Hamiltonian and self-adjoint control systems
type: Item
instance of: scholarly article
title: Hamiltonian and self-adjoint control systems
zbMATH Open document ID: 0616.93016
DOI: 10.1016/0167-6911(87)90093-4
published in: Systems \& Control Letters
publication date: 1987-01-01T00:00:00Z
full work available at URL: hamiltonian-and-selfadjoint-control-systems(47e18222-1518-4ebc-9c9f-8231da1aae1c).html
review text: The paper surveys a remarkable collection of results concerned with Hamiltonian realization of affine analytic control systems. Two results deserve special attention. The first, Theorem 2.3, states a necessary and sufficient condition for an affine system to be Hamiltonian in terms of a special relation between the lifts of the affine system to the tangent and the cotangent bundles the self-adjointness property. Further, Theorem 3.6 characterizes Hamiltonian systems as those affine systems which satisfy the variational criterion \[ \int^{+\infty}_{- \infty}(\delta^ T_ 2y(t)\delta_ 1u(t)\quad -\delta^ T_ 1y(t)\delta_ 2u(t))dt=0, \] for all admissible variations \((\delta_ iu,\delta_ iy)\), \(i=1,2\) of input-output pairs belonging to the external behaviour of the original affine system. The results of the paper generalize to general nonlinear control systems.
Mathematics Subject Classification ID: 93B15
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 47B25
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 58E25
Mathematics Subject Classification ID: 70H05
Mathematics Subject Classification ID: 93B20
Mathematics Subject Classification ID: 93C15
zbMATH DE Number: 3999754
zbMATH Keywords: Hamiltonian realization
zbMATH Keywords: affine analytic control systems
zbMATH Keywords: self- adjointness
zbMATH Keywords: variational criterion
author: Arjan van der Schaft
author: Peter E. Crouch
reviewed by: Krzysztof Tchoń
MaRDI profile type: Publication
OpenAlex ID: W2150859671
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description: scientific article; zbMATH DE number 3999754