Support vector machine adaptive control of nonlinear systems

Abstract

Support vector machine is a new and promising technique for pattern classification and regression estimation. The training of support vector machine is characterized by a convex optimization problem, which involves the determination of a few additional tuning parameters. Moreover, the model complexity follows from that of this convex optimization problem. In this paper we introduce the support vector machine adaptive control by Lyapunov function derivative estimation. The support vector machine is trained by particle filter. The support vector machine is applied to estimate the Lyapunov function derivative for affine nonlinear system, whose nonlinearities are assumed to be unknown. In order to demonstrate the availability of this new method of Lyapunov function derivative estimation, we give a simple example in the form of affine nonlinear system. The result of simulation demonstrates that the sequential training algorithm of support vector machine is effective and support vector machine adaptive control can achieve a satisfactory performance. © Springer-Verlag Berlin Heidelberg 2005.