Piecewise Affine System identification: A least harmonic mean approach

In this paper we consider the problem of identifying piecewise affine approximations of nonlinear dynamic systems directly from input-output measurements. This requires estimating a partition of the regression space and an associated set of affine time-invariant models. By relying on a generic Voronoi type of partition, the proposed approach treats these two tasks jointly via the minimization of an appropriate objective function formed as a weighted sum of errors related to all submodels. We minimize this objective function with respect to both the weights and the parameters (describing the partition and the affine submodels) under some heuristic constraint on the weights. It is later observed that the proposed method attempts indeed to optimize a sum (over the available dataset) of harmonic means. The final estimation algorithm consists in solving iteratively a sequence of convex optimization problems. Numerical experiments tend to suggest that the new method exhibits some nice properties: regular convergence and good estimation performance.

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