Localized adaptive bounds for online based control

On-line approximation based control methods seek improved performance for poorly modeled nonlinear systems by approximating the unknown nonlinearities as a part of the control design. Such on-line approximators cannot be perfect, so there would always remain some inherent approximation error. Recent articles have improved the robustness and convergence properties of such methods by also estimating a function that bounds the approximation error and including terms in the control law to compensate for any approximation errors less than the estimated bound. In this article, we present new algorithms for estimating the bounding function that enhance the local accuracy of the bounding function. The same improvements in robustness and convergence properties are achieved as for the existing results, but with less conservatism. Lyapunov stability analysis and numerical simulations are included.