Adjoint and Hamiltonian input-output differential equations

Peter E. Crouch; Francoise Lamnabhi-Lagarrigue; Arjan J. van der Schaft

doi:10.1109/9.376115

Adjoint and Hamiltonian input-output differential equations

Peter E. Crouch, Francoise Lamnabhi-Lagarrigue, Arjan J. van der Schaft

Faculty of Electrical Engineering, Mathematics and Computer Science

Research output: Contribution to journal › Article › Academic › peer-review

13 Citations (Scopus)

843 Downloads (Pure)

Abstract

Based on developments in the theory of variational and Hamiltonian control systems by Crouch and van der Schaft (1987), this paper answers two questions: given an input-output differential equation description of a nonlinear system, what is the adjoint variational system in input-output differential form and what are the conditions for the system to be Hamiltonian, i.e., such that the variational and the adjoint variational systems coincide? This resulting set of conditions is then used to generalize classical conditions such as the well-known Helmholtz conditions for the inverse problem in classical mechanics.

Original language	English
Pages (from-to)	603-615
Number of pages	13
Journal	IEEE transactions on automatic control
Volume	40
Issue number	4
DOIs	https://doi.org/10.1109/9.376115
Publication status	Published - 1995

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10.1109/9.376115

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13 Citations
2 Report

Adjoint and Hamiltonian input-output differential equations
Crouch, P. E., Lamnabhi-Lagarrigue, F. & van der Schaft, A., 1994, Enschede: University of Twente. 33 p. (Memorandum; no. 1187)
Research output: Book/Report › Report › Professional
Adjoint and Hamiltonian input-output differential equations
Crouch, P. E., Lamnabhi-Lagarrigue, F. & van der Schaft, A. J., 1991, Tempe, FL, USA: Arizona State University. 19 p.
Research output: Book/Report › Report › Professional

Cite this

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title = "Adjoint and Hamiltonian input-output differential equations",

abstract = "Based on developments in the theory of variational and Hamiltonian control systems by Crouch and van der Schaft (1987), this paper answers two questions: given an input-output differential equation description of a nonlinear system, what is the adjoint variational system in input-output differential form and what are the conditions for the system to be Hamiltonian, i.e., such that the variational and the adjoint variational systems coincide? This resulting set of conditions is then used to generalize classical conditions such as the well-known Helmholtz conditions for the inverse problem in classical mechanics.",

author = "Crouch, {Peter E.} and Francoise Lamnabhi-Lagarrigue and {van der Schaft}, {Arjan J.}",

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AU - Crouch, Peter E.

AU - Lamnabhi-Lagarrigue, Francoise

AU - van der Schaft, Arjan J.

PY - 1995

Y1 - 1995

N2 - Based on developments in the theory of variational and Hamiltonian control systems by Crouch and van der Schaft (1987), this paper answers two questions: given an input-output differential equation description of a nonlinear system, what is the adjoint variational system in input-output differential form and what are the conditions for the system to be Hamiltonian, i.e., such that the variational and the adjoint variational systems coincide? This resulting set of conditions is then used to generalize classical conditions such as the well-known Helmholtz conditions for the inverse problem in classical mechanics.

AB - Based on developments in the theory of variational and Hamiltonian control systems by Crouch and van der Schaft (1987), this paper answers two questions: given an input-output differential equation description of a nonlinear system, what is the adjoint variational system in input-output differential form and what are the conditions for the system to be Hamiltonian, i.e., such that the variational and the adjoint variational systems coincide? This resulting set of conditions is then used to generalize classical conditions such as the well-known Helmholtz conditions for the inverse problem in classical mechanics.

U2 - 10.1109/9.376115

DO - 10.1109/9.376115

M3 - Article

SN - 0018-9286

VL - 40

SP - 603

EP - 615

JO - IEEE transactions on automatic control

JF - IEEE transactions on automatic control

IS - 4

ER -

Adjoint and Hamiltonian input-output differential equations

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