On backstepping boundary control for a class of linear port-Hamiltonian systems

Hector Ramirez, Hans Zwart, Yann Le Gorrec, Alessandro Macchelli

Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review

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Abstract

Backstepping boundary control is investigated for a class of linear port-Hamiltonian systems. It is shown that by considering as target system an exponentially stable dissipative PHS, i.e. a PHS with a linear dissipation term and homogeneous boundary conditions, a coordinate transformation based on a multiplicative operator suffices to map the open-loop system into the target system. The condition for the existence of the transformation is algebraic. Hence, the backstepping transformation and the associated matching condition are simpler than the conventional ones that considers Volterra integral terms and kernel conditions in the form of partial differential equations. Since the controller has been developed for a general class of linear PHS it is applicable to a large class of physical systems, as for instance transport, beam and wave equations. The result is illustrated on the examples of a transport equation and a vibrating string on a 1D spatial domain.

Original languageEnglish
Title of host publication2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
Subtitle of host publicationCDC 2017
PublisherIEEE
Pages658-663
Number of pages6
ISBN (Electronic)9781509028733
ISBN (Print)9781509028740
DOIs
Publication statusPublished - 18 Jan 2018
Event56th IEEE Conference on Decision and Control, CDC 2017: CDC 2017 - Melbourne Convention Center, Melbourne, Australia
Duration: 12 Dec 201715 Dec 2017
Conference number: 56
http://cdc2017.ieeecss.org/

Publication series

Name2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
Volume2018-January

Conference

Conference56th IEEE Conference on Decision and Control, CDC 2017
Abbreviated titleCDC
CountryAustralia
CityMelbourne
Period12/12/1715/12/17
Internet address

Fingerprint

Backstepping Control
Hamiltonians
Backstepping
Boundary Control
Hamiltonian Systems
Wave equations
Transport Equation
Partial differential equations
Boundary conditions
Beam Equation
Controllers
Target
Coordinate Transformation
Term
Volterra
Wave equation
Dissipation
Multiplicative
Partial differential equation
Strings

Cite this

Ramirez, H., Zwart, H., Le Gorrec, Y., & Macchelli, A. (2018). On backstepping boundary control for a class of linear port-Hamiltonian systems. In 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017: CDC 2017 (pp. 658-663). (2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017; Vol. 2018-January). IEEE. https://doi.org/10.1109/CDC.2017.8263736
Ramirez, Hector ; Zwart, Hans ; Le Gorrec, Yann ; Macchelli, Alessandro. / On backstepping boundary control for a class of linear port-Hamiltonian systems. 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017: CDC 2017. IEEE, 2018. pp. 658-663 (2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017).
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Ramirez, H, Zwart, H, Le Gorrec, Y & Macchelli, A 2018, On backstepping boundary control for a class of linear port-Hamiltonian systems. in 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017: CDC 2017. 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017, vol. 2018-January, IEEE, pp. 658-663, 56th IEEE Conference on Decision and Control, CDC 2017, Melbourne, Australia, 12/12/17. https://doi.org/10.1109/CDC.2017.8263736

On backstepping boundary control for a class of linear port-Hamiltonian systems. / Ramirez, Hector; Zwart, Hans; Le Gorrec, Yann; Macchelli, Alessandro.

2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017: CDC 2017. IEEE, 2018. p. 658-663 (2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017; Vol. 2018-January).

Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review

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Ramirez H, Zwart H, Le Gorrec Y, Macchelli A. On backstepping boundary control for a class of linear port-Hamiltonian systems. In 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017: CDC 2017. IEEE. 2018. p. 658-663. (2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017). https://doi.org/10.1109/CDC.2017.8263736