The National Natural Science Foundation of China (General Program, Key Program, Major Research Plan)
为了解决非仿射非线性多智能体系统在给定时间区间上一致性完全跟踪问题, 基于迭代学习控制方法设计 出一种分布式一致性跟踪控制算法. 首先, 由引入的虚拟领导者和所有跟随者组成多智能体系统的通信拓扑, 其中虚 拟领导者的作用是提供期望轨迹. 然后, 在只有部分跟随者能够获得领导者信息条件下, 利用每个跟随者及其邻居的 跟踪误差构造每个跟随者的迭代学习一致性跟踪控制器. 同时采用中值定理将非仿射非线性多智能体系统转化仿射 形式, 并基于压缩映射方法证明了所提算法的收敛性, 给出了算法的收敛条件.理论分析表明, 在智能体的非线性函 数未知情况下, 利用所提算法可以使非仿射非线性多智能体系统在给定时间区间上随迭代次数增加逐次实现一致性 完全跟踪. 最后, 通过仿真算例进一步验证了所提算法的有效性.
In order to solve the problem of consensus tracking in the given time interval for non-affine nonlinear multi-agent systems, a distributed consensus tracking control algorithm is designed based on an iterative learning control method. A communication topology of multi-agent systems is firstly composed of introduced virtual leader and all followers, where the role of the virtual leader is to provide the desired trajectory, and then the iterative learning consensus tracking controller for each follower is constructed by using the tracking error of each follower and its neighbors under the condition that only some followers can obtain leader information. At the same time, the non-affine nonlinear multi-agent systems are transformed into affine forms using the mean value theorem, and the convergence of the proposed algorithm is proved based on the contraction mapping method, and thus the convergence conditions of the algorithm are given. Theoretical analysis shows that when the nonlinear function of the agent is unknown, the proposed algorithm can make the non-affine nonlinear multi-agent systems achieve consistent tracking gradually with the increase of iterations in the given time interval. Finally, a simulation example is given to further verify the effectiveness of the proposed algorithm.