Multiple Transformation Matrix-Based Adaptive Projective Vortex Formation Tracking for Multiagent Systems With a Leader of Completely Unknown Input
研究了有向图下线性多智能体系统的投影涡旋编队跟踪问题，提出基于多重变换矩阵的分布式自适应观测器和控制器，在领导者输入完全未知时实现编队跟踪，并通过仿真验证了方法的可靠性。
This article systematically studies projective vortex formation tracking (PVFT) of linear multiagent systems (MASs) on directed graphs through multiple transformation matrices, in which the input of leader and its upper bound information are not available to any follower. First, an innovative class of distributed adaptive observer is designed using the projection matrices to capture multiple desired virtual signals of the leader. Next, a novel kind of distributed PVFT protocol based on distributed observer, local observer and coordinates coupling matrices are proposed. Two different adaptive update mechanisms and nonlinear functions are introduced in the observer and controller to override the unknown input of the leader. Then, an algorithm is given, and the protocol under the algorithm is proved from three processes of estimation, aggregation, and rotation to enable linear systems to achieve PVFT. Finally, the effects of parameters on aggregation and rotation are analyzed systematically, and several simulation examples are given to illustrate the reliability of the results.