State-based optimal supervisor for non-terminating quantitative discrete event systems

Abstract

This paper studies state-based optimal supervisors for non-terminating discrete event systems (DESs) modeled by weighted automata. An optimal supervisor controls the DES to avoid system halts and maximizes the worst-case limit-average weight of the generated infinite sequences. A state-based supervisor controls the DES depending only on its current state, and required only polynomial space of memory in the number of states and events of the DES. An s-minimally restrictive optimal (s-optimal) supervisor is a state-based optimal supervisor whose enabled set of sequences is as large as possible. We propose an algorithm to compute an s-optimal supervisor if it exists. Moreover, we consider the control costs for enabling controllable events. We derive conditions for assigning the control costs in such a way that the optimal supervisor for the DES with the control costs is also optimal for the DES without the control costs.