A first attempt to optimal experiment design for system identification under regularized parameter estimation

This work constitutes a first attempt to investigate the optimal input that must be applied to a dynamic system when regularization is used during the identification procedure. Regularization for parameter estimation has been widely used in function characterization and machine learning techniques. It has been recently shown that the regularized estimation can be very useful in the field of system identification. The key idea lies in manipulating the bias-variance trade-off of the estimated model parameters by introducing a penalty term in the cost function under minimization. Since the penalizing term in the cost function depends on the input-output measured data it is important to investigate which input is going to deliver the optimal bias-variance trade-off measured through the Mean Square Error (MSE) of the estimated parameters. The fact that the regularization penalty can be considered as prior information about the unknown system incorporated in the cost function, can be exploited during the design of the optimal input. Since the penalty depends on the system input under optimization, the problem of optimal input design under regularized estimation boils down to optimizing both the input and the penalty introduced in the cost function.