Dynamic-event-based distributed cooperative learning of unknown nonlinear systems over directed connected graphs

Distributed cooperative learning (DCL) provides an efficient modeling/identification approach for unknown dynamics of multi-agent systems by exploiting the learning capacity of neural networks (NNs) in a collaborative fashion. However, all existing DCL frameworks require the communication topology among agents to be undirected This paper proposes a DCL algorithm featuring a dynamic event-triggered mechanism over directedconnected graphs for a group of uncertain nonlinear systems. The Laplacian matrices of directed graphs do not possess the positive semi-definite property, which significantly complicates the extension of DCL from undirected graphs to directed graphs. First, NN identifiers with cooperative NN weight updating laws are constructed within the context of dynamic event-triggered communication. Second, after ensuring finite-time convergence of the state estimate error subsystems, a novel group-convergence-proof strategy is presented for the identification error systems, and then it is rigorously proved that the NN weight estimates of all agents converge to a small neighborhood of their common optimal values. Third, the unknown nonlinear dynamics are accurately identified along the union of system trajectories of all agents. Compared with static event triggering, the proposed dynamic event-triggered mechanism extends the triggering thresholds while maintaining learning performance, thereby further reducing the communication burden. Finally, the advantages and effectiveness of the proposed DCL algorithm are demonstrated through a simulation example.