论文标题
小组转向：基于力量时刻的方法
Group Steering: Approaches Based on Power Moments
论文作者
论文摘要
本文考虑了转向一组代理的问题，这些试剂由这些动力学由离散时间的一阶线性系统控制。该剂组的特征是概率密度函数和纸张中的职业措施，并给出了两种相应的治疗方法。我们建议使用功率力矩来表征代理的密度函数/职业度量。提出了原始系统的力矩系统表示，并提出了与之相对应的经验控制方案。通过设计的控制定律，每个时间步骤的控制的力矩顺序为正，这确保了对矩系统的控制。然后，我们通过凸优化方案将控制作为函数的分析形式，在我们的先前论文中证明了解决方案的存在和独特性。事实证明，端子密度会融合到所需的终端，这将提出的分配转向方案与其他现有方案区分开。还提供了来自指定的终端密度的误差分析。对于将一组代理人表征为职业度量的问题，通过从实现的分析功能中绘制独立且分布相同的（I.I.D）样本来确定每个代理的控制。最后，我们模拟了一组巨大的药物的不受约束和约束对照，这些对照验证了我们提出的算法。
This paper considers the problem of steering a vast group of agents of which the dynamics are governed by a discrete-time first-order linear system. The group of agents are characterized as a probability density function and an occupation measure respectively in the paper and two corresponding treatments are given. We propose to use the power moments to characterize the density function/occupation measure of the agents. A moment system representation of the original system is put forward for control and an empirical control scheme corresponding to it is proposed. By the designed control law, the moment sequence of the control at each time step is positive, which ensures the existence of the control for the moment system. We then realize the control as an analytic form of function by a convex optimization scheme of which the existence and uniqueness of the solution have been proved in our previous paper. The terminal density is proved to converge to the desired terminal one, which distinguishes the proposed distribution steering scheme from other existing ones. An error analysis of the terminal density from the specified one is also provided. For the problem where the group of agents is characterized as an occupation measure, the control for each agent is determined by drawing independent and identically-distributed(i.i.d) samples from the realized analytic function. Finally we simulate both unconstrained and constrained controls of a vast group of agents, which validate our proposed algorithms.
