Optimal control of MDPs with temporal logic constraints
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Citation (published version)Maria Svorenova, Ivana Cerna, Calin Belta. 2013. "Optimal Control of MDPs with Temporal Logic Constraints." 2013 IEEE 52ND ANNUAL CONFERENCE ON DECISION AND CONTROL (CDC), pp. 3938 - 3943 (6).
In this paper, we focus on formal synthesis of control policies for finite Markov decision processes with non-negative real-valued costs. We develop an algorithm to automatically generate a policy that guarantees the satisfaction of a correctness specification expressed as a formula of Linear Temporal Logic, while at the same time minimizing the expected average cost between two consecutive satisfactions of a desired property. The existing solutions to this problem are sub-optimal. By leveraging ideas from automata-based model checking and game theory, we provide an optimal solution. We demonstrate the approach on an illustrative example.