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Identification of Bilinear Systems Using an Iterative Deterministic-Stochastic Subspace Approach

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3 Author(s)
Lopes dos Santos, P. ; Faculdade de Engenharia da Universidade do Porto, Departamento de Engenharia Electrotécnica e de Computadores, Rua Dr. Roberto Frias, 4200 465 Porto, Portugal. ; Ramos, J.A. ; de Carvalho, J.L.M.

In this paper we introduce a new identification algorithm for MIMO bilinear systems driven by white noise inputs. The new algorithm is based on a convergent sequence of linear deterministic-stochastic state space approximations, thus considered a Picard based method. The key to the algorithm is the fact that the bilinear terms behave like white noise processes. Using a linear Kalman filter, the bilinear terms can be estimated and combined with the system inputs at each iteration, leading to a linear system which can be identified with a linear-deterministic subspace algorithm such as MOESP, N4SID, or CVA. Furthermore, the model parameters obtained with the new algorithm converge to those of a bilinear model. Finally, the dimensions of the data matrices are comparable to those of a linear subspace algorithm, thus avoiding the curse of dimensionality.

Published in:

Decision and Control, 2005 and 2005 European Control Conference. CDC-ECC '05. 44th IEEE Conference on

Date of Conference:

12-15 Dec. 2005