参数不确定Lagrange网络中具有移动领导者的完全分布式群集
Fully Distributed Flocking with a Moving Leader for Lagrange Networks with Parametric Uncertainties
摘要：
研究了具有参数不确定性的网络化Lagrange系统在邻近图下具有移动领导者的领导者-跟随者群集问题。在这里，一组跟随者与移动的领导者一起内聚地移动，以保持连接性并始终避免碰撞，并最终实现速度匹配。在邻近图中，邻居关系根据每对代理之间的相对距离来定义。每个跟随者只能从附近的邻居那里获得信息，只涉及本地交互。我们考虑两种情况：i）领导者以恒定速度移动，ii）领导者以变化的速度移动。在第一种情况下，一个分布式连续的适应控制算法占未知参数提出了一个分布式连续估计器为每个追随者相结合。在第二种情况下，提出了分布式不连续适应控制算法和估计器。然后通过引入增益自适应律，将算法推广到全分布情况。在所有提出的算法中，只有一跳邻居的信息（例如，需要邻居之间的相对位置和速度测量以及绝对位置和速度测量），并且只要在初始时刻确保连接性和冲突避免并且适当地设计控制增益，就可以实现群集。数值模拟来说明理论结果。
英文摘要：
This paper addresses the leader-follower flocking problem with a moving leader for networked Lagrange systems with parametric uncertainties under a proximity graph. Here a group of followers move cohesively with the moving leader to maintain connectivity and avoid collisions for all time and also eventually achieve velocity matching. In the proximity graph, the neighbor relationship is defined according to the relative distance between each pair of agents. Each follower is able to obtain information from only the neighbors in its proximity, involving only local interaction. We consider two cases: i) the leader moves with a constant velocity, and ii) the leader moves with a varying velocity. In the first case, a distributed continuous adaptive control algorithm accounting for unknown parameters is proposed in combination with a distributed continuous estimator for each follower. In the second case, a distributed discontinuous adaptive control algorithm and estimator are proposed. Then the algorithm is extended to be fully distributed with the introduction of gain adaptation laws. In all proposed algorithms, only one-hop neighbors' information (e.g., the relative position and velocity measurements between the neighbors and the absolute position and velocity measurements) is required, and flocking is achieved as long as the connectivity and collision avoidance are ensured at the initial time and the control gains are designed properly. Numerical simulations are presented to illustrate the theoretical results.
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