Optimal control and geometry: integrable systems

by Jurdjevic, Velimir

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Title Statements

Full title :Optimal control and geometry : integrable systems / Velimir Jurdjevic, University of Toronto.

Edition Statements

Publication Date:2016.

Publication Statements

Publisher(s):Cambridge University Press
Place of Publication:Cambridge
Language:eng
Publication Date:2016.

The Physical Object

Description:xx, 415 pages ; : 23 cm.

Edition Identifiers

ISBN:9781107113886, 1107113881
oclc:ocn928777822
LC Classification:QA402.3
Dewey Decimal:515/.642

Ch. 1 The Orbit Theorem and Lie determined systems -- 1.1.Vector fields and differential forms -- 1.2.Flows and diffeomorphisms -- 1.3.Families of vector fields: the Orbit theorem -- 1.4.Distributions and Lie determined systems -- ch. 2 Control systems: accessibility and controllability -- 2.1.Control systems and families of vector fields -- 2.2.The Lie saturate -- ch. 3 Lie groups and homogeneous spaces -- 3.1.The Lie algebra and the exponential map -- 3.2.Lie subgroups -- 3.3.Families of left-invariant vector fields and accessibility -- 3.4.Homogeneous spaces -- ch. 4 Symplectic manifolds: Hamiltonian vector fields -- 4.1.Symplectic vector spaces -- 4.2.The cotangent bundle of a vector space -- 4.3.Symplectic manifolds -- ch. 5 Poisson manifolds, Lie algebras, and coadjoint orbits -- 5.1.Poisson manifolds and Poisson vector fields -- 5.2.The cotangent bundle of a Lie group: coadjoint orbits -- ch. 6 Hamiltonians and optimality: the Maximum Principle -- 6.1.Extremal trajectories -- 6.2.Optimal control and the calculus of variations -- 6.3.The Maximum Principle -- 6.4.The Maximum Principle in the presence of symmetries -- 6.5.Abnormal extremals -- 6.6.The Maximum Principle and Wei…

Subjects

Control theory Géométrie différentielle Geometry, Differential Groupes de Lie Hamiltonian systems Lie groups Manifolds (Mathematics) Systèmes hamiltoniens Théorie de la commande Variétés (Mathématiques)