Robust adaptive control of uncertain non-linear systems using neural networks

Control system design for complex nonlinear systems has been widely studied in the last decade. Many remarkable results in this area have been reported, including feedback linearization techniques (Isidori 1989, Esfandiari and Khalil 1992), backstepping design (Krstic et al. 1995) for systems with unmatched uncertainties (Koshkouei et al. 2004). For uncertain systems, sliding mode control approaches have been developed by some researchers (Zinober 1990, 1994; Levant 2003, 2005). In these methods, the controller gains are computed using upper bound information on the system uncertainties, which is normally unavailable and there is no direct method to obtain them. Therefore, these methods may yield overestimation resulting from a conservative design. To overcome this problem, several adaptive schemes have been developed for affine nonlinear systems in order to deal with the problem of parametric uncertainties (Marino and Tomei 1995, Khalil 1996). During the last decade, adaptive methods based on Neural Networks (NNs) have been developed to control uncertain nonlinear systems by removing the unknown nonlinear part of the system. Most of these approaches have been proposed for affine systems (Lewis et al. 1995, 1996) and some of them consider non-