On the relation between reactive synthesis and supervisory control of non-terminating processes

Abstract

Reactive synthesis and supervisory control theory both provide a design methodology for the automatic and algorithmic design of digital systems from declarative specifications. The reactive synthesis approach originates in computer science, and seeks to synthesise a system that interacts with its environment over time and that, doing so, satisfies a prescribed specification. Here, the distinguishing feature when compared to other synthesis problems in computer science is that the interaction is temporal in that it explicitly refers to a sequence of computation cycles. Supervisory control originates in control theory and seeks to synthesise a controller that-in closed-loop configuration with a plant-enforces a prescribed specification over time. The distinguishing feature compared to other branches of control is that all dynamics are driven by discrete events as opposed to continuous signals. While both methods apparently are closely related, the technical details differ significantly. We provide a formal comparison which allows us to identify conditions under which one can solve one synthesis problem using methods from the other one; we also discuss how the resulting solutions compare. To facilitate this comparison, we give a unified introduction to reactive synthesis and supervisory control and derive formal problem statements and a characterisation of their solutions in terms of ω-languages. Recent contributions to the two fields address different aspects of the respective problem, and we expect the formal relationship identified in this paper to be useful in that it allows the application of algorithmic techniques from one field in the other.

$ω-$nonblocking supervisory control of discrete-event systems with infinite behavior

“…Remark 3. Reference [9] presents how to solve a synthesis problem from supervisory control theory by reactive synthesis or vice-versa. Here the synthesis problem is the same as the problem formulation of the supervisory control theory proposed by Ramadge [1] and Thistle and Wonham [5].…”

“…Here the synthesis problem is the same as the problem formulation of the supervisory control theory proposed by Ramadge [1] and Thistle and Wonham [5]. In the example of the robot, by Theorem 2 in [9], the reactive synthesis algorithm returns an equivalent solution with the Thistle's approach.…”

“…The definition of nonblocking requires that all strings surviving under control be prefixes of the marker behavior. In the existing work, the finite behavior of the controlled DES is nonblocking and meets the safety specification [1]- [9]; the infinite behavior of the controlled DES is deadlock-free and meets the liveness specification [3]- [9]. However, it is not guaranteed that the infinite behavior under supervision is able to visit given marker states, because by the nonblocking property only finite behavior can visit marker states, and meanwhile deadlock-freeness does not take marker states into consideration.…”

“…A compositional supervisory control approach is proposed in [8] by utilizing the reactive synthesis and automated planning. Reference [9] demonstrates the relation between the reactive synthesis and supervisory control of nonterminating processes. Both [8] and [9] endeavor to analyze the supervisory control problem for DES with infinite behavior via automated planning and reactive synthesis methods and pay no special attention to marker states.…”

Environmentally-Friendly GR(1) Synthesis

“…This algorithm has been simplified for two interacting Büchi automata in [21] without proof. We adapt this algorithm to GR(1) games and provide a new, self-contained proof in the framework of two-player games, which is distinct from the supervisory controller synthesis setting (see [12,24] for a recent comparison of both frameworks).…”