Functional Uncertainty Classes, Nonparametric Adaptive Contro Functional Uncertainty Classes for Nonparametric Adaptive Control: the Curse of Dimensionality

Abstract

This paper derives a new class of vector-valued reproducing kernel Hilbert spaces (vRKHS) defined in terms of operator-valued kernels for the representation of functional uncertainty arising in nonparametric adaptive control methods. These are referred to as maneuver or trajectory vRKHS KM in the paper, and they are introduced to address the curse of dimensionality that can arise for some types of nonparametric adaptive control strategies. The maneuver vRKHSs are derived based on the structure of a compact, l-dimensional, smooth Riemannian manifold M that is regularly embedded in the state space X = Rn, where M is assumed to approximately support the ultimate dynamics of the reference system to be tracked.