On-Line Permissive Supervisory Control of Discrete Event Systems for scLTL Specifications

Abstract

We propose an on-line supervisory control scheme for discrete event systems (DESs), where a control specification is described by a fragment of linear temporal logic. On the product automaton of the DES and an acceptor for the specification, we define a ranking function that returns the minimum number of steps required to reach an accepting state from each state. In addition, we introduce a permissiveness function that indicates a time-varying permissive level. At each step during the online control scheme, the supervisor refers to the permissiveness function as well as the ranking function in order to guarantee the control specification while handling the tradeoff between its permissiveness and acceptance of the specification. The proposed scheme is demonstrated in a surveillance problem for a mobile robot.Index Terms-On-line supervisory control, discrete event systems, syntactically co-safe linear temporal logic, ranking function.

On-Line Synthesis of Permissive Supervisors for Partially Observed Discrete Event Systems under scLTL Constraints

“…Since the product automaton captures the behavior of the DES and the DFA at the same time, our goal turns out to reach an accepting state of the product automaton. For that purpose, we introduce a ranking function with the existence of uncontrollable transitions (Sakakibara and Ushio, 2020), which decreases its value if an accepting state is being approached. Definition 3.…”

“…In Sakakibara and Ushio (2020), we propose an algorithm to compute a ranking function for the product automaton.…”

“…Here, we briefly explain the results in Sakakibara and Ushio (2020), where we propose an algorithm to compute a ranking function given the product automaton P of the DES and the DFA. We obtain a ranking function by Algorithm A.2.…”

“…By referring to the permissiveness level together with the ranking function at each step of the on-line control process, the supervisor computes more permissive control patterns. This paper extends the on-line supervisory control scheme proposed in Sakakibara and Ushio (2020) to the setting of partial observation. After each observation, the supervisor arXiv:2003.12274v1 [eess.SY] 27 Mar 2020 dynamically computes its control action with the information of the fully observed product automaton, on which the ranking function is defined.…”

“…In Sakakibara and Ushio (2020), we consider a supervisory control problem of a DES under an scLTL constraint. We propose an on-line control scheme, where we leverage a ranking function that enables us to find desirable behavior with respect to the scLTL specification.…”