Adaptive supervisory control for a class of Petri nets with bimodal transitions

This paper presents a novel notion of a transition that has two kinds of conditions: observable and unobservable modes. In this study, such a transition under the two kinds of conditions is called a bimodal transition. Sensors are normally deployed in discrete event systems, such as automated manufacturing systems, to observe the occurrences of events in order to control a system's evolution and prevent from entering forbidden states such as deadlocks. The events that are observable under normal conditions may become unobservable if sensors that detect their occurrences fail or generate faulty data. In this sense, a transition could have two operational modes: the observable mode under normal conditions and unobservable mode under failure conditions. A system's controller can be disabled if a bimodal transition changes from an observable mode to an unobservable mode. To this end, we propose an adaptive supervisory control strategy that prevents deadlocks in a system whether bimodal transitions are operating in an observable or unobservable mode. The adaptive supervisory controller is composed of control places, making all the siphons in a net system max-controlled, and bimodal transition controllers, re-marking siphons that may become under-marked if bimodal transitions are operating in an unobservable mode.