In this paper, both the fixed-time distributed consensus tracking and the fixed-time distributed average tracking problems for double-integrator-type multi-agent systems with bounded input disturbances are studied, respectively. Firstly, a new practical robust fixed-time sliding mode control method based on the time-based generator is proposed. Secondly, a fixed-time distributed consensus tracking observer for double-integrator-type multi-agent systems is designed to estimate the state disagreements between the leader and the followers under undirected and directed communication, respectively. Thirdly, a fixed-time distributed average tracking observer for double-integrator-type multi-agent systems is designed to measure the average value of reference signals under undirected communication. Note that both the observers for the distributed consensus tracking and the distributed average tracking are devised based on time-based generators and can be extended to that of high-order multi-agent systems trivially. Furthermore, by combing the fixed-time sliding mode control with the fixed-time observers, the fixed-time controllers are designed to solve the distributed consensus tracking and the distributed average tracking problems. Finally, a few numerical simulations are shown to verify the results.

中文翻译：

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双积分器多智能体系统的固定时间协同跟踪控制：基于时间的生成器方法

本文分别研究了输入扰动有界的双积分型多智能体系统的固定时间分布式一致性跟踪问题和固定时间分布式平均跟踪问题。首先，提出了一种基于时基发生器的实用鲁棒固定时间滑模控制方法。其次，设计了双积分型多智能体系统的固定时间分布式共识跟踪观察器，分别估计无向和有向通信下领导者和追随者之间的状态分歧。第三，设计了一种用于双积分型多智能体系统的固定时间分布式平均跟踪观测器，用于测量无向通信下参考信号的平均值。请注意，分布式共识跟踪和分布式平均跟踪的观察者都是基于基于时间的生成器设计的，并且可以简单地扩展到高阶多代理系统的观察者。此外，通过将固定时间滑模控制与固定时间观测器相结合，设计固定时间控制器来解决分布式一致性跟踪和分布式平均跟踪问题。最后，给出了一些数值模拟来验证结果。固定时间控制器旨在解决分布式一致性跟踪和分布式平均跟踪问题。最后，给出了一些数值模拟来验证结果。固定时间控制器旨在解决分布式一致性跟踪和分布式平均跟踪问题。最后，给出了一些数值模拟来验证结果。