A recursive identification algorithm for switched linear/affine models

• Published in: Nonlinear analysis. Hybrid systems 2011-05, Vol.5 (2), p.242-253
• Main Authors: Bako, Laurent, Boukharouba, Khaled, Duviella, Eric, Lecoeuche, Stéphane
• Format: Article
• Language: English
• Subjects: Algorithms; Convergence; Errors; Mathematical analysis; Mathematical models; On-line systems; Open channel systems; Piecewise affine systems; Recursive; Recursive identification; Switched systems; System identification; Vectors (mathematics)
• ISSN: 1751-570X
• DOI: 10.1016/j.nahs.2010.05.003

In this work, a recursive procedure is derived for the identification of switched linear models from input–output data. Starting from some initial values of the parameter vectors that represent the different submodels, the proposed algorithm alternates between data assignment to submodels and parameter update. At each time instant, the discrete state is determined as the index of the submodel that, in terms of the prediction error (or the posterior error), appears to have most likely generated the regressor vector observed at that instant. Given the estimated discrete state, the associated parameter vector is updated based on recursive least squares or any fast adaptive linear identifier. Convergence of the whole procedure although not theoretically proved, seems to be easily achieved when enough rich data are available. It has been also observed that by appropriately choosing the data assignment criterion, the proposed on-line method can be extended to deal also with the identification of piecewise affine models. Finally, performance is tested through some computer simulations and the modeling of an open channel system.