Nonlinear iterative learning by an adaptive Lyapunov technique

We consider parametrically uncertain systems satisfying a matching condition. A standard Lyapunov adaptive design for stabilization is modified to ensure a monotonically decreasing parametric error. This modified controller is used to learn a control which forces the state to reach a neighbourhood of the origin at a time t>0 in a finite number of learning passes of finite length. A performance analysis is completed. The iterative learning tracking problem is also considered. Corresponding results can also be obtained for strict feedback systems via adaptive backstepping, and this is briefly sketched