
3.1 Interval Arithmetic
72(2)
3.2 McCormick Relaxations
74(3)
3.3 Implementation
77(1)
4 Bounds and Relaxations for Implicit Functions
77(9)
4.1 Example
84(2)
5 State Bounds for Semi-explicit Index-One DAEs
86(7)
5.1 Theoretical Considerations
87(2)
5.2 Implementation
89(3)
5.3 Alternative Approaches
92(1)
6 State Relaxations for Semi-explicit Index-One DAEs
93(4)
6.1 Alternative Approaches
97(1)
7 Global Optimization with Semi-explicit Index-One DAEs Embedded
97(7)
7.1 The Spatial Branch-and-Bound Global Optimization Algorithm
98(2)
7.2 A Lower Bounding Procedure for Optimization with DAEs
100(3)
7.3 Alternative Approaches
103(1)
8 Numerical Results and Directions for Improvement
104(8)
8.1 Problem Formulation
104(2)
8.2 Global Dynamic Optimization
106(6)
9 Conclusions
112(5)
References
112(5)
Numerical Linear Algebra Methods for Linear Differential-Algebraic Equations
117(60)
Peter Benner
Philip Losse
Volker Mehrmann
Matthias Voigt
1 Introduction
119(1)
2 Solvability Theory
120(3)
3 Regularization and Derivative Arrays
123(7)
4 Staircase Forms and Properties of Descriptor Systems
130(5)
5 Even Matrix Pencils
135(11)
5.1 Structured Condensed Forms
135(6)
5.2 Computing Eigenvalues and Deflating Subspaces of Regular Index One Even Pencils
141(5)
6 Linear-Quadratic Optimal Control
146(8)
7 H∞ Optimal Control
154(7)
8 L∞-Norm Computation
161(2)
9 Dissipativity Check
163(6)
10 Conclusions
169(8)
References
170(7)
Boundary-Value Problems for Differential-Algebraic Equations: A Survey
177(127)
Rene Lamour
Roswitha Marz
Ewa Weinmuller
1 Introduction
178(10)
2 Analytical Theory
188(49)
2.1 Basic Assumptions and Terminology
188(6)
2.2 The Flow Structure of Regular Linear DAEs
194(7)
2.3 Accurately Stated Two-Point Boundary Conditions
201(6)
2.4 Conditioning Constants and Dichotomy
207(4)
2.5 Nonlinear BVPs
211(11)
2.6 Other Boundary Conditions
222(7)
2.7 Further References, Comments, and Open Questions
229(8)
3 Collocation Methods for Well-Posed BVPs
237(35)
3.1 BVPs Well-Posed in the Natural Setting
239(10)
3.2 Partitioned Equations
249(2)
3.3 BVPs for Index-2 DAEs
251(2)
3.4 BVPs for Singular Index-1 DAEs
253(13)
3.5 Defect-Based a posteriori Error Estimation for Index-1 DAEs
266(4)
3.6 Further References, Comments, and Open Questions
270(2)
4 Shooting Methods
272(15)
4.1 Solution of Linear DAEs
273(12)
4.2 Nonlinear Index-1 DAEs
285(1)
4.3 Further References, Comments, and Open Questions
286(1)
5 Miscellaneous
287(7)
5.1 Periodic Solutions
287(1)
5.2 Abramov Transfer Method
288(1)
5.3 Finite-Difference Methods
289(1)
5.4 Newton-Kantorovich Iterations
290(4)
6 Appendix
294(10)
6.1 Basics Concerning Regular DAEs
294(10)
6.2 List of Symbols and Abbreviations
304(1)
References 304(7)
Index 311
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