具有坐标耦合和处理时滞的二阶离散多智能体系统的一致性

根据系统的拓扑结构、离散步长和旋转矩阵的旋转角,确定系统的渐近行为,给出多智能体系统达成二阶一致性的充要条件。证明了当0是拉普拉斯矩阵的一个简单特征值且离散步长、旋转角小于由代数方程确定的临界值时,会出现渐近一致性。数值模拟结果证明理论结果的正确性。设计了特征参数影响二阶一致性的相关案例,说明特征参数相关结论可为控制理论的一致收敛分析提供重要判据和理论支撑。

Consensus of discrete time second-order multi-agent systems with spatial coordinates coupling and processing delay

The asymptotic behavior was determined in terms of the topological structure of the system, the step length and the rotation angle of the corresponding rotation matrix. Some necessary and sufficient conditions for the multi-agent systems to reach second-order consensus were found. It was shown that the asymptotic consensus appears when 0 is a simple eigenvalue of the Laplacian matrix, the step length and the rotation angle is less than the critical value which was determined by an algebraic equation. Some numerical simulations were presented to demonstrate the theoretical results. Some cases on the influence of characteristic parameters on second-order consensus were designed, which showed that the conclusion of characteristic parameters can provide important criterion and theoretical support for the control theory.