Barrier Lyapunov Functions and Model Reference Adaptive Control with Uncertainty in Native Spaces

Abstract Nonparametric model reference adaptive control (MRAC) theory studies a novel class of nonlinear control systems able to counter functional uncertainties for which no parameterization is selected a priori , and which are contained in a reproducing kernel Hilbert space (RKHS). This paper presents, for the first time, robust nonparametric MRAC systems that, employing barrier Lyapunov functions, enforce user-defined time-varying constraints, or feasible approximations thereof, on the tracking error at all times. The proposed results generalize parametric MRAC systems, that is, MRAC systems that require a regressor vector or an equivalent representation of the matched uncertainties, and existing nonparametric MRAC systems that, presently, rely on the strong assumption of a priori knowledge of some bounded region in which the closed-loop trajectory lies.