ﻻ يوجد ملخص باللغة العربية
This work studies how to estimate the mean-field density of large-scale systems in a distributed manner. Such problems are motivated by the recent swarm control technique that uses mean-field approximations to represent the collective effect of the swarm, wherein the mean-field density (and its gradient) is usually used in feedback control design. In the first part, we formulate the density estimation problem as a filtering problem of the associated mean-field partial differential equation (PDE), for which we employ kernel density estimation (KDE) to construct noisy observations and use filtering theory of PDE systems to design an optimal (centralized) density filter. It turns out that the covariance operator of observation noise depends on the unknown density. Hence, we use approximations for the covariance operator to obtain a suboptimal density filter, and prove that both the density estimates and their gradient are convergent and remain close to the optimal one using the notion of input-to-state stability (ISS). In the second part, we continue to study how to decentralize the density filter such that each agent can estimate the mean-field density based on only its own position and local information exchange with neighbors. We prove that the local density filter is also convergent and remains close to the centralized one in the sense of ISS. Simulation results suggest that the (centralized) suboptimal density filter is able to generate convergent density estimates, and the local density filter is able to converge and remain close to the centralized filter.
This work studies distributed (probability) density estimation of large-scale systems. Such problems are motivated by many density-based distributed control tasks in which the real-time density of the swarm is used as feedback information, such as se
Large-scale agent systems have foreseeable applications in the near future. Estimating their macroscopic density is critical for many density-based optimization and control tasks, such as sensor deployment and city traffic scheduling. In this paper,
This work studies the problem of controlling the probability density of large-scale stochastic systems, which has applications in various fields such as swarm robotics. Recently, there is a growing amount of literature that employs partial differenti
Swarm robotic systems have foreseeable applications in the near future. Recently, there has been an increasing amount of literature that employs mean-field partial differential equations (PDEs) to model the time-evolution of the probability density o
Recent years have seen an increased interest in using mean-field density based modelling and control strategy for deploying robotic swarms. In this paper, we study how to dynamically deploy the robots subject to their physical constraints to efficien