Event-triggered Basis Augmentation for Data-driven Adaptive Control

In this paper, we propose a data-driven adaptive control method for trajectory tracking problems with unmatched uncertainty. The method is characterized by a basis augmentation rule triggered by an expressiveness-based event, which provides extra adaptivity to the controller to overcome unmatched uncertainty. The augmented basis functions take the form of kernel basis functions whose centers are located along the trajectory. The triggering event is defined by setting an upper threshold for the value of power function associated to the dictionary of basis functions. The event-triggered basis augmentation (ETBA) rule can be viewed as a realization of the nonparametric adaptive controller embedded in reproducing kernel Hilbert spaces (RKHS). By leveraging the properties of RKHS, we show that 1) the tracking error asymptotically converges to zero, and 2) the inter-event time of basis augmentation is bounded below by a positive value when the reference trajectory is a set point. A numerical example is presented to illustrate performance of the proposed method and verify the theoretical results.