On the Controller Synthesis for Finite-State Markov Decision Processes

Article type: Research Article

Authors: Kučera, Antonín | Stražovský, Oldřich

Affiliations: Faculty of Informatics, Masaryk University, Botanická 68a, 60200 Brno, Czech Republic. E-mail: kucera@fi.muni.cz; strazovsky@fi.muni.cz

Abstract: We study the problem of effective controller synthesis for finite-state Markov decision processes (MDPs) and the class of properties definable in the logic PCTL extended with long-run average propositions. We show that the existence of such a controller is decidable, and we give an algorithm which computes the controller if it exists. We also address the issue of "controller robustness", i.e., the problem whether there is a controller which still guarantees the satisfaction of a given property when the probabilities in the considered MDP slightly deviate from their original values. From a practical point of view, this is an important aspect since the probabilities are often determined empirically and hence they are inherently imprecise. We show that the existence of robust controllers is also decidable, and that such controllers are effectively computable if they exist.

Keywords: controller synthesis, Markov decision process, PCTL

Journal: Fundamenta Informaticae, vol. 82, no. 1-2, pp. 141-153, 2008