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This article investigates the stability and synchronization of nonautonomous reaction–diffusion neural networks with general time-varying delays. Compared with the existing works concerning reaction–diffusion neural networks, the main innovation of this article is that the network coefficients are time-varying, and the delays are general (which means that fewer constraints are posed on delays; for example, the commonly used conditions of differentiability and boundedness are no longer needed). By Green’s formula and some analytical techniques, some easily checkable criteria on stability and synchronization for the underlying neural networks are established. These obtained results not only improve some existing ones but also contain some novel results that have not yet been reported. The effectiveness and superiorities of the established criteria are verified by three numerical examples. [ABSTRACT FROM AUTHOR]

This article investigates the optimally distributed consensus control problem for discrete-time multiagent systems with completely unknown dynamics and computational ability differences. The problem can be viewed as solving nonzero-sum games with distributed reinforcement learning (RL), and each agent is a player in these games. First, to guarantee the real-time performance of learning algorithms, a data-based distributed control algorithm is proposed for multiagent systems using offline system interaction data sets. By utilizing the interactive data produced during the run of a real-time system, the proposed algorithm improves system performance based on distributed policy gradient RL. The convergence and stability are guaranteed based on functional analysis and the Lyapunov method. Second, to address asynchronous learning caused by computational ability differences in multiagent systems, the proposed algorithm is extended to an asynchronous version in which executing policy improvement or not of each agent is independent of its neighbors. Furthermore, an actor-critic structure, which contains two neural networks, is developed to implement the proposed algorithm in synchronous and asynchronous cases. Based on the method of weighted residuals, the convergence and optimality of the neural networks are guaranteed by proving the approximation errors converge to zero. Finally, simulations are conducted to show the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper considers the tracking synchronization problem for a class of coupled reaction–diffusion neural networks (CRDNNs) with undirected topology. For the case where the tracking trajectory has identical individual dynamic as that of the network nodes, the edge-based and vertex-based adaptive strategies on coupling strengths as well as adaptive controllers, which demand merely the local neighbor information, are proposed to synchronize the CRDNNs to the tracking trajectory. To reduce the control costs, an adaptive pinning control technique is employed. For the case where the tracking trajectory has different individual dynamic from that of the network nodes, the vertex-based adaptive strategy is proposed to drive the synchronization error to a relatively small area, which is adjustable according to the parameters of the adaptive strategy. This kind of adaptive design can enhance the robustness of the network against the external disturbance posed on the tracking trajectory. The obtained theoretical results are verified by two representative examples. [ABSTRACT FROM AUTHOR]

This paper investigates the synchronization issue of coupled reaction–diffusion neural networks with directed topology via an adaptive approach. Due to the complexity of the network structure and the presence of space variables, it is difficult to design proper adaptive strategies on coupling weights to accomplish the synchronous goal. Under the assumptions of two kinds of special network structures, that is, directed spanning path and directed spanning tree, some novel edge-based adaptive laws, which utilized the local information of node dynamics fully are designed on the coupling weights for reaching synchronization. By constructing appropriate energy function, and utilizing some analytical techniques, several sufficient conditions are given. Finally, some simulation examples are given to verify the effectiveness of the obtained theoretical results. [ABSTRACT FROM PUBLISHER]