Optimal Persistent Monitoring of Mobile Targets in One Dimension

TL;DR

This paper establishes the existence of optimal control laws for persistent monitoring of mobile targets in a one-dimensional space, providing explicit solutions and practical parameterizations validated via simulation.

Contribution

It introduces a finite-dimensional reduction of the optimal control problem and develops event-based gradient methods for deriving (locally) optimal solutions.

Findings

Optimal control laws exist for the problem.

Explicit solutions are derived for the control laws.

Simulation validates the proposed methods and parameterizations.

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.