## Abstract

We consider a task assignment problem for a fleet of UAVs in a surveillance/search mission. We formulate the problem as a restless bandits problem with switching costs and discounted rewards: there are N sites to inspect, each one of them evolving as a Markov chain, with different transition probabilities if the site is inspected or not. The sites evolve independently of each other, there are transition costs cy for moving between sites i and j ∈ {1, . . . ,N}, rewards when visiting the sites, and we maximize a mixed objective function of these costs and rewards. This problem is known to be PSPACE-hard. We present a systematic method, inspired from the work of Bertsimas and Ñiño-Mora [1] on restless bandits, for deriving a linear programming relaxation for such locally decomposable MDPs. The relaxation is computable in polynomial-time offline, provides a bound on the achievable performance, as well as an approximation of the cost-to-go which can be used online in conjunction with standard suboptimal stochastic control methods. In particular, the one-step lookahead policy based on this approximate cost-to-go reduces to computing the optimal value of a linear assignment problem of size N. We present numerical experiments, for which we assess the quality of the heuristics using the performance bound. © 2006 IEEE.

Original language | English (US) |
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Title of host publication | Proceedings of the IEEE Conference on Decision and Control |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 5281-5286 |

Number of pages | 6 |

ISBN (Print) | 1424401712 |

DOIs | |

State | Published - Jan 1 2006 |

Externally published | Yes |