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Multistep time-domain method (ARMAX) for discrete-time DCN identification

A discrete-time network model is identified, on the basis of the ARMAX-like polynomial model:

A(q)w(t)=B(q)r(t)+C(q)e(t)A(q)w(t) = B(q)r(t) + C(q)e(t)

where A(q)A(q) is a symmetric non-monic polynomial matrix. A three-step procedure is followed:

  • Step 1: A high-order non-structured ARX model is estimated with the rr-signals as inputs and ww as outputs;
  • Step 2: The non-structured ARX model is approximated by a structured ARMAX-model;
  • Step 3: A weighted nullspace fitting (WNSF [2]) algorithm is applied to optimize the estimated ARMAX model parameters.

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. For subnetwork identification, nonmeasured nodes are immersed from the network, and the immersed network is identified, like in the full network situation.

References​

  1. E.M.M. Kivits and P.M.J. Van den Hof (2023). Identification of diffusively coupled linear networks through structured polynomial models IEEE Trans. Automatic Control, Vol. 68, no. 6, pp. 3513-3528.
  2. M. Galrinho, C. R. Rojas, and H. Hjalmarsson (2019). Parametric identification using weighted null-space fitting. IEEE Trans. Autom. Control, vol. 64, no. 7, pp. 2798–2813, Jul. 2019.