Gradient realization of nonlinear control systems

J. Cortés; A.J. van der Schaft; P.E. Crouch

doi:10.1016/S1474-6670(17)38868-7

Gradient realization of nonlinear control systems

J. Cortés, A.J. van der Schaft, P.E. Crouch

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

4 Citations (Scopus)

154 Downloads (Pure)

Abstract

We investigate necessary and su?cient conditions under which a nonlinear afine control system with outputs can be written as a gradient control system corresponding to some pseudo-Riemannian metric defined on the state space. The results rely on a suitable notion of compatibility of the system with respect to a given afine connection, and on the input-output behavior of the prolonged system and the gradient extension. The symmetric product associated with an afine connection plays a key role in the discussion

Original language	English
Title of host publication	Lagrangian and Hamiltonian methods for nonlinear control
Subtitle of host publication	2nd IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control
Editors	Alessandro Astolfi, Francisco Gordillo, Arjan van der Schaft
Place of Publication	Oxford
Publisher	Pergamon
Pages	73-78
Number of pages	6
ISBN (Print)	978-0-08-044278-5
DOIs	https://doi.org/10.1016/S1474-6670(17)38868-7
Publication status	Published - 2003
Event	2nd IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, LHMNLC 2003 - Sevilla, Spain Duration: 3 Apr 2003 → 5 Apr 2003 Conference number: 2

Publication series

Name	IFAC Proceedings Volumes
Publisher	Pergamon Press
ISSN (Print)	1474-6670

Conference

Conference	2nd IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, LHMNLC 2003
Abbreviated title	LHMNLC
Country/Territory	Spain
City	Sevilla
Period	3/04/03 → 5/04/03

Keywords

Gradient control systems
Symmetric product
prolongation and gradient extension

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10.1016/S1474-6670(17)38868-7

Cortes2003gradientAccepted author version, 167 KB

Cite this

Cortés, J., van der Schaft, A. J., & Crouch, P. E. (2003). Gradient realization of nonlinear control systems. In A. Astolfi, F. Gordillo, & A. van der Schaft (Eds.), Lagrangian and Hamiltonian methods for nonlinear control: 2nd IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control (pp. 73-78). (IFAC Proceedings Volumes). Pergamon. https://doi.org/10.1016/S1474-6670(17)38868-7

Cortés, J. ; van der Schaft, A.J. ; Crouch, P.E. / Gradient realization of nonlinear control systems. Lagrangian and Hamiltonian methods for nonlinear control: 2nd IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control. editor / Alessandro Astolfi ; Francisco Gordillo ; Arjan van der Schaft. Oxford : Pergamon, 2003. pp. 73-78 (IFAC Proceedings Volumes).

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abstract = "We investigate necessary and su?cient conditions under which a nonlinear afine control system with outputs can be written as a gradient control system corresponding to some pseudo-Riemannian metric defined on the state space. The results rely on a suitable notion of compatibility of the system with respect to a given afine connection, and on the input-output behavior of the prolonged system and the gradient extension. The symmetric product associated with an afine connection plays a key role in the discussion",

keywords = "Gradient control systems, Symmetric product, prolongation and gradient extension",

author = "J. Cort{\'e}s and {van der Schaft}, A.J. and P.E. Crouch",

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doi = "10.1016/S1474-6670(17)38868-7",

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editor = "Alessandro Astolfi and Francisco Gordillo and {van der Schaft}, Arjan",

booktitle = "Lagrangian and Hamiltonian methods for nonlinear control",

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note = "2nd IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, LHMNLC 2003, LHMNLC ; Conference date: 03-04-2003 Through 05-04-2003",

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Cortés, J, van der Schaft, AJ & Crouch, PE 2003, Gradient realization of nonlinear control systems. in A Astolfi, F Gordillo & A van der Schaft (eds), Lagrangian and Hamiltonian methods for nonlinear control: 2nd IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control. IFAC Proceedings Volumes, Pergamon, Oxford, pp. 73-78, 2nd IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, LHMNLC 2003, Sevilla, Spain, 3/04/03. https://doi.org/10.1016/S1474-6670(17)38868-7

Gradient realization of nonlinear control systems. / Cortés, J.; van der Schaft, A.J.; Crouch, P.E.
Lagrangian and Hamiltonian methods for nonlinear control: 2nd IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control. ed. / Alessandro Astolfi; Francisco Gordillo; Arjan van der Schaft. Oxford: Pergamon, 2003. p. 73-78 (IFAC Proceedings Volumes).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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T1 - Gradient realization of nonlinear control systems

AU - Cortés, J.

AU - van der Schaft, A.J.

AU - Crouch, P.E.

N1 - Conference code: 2

PY - 2003

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N2 - We investigate necessary and su?cient conditions under which a nonlinear afine control system with outputs can be written as a gradient control system corresponding to some pseudo-Riemannian metric defined on the state space. The results rely on a suitable notion of compatibility of the system with respect to a given afine connection, and on the input-output behavior of the prolonged system and the gradient extension. The symmetric product associated with an afine connection plays a key role in the discussion

AB - We investigate necessary and su?cient conditions under which a nonlinear afine control system with outputs can be written as a gradient control system corresponding to some pseudo-Riemannian metric defined on the state space. The results rely on a suitable notion of compatibility of the system with respect to a given afine connection, and on the input-output behavior of the prolonged system and the gradient extension. The symmetric product associated with an afine connection plays a key role in the discussion

KW - Gradient control systems

KW - Symmetric product

KW - prolongation and gradient extension

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DO - 10.1016/S1474-6670(17)38868-7

M3 - Conference contribution

SN - 978-0-08-044278-5

T3 - IFAC Proceedings Volumes

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EP - 78

BT - Lagrangian and Hamiltonian methods for nonlinear control

A2 - Astolfi, Alessandro

A2 - Gordillo, Francisco

A2 - van der Schaft, Arjan

PB - Pergamon

CY - Oxford

T2 - 2nd IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, LHMNLC 2003

Y2 - 3 April 2003 through 5 April 2003

ER -

Cortés J, van der Schaft AJ, Crouch PE. Gradient realization of nonlinear control systems. In Astolfi A, Gordillo F, van der Schaft A, editors, Lagrangian and Hamiltonian methods for nonlinear control: 2nd IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control. Oxford: Pergamon. 2003. p. 73-78. (IFAC Proceedings Volumes). doi: 10.1016/S1474-6670(17)38868-7

Gradient realization of nonlinear control systems

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