Kernel least mean square algorithm in control of nonlinear systems

Abstract

Although some research has been presented about the application of Kernel Least Mean Square (KLMS) algorithm in the estimation and approximation of functions, this algorithm wasn't applied to the control of nonlinear systems. In this paper, an efficient and novel adaptive Control strategy based on Kernel Least Mean Square is introduced to realize the control of a nonlinear aircraft system. Actually the KLMS algorithm is a growing radial basis function (GRBF) network, when Kernel function is a Gaussian function. In this research, based on Lyapunov theory, KLMS is used as an online method for tuning the kernel size to control nonlinear systems. This technique certifies the stability and provides an acceptable accuracy. Finally, we utilize this algorithm to control a nonlinear fighter aircraft by using a dynamic model of the F-18 aircraft.