On the embedding parameters in kernel identification problem of nonlinear dynamical systems

Abstract

Dynamical models are of fundamental importance in many problems such as simulation, optimization and prediction. In identification problem of dynamical systems an input vector is typically considered as delayed vector of previous outputs. Embedding lag and embedding dimension should be chosen correctly. Identification of nonlinear systems is generally performed using kernel-based methods since they do not require any additional information about system structure. A common question in identification of dynamical system is sensitivity of kernel-based models to selected embedding lag and embedding dimension. The paper presents simulations of the kernel least mean squares algorithm on one-step prediction problem for various values of embedding lag and embedding dimension. It is shown that optimal embedding lag and embedding dimension is dependent on model parameters, while usage of optimal model parameters decreases the value of optimal embedding dimension.