Input design for structured nonlinear system identification

  • Authors:

  • Tyrone L. Vincent;Carlo Novara;Kenneth Hsu;Kameshwar Poolla

  • Affiliations:

  • Division of Engineering, Colorado School of Mines, Golden, CO 80401, United States;Dipartimento di Automatica e Informatica, Politecnico di Torino, Italy;Grantham, Mayo, van Otterloo and Co. LLC 2150 Shattuck Avenue, Suite 900, Berkeley, CA 94704, United States;Department of Mechanical Engineering, University of California, Berkeley, CA 94720, United States

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2010

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Abstract

This paper is concerned with the input design problem for a class of structured nonlinear models. This class contains models described by an interconnection of known linear dynamic systems and unknown static nonlinearities. Many widely used model structures are included in this class. The model class considered naturally accommodates a priori knowledge in terms of signal interconnections. Under certain structural conditions, the identification problem for this model class reduces to standard least squares. We treat the input design problem in this situation. An expression for the expected estimate variance is derived. A method for synthesizing an informative input sequence that minimizes an upper bound on this variance is developed. This reduces to a convex optimization problem. Features of the solution include parameterization of the expected estimate variance by the input distribution, and a graph-based method for input generation.