A Continuous-time Markov Decision Process Based Method on Pursuit-Evasion Problem

This paper presents a method to address the pursuit-evasion problem which incorporates the behaviors of the opponent, in which a continuous-time Markov decision process (CTMDP) model is introduced, where the significant difference from Markov decision process (MDP) is that the influence of the transition time between the states is taken into account. By introducing the concept of situation, the probabilities addressing average behaviors are obtained. Furthermore, these probabilities are introduced to construct the transition matrix in the CTMDP. A policy iteration method for solving the CTMDP is also given. To demonstrate the CTMDP method for pursuit-evasion, examples in a grid environment are computed. The CTMDP-based method presented in this paper offers a new approach to pursuit-evasion modeling and may be extended to similar problems in the sequential decision process.