Prioritized Synchronization Under Mask for Control and Interaction of Partially Observed Event-Driven Systems

This paper introduces a formalism for modeling interaction and control of partially observed discrete event systems (DESs), called prioritized synchronous composition under mask (PSC/M). In PSC/M, each system is associated with an event priority set and an observation mask. The existing formalisms have their limitations and what we propose is a general canonical mode of interaction that is suitable for control under partial observation as well as for modeling a variety of interaction modes such as strict/prioritized synchronization, interleaving, hiding, and renaming. In PSC/M, an event is globally enabled if it is locally enabled by all the interacting systems. The tracking of a globally enabled event is done by executing a transition on an indistinguishable event. PSC/M possesses the useful properties of commutativity and associativity. PSC/M can be applied to compose local controller modules having limited sensing and actuation capabilities to obtain an equivalent global controller module. PSC/M can itself be employed as a control mechanism, in which case it helps remove the control and the observation compatibility requirements of a controller. We study the PSC/M-based control problem where both the plant and the supervisor have their own control and observation limitations. The plant and the specification models need not be at the same level of abstraction and so new classes of control problems can be solved in the framework. The existence condition is the achievability with respect to an augmented plant, which is weaker than controllability and observability combined. The weaker condition is required since we allow supervisors to be nondeterministic, which also facilitates the existence and synthesis to be performed polynomially in the size of the plant and the specification. Note to Practitioners-This paper presents a mechanism of composition for modeling the interaction of DESs. To form the composition one needs to identify for each system the events that it can control (actuator events) and the events that it can observe (sensor events). The composition ensures that a system never blocks its uncontrollable events and never reacts differently to events that are observationally indistinguishable. An event is executable in the composition if it is enabled by all participating systems and either trackable or executable in some participating system. An event is enabled by a participating system if it is either currently executable or a nonpriority event, whereas an event is trackable by a participating system if it is observable and indistinguishable to some currently executable event. A state update on an event, executable in the composition, occurs by executing an indistinguishable event by each participating system in which the event is trackable, whereas the other participating systems retain their current states. The composition is commutative and associative, supporting incrementality. We obtain a condition under which a given system (plant) can be controlled to exhibit the desired behaviors when the proposed mechanism is employed to compose the plant and a controller. The plant and the desired behavior models may differ in their levels of abstraction. The condition can be polynomially verified and a controller can be synthesized in linear complexity.