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. Jul 04, 2016 · 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.

Jul 04, 2016 · Optimal Control and Geometry: Integrable Systems Cambridge Studies in Advanced Mathematics Book 154 - Kindle edition by Jurdjevic, Velimir. Download it once and read it on your Kindle device, PC, phones or tablets. May 08, 2017 · Velimir Jurdjevic. This book offers a new theoretical perspective for optimal control theory that incorporates a synthesis of the calculus of variations and symplectic geometry. The author finds that control theoretic interpretations of variational problems lead directly to a new interpretation in terms of Hamiltonian systems. Optimal control and geometry: integrable systems. [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. Author: Velimir Jurdjevic. Publisher: Cambridge University Press ISBN: 1316586332 Category: Mathematics Page: N.A View: 1279 DOWNLOAD NOW » 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. Jan 28, 2008 · Buy Geometric Control Theory Cambridge Studies in Advanced Mathematics. › Visit Amazon's Velimir Jurdjevic Page. Find all the books, read about the author, and more. mechanics and mathematics especially dynamical systems and differential geometry, as well as for the mathematician new to control theory.

Abstract. This essay highlights the contributions of geometric control theory to the calculus of variations. The Maximum Principle is recognized as a covariant necessary condition of optimality valid for variational problems defined on subsets C of the tangent bundle of the ambient manifold, rather than the entire tangent bundle, as was commonly assumed by the classical theory. Optimal Control on Lie Groups: Integrable Hamiltonian systems by Velimir Jurdjevic, University of Toronto. Cambridge Studies in Advanced mathematics 51, Cambridge Press, 1997. [3] Jurdjevic V. Hamiltonian Systems on Complex Lie groups, Memoirs AMS no 838 178, 2005. An overlap with mathematical physics is demonstrated by the Maximum principle, a fundamental principle of optimality arising from geometric control, which is applied to time-evolving systems governed by physics as well as to man-made systems governed by controls. Applications are drawn from geometry, mechanics, and control of dynamical systems. Read "Optimal Control and Geometry: Integrable Systems" by Velimir Jurdjevic available from Rakuten Kobo. The synthesis of symplectic geometry, the calculus of variations and control theory offered in this book provides a cruc.

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