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      • Department of Electrical and Electronics Engineering
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      Infinite dimensional and reduced order observers for Burgers equation

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      Author(s)
      Efe, M. Ö.
      Özbay, Hitay
      Samimy, M.
      Date
      2005
      Source Title
      International Journal of Control
      Print ISSN
      0020-7179
      Publisher
      Taylor & Francis
      Volume
      78
      Issue
      11
      Pages
      864 - 874
      Language
      English
      Type
      Article
      Item Usage Stats
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      Abstract
      Obtaining a representative model in feedback control system design problems is a key step and is generally a challenge. For spatially continuous systems, it becomes more difficult as the dynamics is infinite dimensional and the well known techniques of systems and control engineering are difficult to apply directly. In this paper, observer design is reported for one-dimensional Burgers equation, which is a non-linear partial differential equation. An infinite dimensional form of the observer is demonstrated to converge asymptotically to the target dynamics, and proper orthogonal decomposition is used to obtain the reduced order observer. When this is done, the corresponding observer is shown to be successful under certain circumstances. The paper unfolds the connections between target dynamics, observer and their finite dimensional counterparts. A set of simulation results has been presented to justify the theoretical claims of the paper.
      Keywords
      Computer simulation
      Partial differential equations
      Problem solving
      Control engineering
      One-dimensional Burger's equations
      Feedback control
      Permalink
      http://hdl.handle.net/11693/24016
      Published Version (Please cite this version)
      http://dx.doi.org/10.1080/00207170500158813
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      • Department of Electrical and Electronics Engineering 4011
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