PREDICTABILITY IN DISCRETE-EVENT SYSTEMS UNDER PARTIAL OBSERVATION 1 Sahika Genc, St´ ephane Lafortune ∗ ∗ Department of Electrical Engineering and Computer Science, University of Michigan, 1301 Beal Avenue, Ann Arbor, MI 48109-2122, USA sgenc,stephane@eecs.umich.edu Copyright c  2006 IFAC Abstract: This paper studies the problem of predicting occurrences of a significant event in a discrete-event system. The predictability of occurrences of an event in a system is defined in the context of formal languages. The predictability of a language is a stronger condition than the diagnosability of the language. An implementable necessary and sufficient condition for predictability of occurrences of an event in systems modeled by regular languages is presented. Keywords: Discrete-event systems, prediction, diagnosis. 1. INTRODUCTION This paper addresses the problem of predicting occurrences of a significant (e.g., fault) event in a discrete-event system (DES). The system un- der consideration is modeled by a language over an event set. The event set is partitioned into observable events (e.g., sensor readings, changes in sensor readings) and unobservable events, i.e., the events that are not directly recorded by the sensors attached to the system. The objective is to predict occurrences of a possibly unobserv- able event in the system behavior, based on the strings of observable events. If it is possible to predict occurrences of an event in the system, then depending on the nature of the event the system operator can be warned and the operator may decide to halt the system or otherwise take preventive measures. 1 This research is supported in part by NSF grant CCR- 0325571 and by ONR grant N00014-03-1-0232. The first author wishes to acknowledge support from a Barbour Fel- lowship from the Horace H. Rackham School of Graduate Studies at the University of Michigan. To the best of our knowledge, the notion of predictability that is introduced and studied in this paper is different from prior works on other notions of predictability in (Cao, 1989; Buss et al., 1991; Shengbing and Kumar, 2004; Fadel and Holloway, 1999). For instance, the prediction problem considered in (Cao, 1989) is related to the properties of a special type of projection be- tween two languages (sets of trajectories); this is is much more general than our objective, which is to predict occurrences of specific events, but our work is not a special case. The state prediction of coupled automata studied in (Buss et al., 1991) is formulated as computing the state vector of n identical automata after T steps in the operation of the system; the system structure in this work is different from ours. In our case the interest is on a single automaton and event prediction, not state, under partial observation. The notion of prediction considered in (Shengbing and Ku- mar, 2004) differs from the one in our work in the sense that in (Shengbing and Kumar, 2004) predictability of a system is a necessary condi- tion for diagnosability of the system while in our work diagnosability is a necessary condition for