Newton Bases and Event-Triggered Adaptive Control in Native Spaces

This paper extends recent methods of native space embedding for adaptive control by deriving event-driven controllers that modify the basis used for approximation of the functional uncertainty. Using the power function for the native space, trigger conditions are defined that determine when and how many new basis functions are introduced. Bases are selected using a greedy method and augmentation process at each triggering event. By using a recursive Newton basis, coordinate implementations of the adaptive law do not require the inversion of the leading Grammian matrix, which yields a substantial improvement in numerical efficiency and numerical stability. This paper derives upper bounds on the ultimate tracking performance of the closed-loop control scheme in terms of known functions of the approximation dimension after each triggering event. These upper bounds are quite general and hold for bounded uncertainty classes in a variety of reproducing kernel Hilbert spaces (RKHS). A numerical example shows the applicability of the proposed results.