MDP Optimal Control under Temporal Logic Constraints

TL;DR

This paper presents a method to automatically generate control policies for MDPs that satisfy complex temporal logic specifications while optimizing a cost criterion, applicable to persistent robotic tasks.

Contribution

It introduces a novel approach combining LTL specifications with cost optimization in MDP control synthesis, including a dynamic programming algorithm for near-optimal policies.

Findings

Synthesizes control policies satisfying LTL specifications almost surely.

Develops a dynamic programming algorithm for optimal or near-optimal control.

Applicable to persistent robotic tasks like monitoring and data gathering.

Abstract

In this paper, we develop a method to automatically generate a control policy for a dynamical system modeled as a Markov Decision Process (MDP). The control specification is given as a Linear Temporal Logic (LTL) formula over a set of propositions defined on the states of the MDP. We synthesize a control policy such that the MDP satisfies the given specification almost surely, if such a policy exists. In addition, we designate an "optimizing proposition" to be repeatedly satisfied, and we formulate a novel optimization criterion in terms of minimizing the expected cost in between satisfactions of this proposition. We propose a sufficient condition for a policy to be optimal, and develop a dynamic programming algorithm that synthesizes a policy that is optimal under some conditions, and sub-optimal otherwise. This problem is motivated by robotic applications requiring persistent tasks, such as environmental monitoring or data gathering, to be performed.