Robust feedforward boundary control of hyperbolic conservation laws

Xavier Litrico; Vincent Fromion; Gérard Scorletti; Xavier Litrico; Vincent Fromion; Gérard Scorletti

doi:10.3934/nhm.2007.2.717

Networks and Heterogeneous Media

2007, Volume 2, Issue 4: 717-731. doi: 10.3934/nhm.2007.2.717

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Robust feedforward boundary control of hyperbolic conservation laws

1.
Cemagref, UMR G-EAU, 361 rue JF Breton, F-34196 Montpellier Cedex 5
2.
INRA, Unité Mathématique Informatique et Génome, UR1077, INRA-MIG, F-78350 Jouy-en-Josas
3.
GREYC Equipe Auto, Université de Caen, 6 boulevard du Maréchal Juin, F-14050 Caen Cedex

Received: 01 May 2007 Revised: 01 August 2007
Primary: 35B37, 93C20, 93C80, 35L65; Secondary: 35C05, 35Q35.

The paper proposes a feedforward boundary control to reject measured disturbances for systems modelled by hyperbolic partial differential equations obtained from conservation laws. The controller design is based on fre- quency domain methods. Perfect rejection of measured perturbations at one boundary is obtained by controlling the other boundary. This result is then extended to design robust open-loop controller when the model of the system is not perfectly known, e.g. in high frequencies. Frequency domain comparisons and time-domain simulations illustrates the good performance of the feedforward boundary controller.
- feedforward control,
- hyperbolic systems,
- shallow water equations,
- frequency domain approach
Citation: Xavier Litrico, Vincent Fromion, Gérard Scorletti. Robust feedforward boundary control of hyperbolic conservation laws[J]. Networks and Heterogeneous Media, 2007, 2(4): 717-731. doi: 10.3934/nhm.2007.2.717

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Abstract

The paper proposes a feedforward boundary control to reject measured disturbances for systems modelled by hyperbolic partial differential equations obtained from conservation laws. The controller design is based on fre- quency domain methods. Perfect rejection of measured perturbations at one boundary is obtained by controlling the other boundary. This result is then extended to design robust open-loop controller when the model of the system is not perfectly known, e.g. in high frequencies. Frequency domain comparisons and time-domain simulations illustrates the good performance of the feedforward boundary controller.
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