Identification of Feedback and Nonlinear Systems by using Subspace Methods

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Based on the orthogonal decomposition (ORT) method 1996, we have developed a new closed loop subspace identification algorithm under the assumption that measurable disturbances are available, and obtained successful numerical results for both simulated and industrial data. We have also considered an LQ decomposition based subspace identification method for identifying the stochastic part of a combined deterministic stochastic system, showing that the stochastic part is derived by using a single LQ decomposition under the assumption that the past horizon is sufficiently large. This result complements the well-known MOESP method, for which the identification of stochastic part has been ignored for many years. Concerning the identification of nonlinear dynamical systems, a method of identifying Wiener-Hammerstein systems, in which a static nonlinearity is sandwiched by two linear systems, is derived by using a method of alternately identifying Hammerstein system and a linear system, where the data driven local coordinate-based gradient method is used for minimizing output errors. The algorithm and numerical results for the benchmark problem are presented at the special session of SYSID 2009, Saint-Malo.