A Spline Kernel-Based Approach for Nonlinear System Identification with Dimensionality Reduction

Abstract

This paper proposes a novel approach for identification of nonlinear systems. By transforming the data space into a feature space, kernel methods can be used for modeling nonlinear systems. The spline kernel is adopted to produce a Hilbert space. However, a problem exists as the spline kernel-based identification method cannot deal with data with high dimensions well, resulting in huge computational cost and slow estimation speed. Additionally, owing to the large number of parameters to be estimated, the amount of training data required for accurate identification must be large enough to satisfy the persistence of excitation conditions. To solve the problem, a dimensionality reduction strategy is proposed. Transformation of coordinates is made with the tool of differential geometry. The purpose of the transformation is that no intersection of information with relevance to the output will exist between different new states, while the states with no impact on the output are extracted, which are then abandoned when constructing the model. Then, the dimension of the kernel-based model is reduced, and the number of parameters to be estimated is also reduced. Finally, the proposed identification approach was validated by simulations performed on experimental data from wind tunnel tests. The identification result turns out to be accurate and effective with lower dimensions.