Optimal Control and Geometry: Integrable Systems by Velimir Jurdjevic

Optimal Control and Geometry: Integrable Systems by Velimir Jurdjevic

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.

'The book is written in a very refreshing style that reflects the author's contagious enthusiasm for the subjectIt manages this by focusing on the geometry, using the precise language of differential geometry, while not getting bogged down by analytic intricacies. Throughout, the book pays much attention to historical developments and evolving and contrasting points of view, which is also reflected in the rich bibliography of classical resources.' Matthias Kawski, MathSciNet

Professor Velimir Jurdjevic is one of the founders of geometric control theory. His pioneering work with H. J. Sussmann was deemed to be among the most influential papers of the century and his book, Geometric Control Theory, revealed the geometric origins of the subject and uncovered important connections to physics and geometry. It remains a major reference on non-linear control. Jurdjevic's expertise also extends to differential geometry, mechanics and integrable systems. His publications cover a wide range of topics including stability theory, Hamiltonian systems on Lie groups, and integrable systems. He has spent most of his professional career at the University of Toronto.

SKU	Unavailable
ISBN 13	9781107113886
ISBN 10	1107113881
Title	Optimal Control and Geometry: Integrable Systems
Author	Velimir Jurdjevic
Series	Cambridge Studies In Advanced Mathematics
Condition	Unavailable
Binding Type	Hardback
Publisher	Cambridge University Press
Year published	2016-07-04
Number of pages	423
Cover note	Book picture is for illustrative purposes only, actual binding, cover or edition may vary.