Robust feedforward boundary control of hyperbolic conservation laws

  • 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.

    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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  • 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.


  • This article has been cited by:

    1. Tarek S. Rabbani, Florent Di Meglio, Xavier Litrico, Alexandre M. Bayen, Feed-Forward Control of Open Channel Flow Using Differential Flatness, 2010, 18, 1063-6536, 213, 10.1109/TCST.2009.2014640
    2. Luciano Pandolfi, On-line input identification and application to Active Noise Cancellation, 2010, 34, 13675788, 245, 10.1016/j.arcontrol.2010.07.001
    3. Florent Di Meglio, Tarek Rabbani, Xavier Litrico, Alexandre M. Bayen, 2008, Feed-Forward river flow control using differential flatness, 978-1-4244-3123-6, 3895, 10.1109/CDC.2008.4738968
    4. Georges Bastin, Jean-Michel Coron, Amaury Hayat, Feedforward boundary control of 2×2 nonlinear hyperbolic systems with application to Saint-Venant equations, 2021, 57, 09473580, 41, 10.1016/j.ejcon.2020.11.002
    5. L. Pandolfi, On-line input identification and Active Noise Cancellation: an overview of recent results, 2009, 42, 14746670, 1, 10.3182/20090901-3-RO-4009.00003
    6. 2009, Chapter 9, 978-1-84882-623-6, 235, 10.1007/978-1-84882-624-3_9
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  • © 2007 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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