Lazy controller synthesis for monotone transition systems and directed safety specifications

Abstract

In this paper, we provide a lazy control synthesis algorithm for monotone transition systems and directed safety specifications. Two classes of monotone transition systems are presented: state monotone transition systems and input-state monotone transition systems. For the first class of systems, a partial order is defined only on the state space. For the second, the input space is ordered as well. The introduced lazy synthesis approach is based on the efficient computation of predecessors. It benefits not only from a monotone property of transition systems but also from the ordered structure of the state (input) space and the fact that directed safety specifications are considered. To enrich the class of the considered specifications, we also present an incremental controller synthesis framework, which allows us to deal with intersections of upper and lower-closed safety requirements. We then compare the proposed approach with the classical safety synthesis algorithm and illustrate the advantages, in terms of run-time and memory efficiency, on an adaptive cruise control problem.