On the Use of Regularization in System Identification

Regularization is a standard statistical technique to deal with ill-conditioned parameter estimation problems. We discuss in this contribution what possibilities and advantages regularization ooers in system identiication. In the rst place regularization reduces the variance error of a model, but at the same time it introduces a bias. The familiar trade-oo between bias and variance error for the choice of model order/structure can therefore be discussed in terms of the regularization parameter. We also show how the well-known problem of parametrizing multivariable system can be dealt with using over-parametrization plus regularization. A characteristic feature for this way of letting the parametrization/model structure/model order be solved by regu-larization is that it is an easy and \automatic" way of nding the important parameters and good parametrization. No statistical penalty is paid for the overparametrization, but there is a penalty of higher computational burden.