This article discusses the couple-group consensus for heterogeneous multiagent systems via event-triggered and pinning control methods. Considering cooperative-competitive interaction among the agents, a novel group consensus protocol is designed. As inducing the time-correlation threshold function, a class of fully distributed event-triggered conditions without depending on any global information is proposed. Utilizing the Lyapunov stability theory, some sufficient conditions are obtained. Under hybrid event triggered and pinning control, pinning control strategies are first introduced. It is shown that under the proposed strategies, all agents can asymptotically achieve pinning couple-group consensus with discontinuous communication in a fully distributed way. Furthermore, the Zeno behavior for each agent is overcome. Finally, the reduction of the systems' controller update frequency and the correctness of our conclusions are illustrated by some simulations.

This article is centered on the optimal consensus problem of the multiagent systems (MASs) with time delays. By designing a new augmented state, the delayed MASs are reformulated as a delay-free system, and each agent is to minimize its local cost that may depend on the decisions of the other agents, which is regarded as a Nash equilibrium problem. To this end, we propose a multiagent deterministic policy gradient (MADPG) method based on actor–critic (AC) networks to minimize the local cost ( $Q$ -function) by introducing the policy gradient technique, and its convergence and optimality are proven as well. In particular, we develop an optimized prioritized experience replay (PER) strategy that allows high-value samples to be selected with a higher probability, which enhance networks’ data utilization. Finally, the effectiveness of the algorithm and the advantages of PER are demonstrated with a simulated example and a comparative simulation.

The group consensus problems of heterogeneous multiagent networks with input time delays are investigated in this paper. In this complex networks, the agents' dynamics are modeled by the first-order and the second-order multiagent systems, where a novel dynamic group consensus protocol is designed through the competitive relationship among the agents. By using matrix theory and the frequency-domain method, some algebraic criteria are theoretically established for reaching a group consensus in the following two cases: 1) with the identical and 2) different input time delays. Meanwhile, the conservative assumptions existed in the relevant literatures are absolutely relaxed, i.e., the in-degree balance and the geometric multiplicity of zero eigenvalue of Laplacian matrix are at least two. Finally, the effectiveness of our results is illustrated by numerical examples.