Control algorithms for oscillations in Hamiltonian systems
type: Item
instance of: scholarly article
title: Control algorithms for oscillations in Hamiltonian systems
zbMATH Open document ID: 0966.93051
author: I. A. Makarov
author: Alexander Fradkov
published in: Doklady Mathematics
publication date: 2001-01-28T00:00:00Z
review text: The paper studies control algorithms for oscillations in Hamiltonian systems. The authors consider the Hamiltonian system with the phase vector \(x= (q,p)\) and with the Hamiltonian \[ H(q,p,u)= H_0(q,p)+ \sum^m_{j=1} H_j(q,p)u_j,\quad j= 1,\dots, m \] which is linear with respect to the control actions \(u= (q,p)\). They study a general class of problems where the set of integrals of motion \(F_i\), \(i=1,\dots, k\), of the uncontrolled (free) system is given, and the control objective is to reach their arbitrary prescribed values \(f_i\). Control algorithms ensuring this objective are obtained by the speed gradient method used for the adaptive control of nonlinear systems. The results are applied in oscillation studies of the simple spherical pendulum. The results obtained establish the compatibility and limitations of the speed gradient algorithm applied to the control of oscillatory motion in nonlinear systems.
reviewed by: Ştefan Zanfir
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 70Q05
Mathematics Subject Classification ID: 93C40
Mathematics Subject Classification ID: 70H05
zbMATH DE Number: 1557483
zbMATH Keywords: oscillations in Hamiltonian systems
zbMATH Keywords: Hamiltonian system
zbMATH Keywords: speed gradient method
zbMATH Keywords: adaptive control of nonlinear systems
zbMATH Keywords: spherical pendulum
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1557483