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    Inverse optimal filtering of linear distributed parameter systems

    197420_110055_80323.pdf (148.6Kb)
    Access Status
    Open access
    Authors
    Do, Khac Duc
    Date
    2013
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Do, K.D. 2013. Inverse optimal filtering of linear distributed parameter systems. Applied Mathematical Sciences. 7 (119): pp. 5901-5925.
    Source Title
    Applied Mathematical Sciences
    DOI
    10.12988/ams.2013.37361
    ISSN
    1312-885X
    Remarks

    This article is published under the Open Access publishing model and distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0/ Please refer to the licence to obtain terms for any further reuse or distribution of this work.

    URI
    http://hdl.handle.net/20.500.11937/36433
    Collection
    • Curtin Research Publications
    Abstract

    A constructive method is developed to design inverse optimal filters to estimate the states of a class of linear distributed parameter systems (DPSs) based on the calculus of variation approach. Inverse optimality guarantees that the cost functional to be minimized is meaningful in the sense that the symmetric and positive definite weighting kernel matrix on the states is chosen after the filter design instead of being specified at the start of the filter design. Inverse optimal design enables that the Riccati nonlinear partial differential equation (PDE) can be simplified to a Bernoulli PDE, which can be solved analytically. The filter design is based on a new Green matrix formula, a new unique and bounded solution of a linear PDE, and analytical solution of a Bernoulli PDE. The inverse optimal filter design is first developed for the case where the measurements are spatially available, then is extended to the practical case where only a finite number of measurements is available.

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