Nonlinear adaptive control using radial basis function approximants

Abstract

The purpose of this research is to present an adaptive control strategy using the radial basis function approximation method. Surface approximation methods using radial basis function approximants will first be discussed. The Hamiltonian dynamical equations used for the tracking control problem are then introduced, and the stability of the system is investigated employing a Lyapunov stability analysis. The extension of the radial basis function approximation method for the adaptive tracking control problem is presented, as well as an adaptation of centers of approximation algorithm. The adaptation of centers of approximation algorithm is shown to increase the rate of convergence of the tracking solution. The stability of the adaptation of centers of approximation algorithm will be discussed through a probability analysis. Under appropriate hypothesis, the algorithm has been shown to have asymptotic stability.