Distributed adaptive robust containment control for reaction-diffusion neural networks with external disturbances under directed graphs.

In this paper, the leader-follower robust synchronization issue is mainly addressed for reaction-diffusion neural networks (RDNNs) with multiple leaders and external disturbances under directed graphs. Based on the σ modification approach, we propose a novel distributed adaptive controller by adding a term [Formula: see text] to avoid the phenomenon of parameter drift, that is, the adaptive parameters grow to infinity. Meanwhile, different from the adaptive control algorithm proposed in the undirected graph, we introduce a new function χ(t) to provide additional freedom for the design to achieve robust containment when confronted with external disturbances. Further, the robustness of tracking synchronization with one leader is guaranteed by the proposed adaptive controller when the external disturbances concerning L norm are bounded. Finally, relevant numerical simulation graphics are displayed separately to verify the correctness of the related theoretical results.