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Mathematics > Optimization and Control

arXiv:2210.01294 (math)
[Submitted on 4 Oct 2022]

Title:Optimal Persistent Monitoring of Mobile Targets in One Dimension

Authors:Jonas Hall, Sean B. Andersson, Christos G. Cassandras
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Abstract:This work shows the existence of optimal control laws for persistent monitoring of mobile targets in a one-dimensional mission space and derives explicit solutions. The underlying performance metric consists of minimizing the total uncertainty accumulated over a finite mission time. We first demonstrate that the corresponding optimal control problem can be reduced to a finite-dimensional optimization problem, and then establish existence of an optimal solution. Motivated by this result, we construct a parametric reformulation for which an event based gradient descent method is utilized with the goal of deriving (locally optimal) solutions. We additionally provide a more practical parameterization that has attractive properties such as simplicity, flexibility, and robustness. Both parameterizations are validated through simulation.
Comments: Submitted to ACC 2023
Subjects: Optimization and Control (math.OC); Dynamical Systems (math.DS)
Cite as: arXiv:2210.01294 [math.OC]
  (or arXiv:2210.01294v1 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.2210.01294

Submission history

From: Jonas Hall [view email]
[v1] Tue, 4 Oct 2022 00:43:20 UTC (19,007 KB)
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