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Multistep frequency-domain method for DCN identification

Frequency domain method for identification of diffusively coupled networks.

A(⋅)w(t)=B(⋅)r(t)+F(⋅)e(t)A(\cdot)w(t) = B(\cdot)r(t) + F(\cdot)e(t)

in either discrete-time (q)(q) or continuous-time (p)(p), where A(⋅)A(\cdot) is a symmetric non-monic polynomial matrix, B(⋅)B(\cdot) polynomial, and F(⋅)F(\cdot) possibly rational. A three-step procedure is followed:

  • Step 1: Estimate a non-parametric frequency-domain model with the rr-signals as inputs and ww as outputs, applying the Local Polynomial Method (LPM) from [3];
  • Step 2: Fit a structured network model through an SK-iterative procedure;
  • Step 3: Use the estimated model as an initial guess in a non-convex Gauss-Newton procedure.

For satisfying identifiability conditions, a sufficient number of constraints need to be imposed on the model parameters.

The method can be applied for estimating a full network or a subnetwork.

Subnetwork identification​

For subnetwork identification, nonmeasured nodes are immersed from the network, and the immersed network is identified, like in the full network situation. One complication then is that the right lower block of the AA-matrix can become rational, in stead of polynomial, see [2]. This block corresponds to those nodes that have a link to unmeasured nodes, that are immersed from the network. In the current implementation of the app, this right lower rational block is then parametrized as a proper FIR (series expansion) model, of which the parameters are estimated. The order of the FIR model can be set in the tools menu of the algorithm.

Implementation aspects:​

  • No use is made of prior information on particular components/links.
  • Included algorithms resulting from [3] are copyrighted by Rik Pintelon, and their use for non-commercial purposes is acknowledged.

References​

[1] D. Liang, E.M.M. Kivits, M. Schoukens and P.M.J. Van den Hof (2025). A frequency-domain approach for estimating continuous-time diffusively coupled linear networks. Proc. 2025 European Control Conference, Thessaloniki, Greece, 25-27 June 2025, pp. 2285-2290.

[2] D. Liang, E.M.M. Kivits, M. Schoukens and P.M.J. Van den Hof (2024). A frequency-domain approach for estimating continuous-time diffusively coupled linear networks. ArXiv: 2410.18773 [eess.sY].

[3] R. Pintelon, J. Schoukens, G. Vandersteen and K. Barbé (2010). Estimation of nonparametric noise and FRF models for multivariable systems—Part I: Theory, Mechanical Systems and Signal Processing, Vol. 24, Issue 3, pp. 573-595.