Controller Synthesis for Omega-Regular and Steady-State Specifications
This addresses the problem of designing controllers for systems with both temporal and long-term behavioral requirements, which is incremental as it combines existing steady-state planning with linear-time specifications.
The paper tackles the controller synthesis problem for Markov decision processes with both ω-regular specifications and steady-state constraints on asymptotic behavior, presenting an algorithm that formulates solutions as an integer linear program and experimentally evaluates it.
Given a Markov decision process (MDP) and a linear-time ($ω$-regular or LTL) specification, the controller synthesis problem aims to compute the optimal policy that satisfies the specification. More recently, problems that reason over the asymptotic behavior of systems have been proposed through the lens of steady-state planning. This entails finding a control policy for an MDP such that the Markov chain induced by the solution policy satisfies a given set of constraints on its steady-state distribution. This paper studies a generalization of the controller synthesis problem for a linear-time specification under steady-state constraints on the asymptotic behavior. We present an algorithm to find a deterministic policy satisfying $ω$-regular and steady-state constraints by characterizing the solutions as an integer linear program, and experimentally evaluate our approach.