IDENTIFICATION AND CONTROL OF DISCRETE-TIME NONLINEAR SYSTEMS USING AFFINE SUPPORT VECTOR MACHINES

Abstract

Support vector machine (SVM) is a universal learning method. In this paper, an affine support vector machine (ASVM) for regression is presented for identification and control of input-affine nonlinear models. ASVM is a variant of SVM and so inherits its merits. The solution to ASVM is cast into a convex quadratic programming (QP). Hence ASVM has a unique global solution. In addition, the curse of dimensionality is avoided because ASVM is insensitive to the dimensionality of data. A commonly used model for a nonlinear system is a nonlinear autoregressive exogenous (NARX) model. ASVM could get good performance in both identification and control if a NARX model can be well represented by an input-affine nonlinear model. The experimental results validate the efficiency of ASVM in identification and control of discrete-time nonlinear systems.