An Optimal Control Approach for the Persistent Monitoring Problem

TL;DR

This paper introduces an optimal control framework for persistent monitoring, enabling mobile agents to minimize uncertainty in a mission space through a parametric optimization approach and real-time receding horizon control.

Contribution

It develops a novel optimal control method for persistent monitoring, including a gradient-based algorithm and a receding horizon controller for near-optimal solutions.

Findings

Optimal solutions are characterized by switching locations for a single agent.

Gradient-based algorithms effectively solve the parametric optimization problem.

Receding horizon control provides near-optimal solutions in real-time.

Abstract

We propose an optimal control framework for persistent monitoring problems where the objective is to control the movement of mobile agents to minimize an uncertainty metric in a given mission space. For a single agent in a one-dimensional space, we show that the optimal solution is obtained in terms of a sequence of switching locations, thus reducing it to a parametric optimization problem. Using Infinitesimal Perturbation Analysis (IPA) we obtain a complete solution through a gradient-based algorithm. We also discuss a receding horizon controller which is capable of obtaining a near-optimal solution on-the-fly. We illustrate our approach with numerical examples.