Weighted Group Consensus for Discrete-Time Heterogeneous Multi-Agent Systems in the Cooperative-Competitive Network With Time Delays

Abstract

Group consensus is investigated for a class of discrete-time heterogeneous multi-agent systems which are composed of first-order and second-order agents with communication and input time delays in this paper. Based on the cooperative-competitive relationship between the agents in the system, a novel weighted group consensus protocol is proposed. Some sufficient conditions are given to guarantee the success of group consensus in some special situations by using z-transformation, matrix analysis and algebraic graph theory. The upper bound of time delays can be reckoned by utilizing Gershgorin disk theorem and generalized Nyquist's criterion. The results show that group consensus has no relationship with communication time delay. Only if the input time delay, the coupling weight between the agents, and the system's control parameters satisfy the given conditions, the multi-agent systems can realize group consensus. Some simulation results show that the proposed novel protocol can effectively promote the multi-agent systems to achieve weighted group consensus. INDEX TERMS Weighted group consensus, cooperative-competitive network, discrete-time, heterogeneous multi-agent systems, time delays.

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 [40], couple-group consensus was discussed for a kind of discrete-time heterogeneous multi-agent systems with cooperative-competitive interactions and time delays. In [41], a novel weighted group consensus protocol was proposed for a class of discrete-time heterogeneous multi-agent systems which was composed of first-order and second-order agents with communication and input time delays.…”

“…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.…”