Metrics for ergodicity and design of ergodic dynamics for multi-agent systems
Metrics for ergodicity and design of ergodic dynamics for multi-agent systems
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DOI：
10.1016/j.physd.2010.10.010
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发表时间：
2011-02-15
影响因子：
4
通讯作者：
Mezic, Igor
中科院分区：
文献类型：
--
作者：
Mathew, George;Mezic, Igor
在这篇文章中，我们提出了一种度量，它量化了轨迹相对于给定概率度量的遍历距离。该度量基于将球形集合中的轨迹所花费的时间分数与球形集合的度量进行比较。该度量被证明等同于作为轨迹上的某一类增量分布与期望的概率分布之间的距离而获得的度量。利用这一度量，我们制定了多智能体系统的集中反馈控制律，使智能体轨迹尽可能均匀地采样给定的概率分布。我们得到的反馈控制本质上是当滚动的地平线趋于零时的极限模型预测控制，并且智能体以恒定的速度或恒定的强迫(在二阶动力学的情况下)移动。数值分析了多智能体系统在不同场景下的闭环系统动力学。本文提出的遍历动态设计算法称为谱多尺度覆盖(SMC)。(C)2010爱思唯尔B.V.保留所有权利。
In this paper we propose a metric that quantifies how far trajectories are from being ergodic with respect to a given probability measure. This metric is based on comparing the fraction of time spent by the trajectories in spherical sets to the measure of the spherical sets. This metric is shown to be equivalent to a metric obtained as a distance between a certain delta-like distribution on the trajectories and the desired probability distribution. Using this metric, we formulate centralized feedback control laws for multi-agent systems so that agents trajectories sample a given probability distribution as uniformly as possible. The feedback controls we derive are essentially model predictive controls in the limit as the receding horizon goes to zero and the agents move with constant speed or constant forcing (in the case of second-order dynamics). We numerically analyze the closed-loop dynamics of the multi-agents systems in various scenarios. The algorithm presented in this paper for the design of ergodic dynamics will be referred to as Spectral Multiscale Coverage (SMC). (C) 2010 Elsevier B.V. All rights reserved.