Exponential stabilization of boundary controlled port-Hamiltonian systems with dynamic feedback

Hector Ramirez; Yann Le Gorrec; Alessandro Macchelli; Heiko J. Zwart

doi:10.1109/TAC.2014.2315754

Exponential stabilization of boundary controlled port-Hamiltonian systems with dynamic feedback

Hector Ramirez, Yann Le Gorrec, Alessandro Macchelli, Heiko J. Zwart

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Abstract

It is shown that a strictly-input passive linear finite dimensional controller exponentially stabilizes a large class of partial differential equations actuated at the boundary of a one dimensional spatial domain. This follows since the controller imposes exponential dissipation of the total energy. The result can by use for control synthesis and for the stability analysis of complex systems modeled by sets of coupled PDE's and ODE's. The result is specialized to port-Hamiltonian control systems and a simplified DNA-manipulation process is used to illustrate the result.

Original language	English
Pages (from-to)	2849-2855
Number of pages	7
Journal	IEEE transactions on automatic control
Volume	59
Issue number	10
DOIs	https://doi.org/10.1109/TAC.2014.2315754
Publication status	Published - Oct 2014

Keywords

Partial Differential Equations (PDEs)
Boundary control systems (BCS)
22/4 OA procedure

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10.1109/TAC.2014.2315754

ArticleFinal published version, 308 KBLicence: Taverne

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title = "Exponential stabilization of boundary controlled port-Hamiltonian systems with dynamic feedback",

abstract = "It is shown that a strictly-input passive linear finite dimensional controller exponentially stabilizes a large class of partial differential equations actuated at the boundary of a one dimensional spatial domain. This follows since the controller imposes exponential dissipation of the total energy. The result can by use for control synthesis and for the stability analysis of complex systems modeled by sets of coupled PDE's and ODE's. The result is specialized to port-Hamiltonian control systems and a simplified DNA-manipulation process is used to illustrate the result.",

keywords = "Partial Differential Equations (PDEs), Boundary control systems (BCS), 22/4 OA procedure",

author = "Hector Ramirez and {Le Gorrec}, Yann and Alessandro Macchelli and Zwart, {Heiko J.}",

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AU - Ramirez, Hector

AU - Le Gorrec, Yann

AU - Macchelli, Alessandro

AU - Zwart, Heiko J.

PY - 2014/10

Y1 - 2014/10

N2 - It is shown that a strictly-input passive linear finite dimensional controller exponentially stabilizes a large class of partial differential equations actuated at the boundary of a one dimensional spatial domain. This follows since the controller imposes exponential dissipation of the total energy. The result can by use for control synthesis and for the stability analysis of complex systems modeled by sets of coupled PDE's and ODE's. The result is specialized to port-Hamiltonian control systems and a simplified DNA-manipulation process is used to illustrate the result.

AB - It is shown that a strictly-input passive linear finite dimensional controller exponentially stabilizes a large class of partial differential equations actuated at the boundary of a one dimensional spatial domain. This follows since the controller imposes exponential dissipation of the total energy. The result can by use for control synthesis and for the stability analysis of complex systems modeled by sets of coupled PDE's and ODE's. The result is specialized to port-Hamiltonian control systems and a simplified DNA-manipulation process is used to illustrate the result.

KW - Partial Differential Equations (PDEs)

KW - Boundary control systems (BCS)

KW - 22/4 OA procedure

U2 - 10.1109/TAC.2014.2315754

DO - 10.1109/TAC.2014.2315754

M3 - Article

VL - 59

SP - 2849

EP - 2855

JO - IEEE transactions on automatic control

JF - IEEE transactions on automatic control

SN - 0018-9286

IS - 10

ER -

Exponential stabilization of boundary controlled port-Hamiltonian systems with dynamic feedback

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