文章基本信息

标题：The Linear Programming Approach to Reach-Avoid Problems for Markov Decision Processes
本地全文：下载
作者：Nikolaos Kariotoglou ; Maryam Kamgarpour ; Tyler H. Summers 等
期刊名称：Journal of Artificial Intelligence Research
印刷版ISSN：1076-9757
出版年度：2017
卷号：60
页码：263-285
出版社：American Association of Artificial
摘要：One of the most fundamental problems in Markov decision processes is analysis and control synthesis for safety and reachability specifications. We consider the stochastic reach-avoid problem, in which the objective is to synthesize a control policy to maximize the probability of reaching a target set at a given time, while staying in a safe set at all prior times. We characterize the solution to this problem through an infinite dimensional linear program. We then develop a tractable approximation to the infinite dimensional linear program through finite dimensional approximations of the decision space and constraints. For a large class of Markov decision processes modeled by Gaussian mixtures kernels we show that through a proper selection of the finite dimensional space, one can further reduce the computational complexity of the resulting linear program. We validate the proposed method and analyze its potential with numerical case studies.