In this paper, we propose two recursive algorithms for closed loop identification under the framework of a tailor made parameterization. The closed loop transfer function is parameterized using the parameters of the open loop plant model, and utilizing knowledge of the feedback controller. When the plant model and feedback controller are all polynomial forms, a recursive least squares method with forgetting schemes is proposed to verify that this recursive method can be regarded as regularization least squares problem. Furthermore we also extend the tailor made parameterization method to nonlinear system and nonlinear controller, then an iterative least squares algorithm is applied to solve one nonlinear optimization problem.
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