Discrete-Time Feedback Error Learning for Unknown Nonlinear Systems

In this study, the technique of discrete-time feedback error learning for nonlinear systems(DTFELN) is extended to control unknown nonlinear systems. First, the relationship between DTFEL and nonlinear discrete-time adaptive control with adaptive feedback linearization is discussed. It shows that DTFEL can be interpreted as a form of nonlinear adaptive control. Second, Lyapunov analysis of the controlled system is presented. It suggests that the condition of strictly positive realness (s.p.r.) associated with the tracking error dynamics is a sufficient condition for asymptotic stability of the closed-loop dynamics. Then, radial basis function is used to characterize as an approximation of the unknown basis function. Finally, numerical simulations is presented to illustrate the tracking performance of DTFELN.