Consensus-based distributed cooperative learning from closed-loop neural control systems.

In this paper, the neural tracking problem is addressed for a group of uncertain nonlinear systems where the system structures are identical but the reference signals are different. This paper focuses on studying the learning capability of neural networks (NNs) during the control process. First, we propose a novel control scheme called distributed cooperative learning (DCL) control scheme, by establishing the communication topology among adaptive laws of NN weights to share their learned knowledge online. It is further proved that if the communication topology is undirected and connected, all estimated weights of NNs can converge to small neighborhoods around their optimal values over a domain consisting of the union of all state orbits. Second, as a corollary it is shown that the conclusion on the deterministic learning still holds in the decentralized adaptive neural control scheme where, however, the estimated weights of NNs just converge to small neighborhoods of the optimal values along their own state orbits. Thus, the learned controllers obtained by DCL scheme have the better generalization capability than ones obtained by decentralized learning method. A simulation example is provided to verify the effectiveness and advantages of the control schemes proposed in this paper.