Discrete event control under nondeterministic partial observation

Most prior work on control of discrete event systems assume that sensors are reliable so that they can be modeled as a deterministic (point-valued) observation mask. However in certain harsh environments such as nuclear systems, sensors may not be reliable. This results in a nondeterministic (set-valued) observation mask. In this paper, we allow the observation mask to be nondeterministic to capture unreliability of sensors. In this setting finding a supervisor to enforce a given specification has the additional challenge of deciding which observations of a trace of the specification must be enabled (note a trace of the specification is enabled as long as one of its observations is enabled). We propose a method to deal with this challenge by introducing the notion of lifting, and defining the lifting of events, plant, specification, and observation mask. A lifted-specification is said to be safe if its projection on the original events equals the given specification. We show that a supervisor exists if and only if exists a lifted-specification that satisfies closure, safety, controllability, observability, together with a new property called conformity. The class of such languages is not closed under union or intersection, but is closed under union over an increasing chain. As a result, finding a desired liftedspecification can be difficult. We propose a work around this difficulty by replacing the property of observability with the stronger property of normality. The corresponding class of languages is shown to be closed under union, and its nonemptiness serves as a constructive sufficient condition for the existence of a supervisor. We also provide an automaton representation of a control policy based on a nondeterministic observation mask.