Abstract:

A fixed-time consensus control method was proposed for full-state constrained Multi-Agent System （MAS） with unknown perturbations in a fixed undirected graph topology. Firstly， a novel Unified Universal Barrier Function （UUBF） was designed to convert the constrained MAS into a unconstrained system. Secondly， based on the unconstrained system， a neural network was used to approximate the unknown nonlinear term in the system， and a fixed-time state observer was constructed to compensate the neural network update rate through the observation error and improve the approximation ability of the neural network. Thirdly， a new fixed-time disturbance observer was designed to accurately estimate composite perturbation consisting of the unknown perturbation and the approximation error. Fourthly， according to the observed values， a fixed-time control law was constructed using backstepping， and a fixed-time differentiator was designed to solve “differential explosion” problem in backstepping design. Finally， the fixed-time consensus stability condition of MAS was derived and obtained by using the fixed-time consensus theory and Lyapunov stability theorem， and the effectiveness of the designed control method was verified by simulation.

Key words: full-state constraint, fixed-time consensus, Multi-Agent System (MAS), neural network, disturbance observe, state observer

摘要：

针对固定无向图拓扑下具有未知扰动的全状态受限多智能体系统（MAS），提出一种固定时间一致性控制方法。首先，设计一种新型全局通用障碍函数（UUBF），从而将受限MAS转化为无约束系统；其次，基于无约束系统，利用神经网络逼近系统中的未知非线性项，并构建固定时间状态观测器，通过观测误差补偿神经网络的更新率，增强神经网络的逼近能力；再次，设计新型固定时间扰动观测器，精确估计未知扰动和逼近误差构成的复合扰动；继次，根据观测值，使用反步法构建固定时间控制律，并设计固定时间微分器解决反步法设计中的“微分爆炸”问题；最后，利用固定时间一致性理论和李雅普诺夫稳定性定理推导得到MAS固定时间一致性稳定条件，通过仿真验证了所设计的控制方法的有效性。

关键词: 全状态约束, 固定时间一致性, 多智能体系统, 神经网络, 扰动观测器, 状态观测器