On Tikhonov regularization, bias and variance in nonlinear system identification

Regularization is a general method for solving ill-posed and ill-conditioned problems. Traditionally, ill-conditioning in system identiication problems is usually approached using regularization methods such as ridge regression and principal component regression. In this work it is argued that the Tikhonov regularization method is a powerful alternative for regulariza-tion of non-linear system identiication problems by introducing smoothness of the model as a prior. Its properties is discussed in terms of an analysis of bias and variance, and illustrated by a semi-realistic simulation example.