Abstract: This paper discusses the consensus problem of fractional-order multi-agent systems with nonlinear dynamics in fixed network topology. Because the state variables can not be measured completely in reality control systems, the reconstructed states from the state observer are employed to overcome this obstacle in the state-feedback controller design. Based on the Lyapunov stability theory of fraction-order systems, the nonlinear multiple agents in the network can eventually converge to the given objective state when the feedback gain matrix satisfies a certain LMI condition. The simulation results demonstrate the effectiveness and validity of the proposed method by using the fractional calculus predictor-corrector algorithm.

Key words: state observer, fractional-order, multi-agent systems

摘要： 研究固定拓扑结构下的分数阶非线性多智能体系统协调控制的动力学模型问题。由于实际多智能体系统中，系统的状态变量难以全部测量，为了克服这一困难，利用状态观测器对系统状态进行重构并基于重构状态进行状态反馈。利用分数阶Lyapunov稳定性理论，证明了当反馈增益矩阵满足一定的线性矩阵不等式（LMI）条件时，系统中的智能体最终趋于所给定的目标状态。最后利用分数阶微积分的预估—校正算法进行数值仿真验证了理论分析的有效性和可行性。

关键词: 状态观测器, 分数阶, 多智能体系统