协同集聚合用于多拉格朗日系统
Cooperative Set Aggregation for Multiple Lagrangian Systems
AI总结：
本文研究多拉格朗日系统协同集跟踪问题，通过自适应控制与信息交换实现系统在局部集交集处聚拢，并保证碰撞避免。
摘要：
本文研究了一组拉格朗日系统的协同集跟踪问题。每个系统观察一个凸集作为本地目标，这些局部集的交集是群体聚合目标。我们首先提出了一种基于每个系统自身目标感知和与邻居信息交换的控制律。在固定和切换通信图的必要连通性条件下，多个拉格朗日系统被证明能够在所有局部目标集的交集处实现 rendezvous，同时广义坐标导数向量被驱动到零。然后，我们引入碰撞避免控制项到集聚合控制中以确保群体分散。通过定义每个系统与所有局部目标集交集之间最终广义坐标的上界，我们证明多个拉格朗日系统在运动过程中接近交集附近的有界区域，同时保证碰撞避免。此外，所有机械系统的广义坐标导数向量被证明被驱动到零。仿真结果用于验证理论结果。
英文摘要：
In this paper, we study the cooperative set tracking problem for a group of Lagrangian systems. Each system observes a convex set as its local target. The intersection of these local sets is the group aggregation target. We first propose a control law based on each system's own target sensing and information exchange with neighbors. With necessary connectivity for both cases of fixed and switching communication graphs, multiple Lagrangian systems are shown to achieve rendezvous on the intersection of all the local target sets while the vectors of generalized coordinate derivatives are driven to zero. Then, we introduce the collision avoidance control term into set aggregation control to ensure group dispersion. By defining an ultimate bound on the final generalized coordinate between each system and the intersection of all the local target sets, we show that multiple Lagrangian systems approach a bounded region near the intersection of all the local target sets while the collision avoidance is guaranteed during the movement. In addition, the vectors of generalized coordinate derivatives of all the mechanical systems are shown to be driven to zero. Simulation results are given to validate the theoretical results.
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