Using Decoupling Methods to Reduce Polynomial NARX Models

David T. Westwick, Gabriel Hollander, Kiana Karami, Johan Schoukens

    Research output: Contribution to journalArticlepeer-review

    Abstract

    The polynomial NARX model, where the output is a polynomial function of past inputs and outputs, is a commonly used equation error model for nonlinear systems. While it is linear in the variables, which simplifies its identification, it suffers from two major drawbacks: the number of parameters grows combinatorially with the degree of the nonlinearity, and it is a black box model, which makes it difficult to draw any insights from the identified model. Polynomial decoupling techniques are used to replace the multiple-input single-output polynomial with a decoupled polynomial structure comprising a transformation matrix followed by bank of SISO polynomials, whose outputs are then summed. This approach is demonstrated on two benchmark systems: The Bouc-Wen friction model and the data from the Silverbox model. In both cases, the decoupling results in a substantial reduction in the number of parameters, and allows some insight into the nature of the nonlinearities in the system.

    Original languageEnglish (US)
    Pages (from-to)796-801
    Number of pages6
    JournalIFAC-PapersOnLine
    Volume51
    Issue number15
    DOIs
    StatePublished - Jan 1 2018

    All Science Journal Classification (ASJC) codes

    • Control and Systems Engineering

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