State-Partition-Based Control of Discrete Event Systems for Enforcement of Regular Language Specifications

Abstract

We consider the solution of supervisory control problems for discrete event systems modeled by automata or bounded Petri nets where the specification is expressed as a regular sublanguage of the system language and where the supervisor is restricted to be state-partition-based with respect to original system state space, i.e., the state space of the automaton or the set of reachable markings of the Petri net. State-partition-based supervisors are completely characterized by a partition of the original system state space into legal and illegal states: transitions between legal states are always enabled while transitions from legal to illegal states are always disabled. We present a general algorithm that calculates all state-partition-based supervisors that result in safe and non-blocking controlled languages. The algorithm uses a vertex-cover-type algorithm on the representation of the supremal controllable sublanguage in order to obtain the desired partitions. This work is motivated by the application of discrete event control techniques to the avoidance of classes of concurrency bugs in multithreaded programs. State-partition-based supervisors are especially advantageous in that application as they allow more concurrency at run-time. More generally, this class of supervisors is required when the representation of the supervisor must be based on the system's original state space; this occurs for memoryless supervisors in automaton-based control or in supervision based on place invariants in Petri-net-based control, for instance.