Weighted Couple‐Group Consensus Analysis of Heterogeneous Multiagent Systems with Cooperative‐Competitive Interactions and Time Delays

Abstract

In this paper, the weighted couple-group consensus of continuous-time heterogeneous multiagent systems with input and communication time delay is investigated. A novel weighted couple-group consensus protocol based on cooperation and competition interaction is designed, which can relax the in-degree balance condition. By using graph theory, general Nyquist criterion and Gerschgorin disc theorem, the time delay upper limit that the system may allow is obtained. The conclusions indicate that there is no relationship between weighted couple-group consensus and communication time delay. When the agents input time delay, the coupling weight between the agents, and the systems control parameters are satisfied, the multiagent system can converge to any given weighted coupling group consistent state. The experimental simulation results verify the correctness of the conclusion.

The Weighted Couple-Group Consensus for a Kind of Continuous Heterogeneous Multi-Agent Systems Based on Self-Adaptive and Cooperative-Competitive Mechanism

“…In this section, we mainly seek for the condition of the couplegroup consensus for systems (1) and (2). Based on [22], [33], [41],a novel couple-group consensus control protocol is designed as:…”

“…Remark 1: In fact, couple-group consensus protocols in literatures [22], [24], [33] and [41] are special cases of the consensus protocol (3) and (4). Hence, the control protocol (3) and (4) may be called the unified couple-group control consensus and related results are more applicable to real problems.…”

“…In [22], couple-group consensus of a kind of discrete-time heterogeneous systems was investigated. In [33], the weighted couple-group consensus was discussed for a kind of continuous-time heterogeneous multi-agent system with input and communication time delay and a novel weighted couple-group consensus protocol was designed based on cooperation and competition interaction. In [34], the distributed consensus tracking problem of heterogeneous multi-agent chaotic delayed nonlinear systems was investigated and a distributed adaptive control law was proposed.…”

“…However, in many real multi-agent systems, the relationship among the agents can be either cooperative or competitive, or both cooperative and competitive [22], [33], [40], [41]. Furthermore, input time delays can arise due to various reasons, including data processing, decision-making, computational times and so on.…”

“…Firstly, based on [15], [22], [33], [35], [38], [40], [41], a novel weighted couple-group consensus control protocol is proposed for a kind of continuous heterogeneous multi-agent system. In this new protocol, positions, speed, self-adaptive regulation and competitive interaction are all considered, it extends the scope of the existing research [22], [33], [41] and it is more related to real situation. Secondly, some sufficient conditions have been obtained for the weighted couple-group consensus by using graph theory, complex frequency analysis method and linear algebra theory.…”