Consensus-based distributed cooperative learning control for a group of discrete-time nonlinear multi-agent systems using neural networks

This paper focuses on the cooperative learning capability of radial basis function neural networks in adaptive neural controllers for a group of uncertain discrete-time nonlinear systems where system structures are identical but reference signals are different. By constructing an interconnection topology among learning laws of NN weights in order to share their learned knowledge on-line, a novel adaptive NN control scheme, called distributed cooperative learning control scheme, is proposed. It is guaranteed that if the interconnection topology is undirected and connected, all closed-loop signals are uniform ultimate bounded and tracking errors of all systems can converge to a small neighborhood around the origin. Moreover, it is proved that all estimated NN weights converge to a small neighborhood of their common optimal value along the union of all state trajectories, which means that the estimated NN weights reach consensus with a small consensus error. Thus, all learned NN models have the better generalization capability than ones obtained by the deterministic learning method. The learned knowledge is also adopted to control a class of uncertain systems with the same structure but different reference signals. Finally, a simulation example is provided to verify the effectiveness and advantages of the distributed cooperative learning control scheme developed in this paper.