On Overparametrization of Nonlinear Discrete Systems

One of the subjects which has received a great deal of attention is the overparametrization problem. It is known that the dynamical performance of the model representations deteriorates if the respective model structure is too complex. This paper investigates the problem of model overparametrization. Two new types of overparametrization, fixed-point and dimension overparametrization, are introduced and based upon this a new procedure for improving structure detection of nonlinear models is developed. This procedure uses all the information from the cluster cancellation and the location of the fixed points. Numerous examples are given to illustrate the ideas.