A General Approach for Synthesis of Supervisors for Partially-Observed Discrete-Event Systems

We revisit the synthesis of supervisors for partially-observed discrete-event systems from a new angle, based on the construction of a new structure called the All Inclusive Controller (or AIC). We consider control problems for safety specifications, where the legal language is a prefix-closed sublanguage of the system language. We define the AIC as a bipartite transition system that embeds all safe supervisors and thus all controllable and observable sublanguages of the legal language. The structure of the AIC is that of a bipartite graph, reminiscent of a game between the supervisor and the system, with (i) control states, where all safe control decisions are enumerated, and (ii) system states, where all feasible observable system events are executed. The states of the AIC are information states, i.e., subsets of system states. We present an algorithm for the construction of the AIC. This algorithm exploits the pre-computation of the so-called extended specification, which makes the safety of a control state a function of the current information state alone, thereby allowing for on-the-fly construction of the AIC, if so desired. We discuss the properties of the AIC. We also describe how the AIC can be used for synthesis of supervisors that possess a desired maximality property.