Backstepping Tracking Control Using Gaussian Processes With Event-Triggered Online Learning

In this letter, we present a trajectory tracking control law for a class of partially unknown nonlinear systems that combines backstepping and event-triggered online learning. We employ Gaussian processes to learn the unknown system model using measurement data collected online, while the proposed control law is active. Our approach uses an efficient event-triggered online learning scheme that exclusively collects informative data to update the estimated model used for control. The resulting control law guarantees that the tracking error is globally uniformly ultimately bounded. The inter-event time is shown to be lower-bounded by a positive constant. Moreover, we also discuss how to obtain a trade-off between the cardinality of the collected training data and the size of the ultimate tracking error bound. In a simulation example, our approach is shown to outperform a state-of-the-art offline learning-based approach both in terms of tracking performance and data efficiency.