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Bilinear state space systems for nonlinear dynamical modelling

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Summary

We discuss the identification of multiple input, multiple output, discrete-time bilinear state space systems. We consider two identification problems. In the first case, the input to the system is a measurable white noise sequence. We show that it is possible to identify the system by solving a nonlinear optimization problem. The number of parameters in this optimization problem can be reduced by exploiting the principle of separable least squares. A subspace-based algorithm can be used to generate initial estimates for this nonlinear identification procedure. In the second case, the input to the system is not measurable. This makes it a much more difficult identification problem than the case with known inputs. At present, we can only solve this problem for a certain class of single input, single output bilinear state space systems, namely bilinear systems in phase variable form.

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Authors and Affiliations

  1. Faculty of Applied Physics, University of Twente, P.O. Box 217, NL-7500 AE, Enschede, The Netherlands

    Vincent Verdult & Michel Verhaegen

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  1. Vincent Verdult
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  2. Michel Verhaegen
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Correspondence to Vincent Verdult.

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Verdult, V., Verhaegen, M. Bilinear state space systems for nonlinear dynamical modelling. Theory Biosci. 119, 1–9 (2000). https://doi.org/10.1007/s12064-000-0001-9

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