Optimal control and geometry : integrable systems / Velimir Jurdjevic, University of Toronto.
The synthesis of symplectic geometry, the calculus of variations and control theory offered in this book provides a crucial foundation for the understanding of many problems in applied mathematics. Focusing on the theory of integrable systems, this book introduces a class of optimal control problems...
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| Online Access: |
Full Text (via Cambridge) |
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| Main Author: | |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge, United Kingdom :
Cambridge University Press,
2016.
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| Series: | Cambridge studies in advanced mathematics ;
154. |
| Subjects: |
| Summary: | The synthesis of symplectic geometry, the calculus of variations and control theory offered in this book provides a crucial foundation for the understanding of many problems in applied mathematics. Focusing on the theory of integrable systems, this book introduces a class of optimal control problems on Lie groups, whose Hamiltonians, obtained through the Maximum Principle of optimality, shed new light on the theory of integrable systems. These Hamiltonians provide an original and unified account of the existing theory of integrable systems. The book particularly explains much of the mystery surrounding the Kepler problem, the Jacobi problem and the Kovalevskaya Top. It also reveals the ubiquitous presence of elastic curves in integrable systems up to the soliton solutions of the non-linear Schroedinger's equation. Containing a useful blend of theory and applications, this is an indispensable guide for graduates and researchers in many fields, from mathematical physics to space control. |
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| Physical Description: | 1 online resource (xx, 415 pages) |
| Bibliography: | Includes bibliographical references and index. |
| ISBN: | 9781316286852 1316286851 9781316585795 1316585794 |
| DOI: | 10.1017/CBO9781316286852 |
| Source of Description, Etc. Note: | Print version record. |