Feedback-invariant optimal control theory and differential geometry. I: Regular extremals
type: Item
instance of: scholarly article
title: Feedback-invariant optimal control theory and differential geometry. I: Regular extremals
zbMATH Open document ID: 0952.49019
DOI: 10.1007/BF02463256
author: R. V. Gamkrelidze
author: A. A. Agrachev
published in: Journal of Dynamical and Control Systems
publication date: 2000-04-13T00:00:00Z
review text: This paper is devoted to the unification of the theory of smooth optimal control problems and that part of differential geometry which deals with geodesics of different kinds. Section 1 analyses the \({\mathcal L}\)-derivatives of smooth mappings. Section 2 realizes a connection between smooth control systems and basic structures of differential geometry. Section 3 gives the computation of \({\mathcal L}\)-derivative of the boundary-value mapping and studies the regular extremals (which are trajectories of a fixed Hamiltonian system). Section 4 introduces and investigates Jacobi curves as curves in a Lagrangian Grassmannian. Section 5 studies the canonical connections of Hamiltonian systems and of DEs of second-order. Section 6 finds explicit geometrical objects defined by two-dimensional control systems.
Mathematics Subject Classification ID: 49K15
Mathematics Subject Classification ID: 53C22
Mathematics Subject Classification ID: 93B52
Mathematics Subject Classification ID: 58E25
Mathematics Subject Classification ID: 53B05
Mathematics Subject Classification ID: 53B15
zbMATH DE Number: 1431841
zbMATH Keywords: smooth optimal control
zbMATH Keywords: geodesics
zbMATH Keywords: regular extremals
zbMATH Keywords: canonical connections
zbMATH Keywords: Hamiltonian systems
Wikidata QID: Q115392145
reviewed by: Constantin Udrişte
MaRDI profile type: Publication
cites work: Q4195269
cites work: Q3713037
cites work: Local invariants of smooth control systems
cites work: Feedback Equivalence for Nonlinear Systems and the Time Optimal Control Problem
full work available at URL: https://doi.org/10.1007/bf02463256
OpenAlex ID: W2000446903
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description: scientific article; zbMATH DE number 1431841