Department of Applied Mathematics & Physics, Kyoto University

Technical Report 2002-003 (February 12, 2002)

Subspace Identification of Closed Loop Systems by Orthogonal Decomposition Method
by Tohru Katayama, Hidetoshi Kawauchi, Tohru Inoue, and Giorgio Picci

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We consider the problem of identifying closed loop systems by applying the stochastic realization technique of (Picci and Katayama, 1996b) to the joint input-output process. It is assumed that the exogenous input is feedback-free and persistently exciting (PE). We show that under the preliminary orthogonal decomposition, the identification of closed loop system is divided into two subproblems: the deterministic identification of plant and controller, and the stochastic identification of noise filter. The subspace method of computing the deterministic and stochastic components of the joint input-output process is presented, and then subspace methods of identifying the deterministic and stochastic components are derived by adapting the standard subspace methods both components. In each case, a model reduction procedure should be applied for deriving lower order models from obtained higher order non-minimal models by canceling poles and zeros situated closely. Some numerical results are included to show the applicability of the present technique.