双积分器多智能体系统的固定时间协同跟踪控制：基于时间生成器的方法
Fixed-Time Cooperative Tracking Control for Double-Integrator Multi-Agent Systems: A Time-Based Generator Approach
摘要：
本文分别研究了具有有界输入扰动的双积分型多智能体系统的固定时间分布式共识跟踪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，针对双积分型多智能体系统，设计了一种固定时间的分布式共识跟踪观测器，分别用于估计无向通信和有向通信下领导者和跟随者之间的状态分歧。再次，设计了双积分器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。注意，分布式共识跟踪和分布式平均跟踪的观测器都是基于时基生成器设计的，并且可以简单地扩展到高阶多智能体系统的观测器。此外，将固定时间滑模控制与固定时间观测器相结合，设计了固定时间控制器，解决了分布式共识跟踪和分布式平均跟踪问题。最后，进行了一些数值模拟来验证结果。
英文摘要：
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.
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