2019/09/30 by Samuel C. Pinto, Sean B. Andersson, Pinto, Samuel C. +5
Computer Science · Mathematics · Medicine · #Distributed Control Multi-Agent Systems #FOS: Electrical engineering #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1909.13783
openalex publication_date 2019/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the problem of persistently monitoring a finite set of targets\nwith internal states that evolve with linear stochastic dynamics using a finite\nset of mobile agents. We approach the problem from the infinite-horizon\nperspective, looking for periodic movement schedules for the agents. Under\nlinear dynamics and some standard assumptions on the noise distribution, the\noptimal estimator is a Kalman-Bucy filter and the mean estimation error is a\nfunction of its covariance matrix, which evolves as a differential Riccati\nequation. It is shown that when the agents are constrained to move only over a\nline and they can see at most one target at a time, the movement policy that\nminimizes the mean estimation error over time is such that the agent is always\neither moving with maximum speed or dwelling at a fixed position. This type of\ntrajectory can be fully defined by a finite set of parameters. For periodic\ntrajectories, under some observability conditions, the estimation error\nconverges to a steady state condition and the stochastic gradient estimate of\nthe cost with respect to the trajectory parameters of each agent and the global\nperiod can be explicitly computed using Infinitesimal Perturbation Analysis. A\ngradient-descent approach is used to compute locally optimal parameters. This\napproach allows us to deal with a very long persistent monitoring horizon using\na small number of parameters.\n