Subspace identification of Bilinear and LPV systems for open- and closed-loop data

  • Authors:

  • Jan-Willem van Wingerden;Michel Verhaegen

  • Affiliations:

  • Delft Center for Systems and Control, Delft University of Technology, Mekelweg 2, 2628CD Delft, The Netherlands;Delft Center for Systems and Control, Delft University of Technology, Mekelweg 2, 2628CD Delft, The Netherlands

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2009

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Abstract

In this paper we present a novel algorithm to identify LPV systems with affine parameter dependence operating under open- and closed-loop conditions. A factorization is introduced which makes it possible to form a predictor that predicts the output, which is based on past inputs, outputs, and scheduling data. The predictor contains the LPV equivalent of the Markov parameters. Using this predictor, ideas from closed-loop LTI identification are developed to estimate the state sequence from which the LPV system matrices can be constructed. A numerically efficient implementation is presented using the kernel method. It turns out that if structure is present in the scheduling sequence the computational complexity reduces even more.