Formation of Time-Varying Multi-AUVs Under Directed Graphs With Event-Triggered Control: An Online Model-Free Parameter Learning

This paper delves into the study of the leader-following formation of multiple autonomous underwater vehicles (AUVs) under a directed graph, encompassing both cases with unknown time-invariant and time-varying model parameters. This investigation employs an online model-free parameter learning mechanism, and develops a fully distributed event-triggered communication (ETC)- and actuation (ETA)- based control protocol. Initially, given the challenge of accurately modeling the intricate dynamics of AUVs, we construct a formulation of AUV with a well-defined inverse-matrix-based regression function and a vector of unknown model parameters. Thus, an online model-free parameter learning approach is designed for its estimation. Subsequently, a fully distributed ETC-based leader observer is developed for constructing the reference formation trajectory for each AUV. Then, we devise an ETA-based control protocol, which enables the asymptotic model-free formation of multiple AUVs with unknown time-invariant model parameters. For scenarios involving time-varying unknown model parameters, we extend our methodology by incorporating $\sigma$-modification, which achieves the bounded formation. Both ETC-based observer and ETA-based control algorithm will not exhibit the Zeno behavior with determining a minimum interval for the proposed event-triggered mechanisms (ETMs). Finally, the effectiveness of the proposed control schemes has been verified by some numerical simulations and comparisons.