Distributed Group Consensus Control for Multi-Agent Systems Based on Combined State Information

This paper addresses group consensus control for a class of multi-agent systems (MASs) by proposing a novel distributed group consensus protocol that leverages the combined state information (including both current and outdated states) of MASs. Unlike the standard protocol that uses either only current states or only outdated states, our approach integrates combined state information to achieve consensus. We derive sufficient conditions for the MASs to achieve group consensus, eliminating the dependence on two conservative assumptions present in previous literature. Furthermore, our proposed protocol improves the upper bound of input time delays compared to the standard approach. Several examples are provided to illustrate the effectiveness of our results. Note to Practitioners—The motivation behind this paper stems from the imperative to tackle the challenge of achieving group consensus control in multi-agent systems (MASs). Specifically, it focuses on the complexities and practical considerations inherent in MASs, such as the impact of competition and the influence of outdated states and input delays on system performance and stability. To address this issue, the paper introduces a novel group consensus protocol designed for second-order multi-agent systems that closely resemble real-world scenarios. This protocol integrates both position and velocity information as control inputs, enabling consensus under competitive conditions. By combining real-time and outdated states, the paper establishes conditions for achieving group consensus convergence while improving the bounds on input delays. Additionally, the paper extends the traditional bipartite graph representation to a directed graph, relaxing conservative assumptions and validating the effectiveness of the proposed protocol through theoretical analysis, numerical simulations, and comparative analysis with existing literature.