Event-Triggered Basis Augmentation for Multiagent Collaborative Adaptive Estimation

Parameterization is a necessary step for learning unstructured unknown dynamical systems. In this article, we aim to balance the tradeoff between expressiveness and complexity when selecting models for parameterizing unstructured dynamics using universal regression models. Rather than using a fixed set of basis functions in the regression model, we introduce the event-triggered basis augmentation (ETBA) technique for adaptive estimation, which gradually builds up an expressive regression model on the fly. Kernel regression is applied in ETBA to approximate a general class of unstructured dynamics. With the inner product structure of reproducing kernel Hilbert spaces (RKHS), the residue of the regression model is characterized as the component of unknown dynamics that is orthogonal to all the existing basis functions. With this characterization, new basis functions can be strategically included in the regression model to meet certain stability certificates of adaptive estimation. Among existing basis augmentation methods for learning dynamical systems, the unique advantage of ETBA is that it does not require state derivatives to accomplish the learning. Compared to traditional methods of learning dynamical systems, ETBA uses fewer basis functions without sacrificing expressiveness of the model. We illustrate these two advantages in numerical example. We further study the formulation of ETBA in multiagent systems, for which we propose the condition of collaborative persistent excitation in RKHS to guarantee convergence of function estimation.