On Prediction-Based Properties of Discrete-Event Systems: Notions, Applications and Supervisor Synthesis

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In this work, we investigate the problem of synthesizing property-enforcing supervisors for partially-observed discrete-event systems (DES). Unlike most existing approaches, where the enforced property depends solely on the executed behavior of the system, here we consider a more challenging scenario in which the property relies on predicted future behaviors that have not yet occurred. This problem arises naturally in applications involving future information, such as active prediction or intention protection. To formalize the problem, we introduce the notion of prediction-based properties, a new class of observational properties tied to the system's future information. We demonstrate that this notion is very generic and can model various practical properties, including predictability in fault prognosis and pre-opacity in intention security. We then present an effective approach for synthesizing supervisors that enforce prediction-based properties. Our method relies on a novel information structure that addresses the fundamental challenge arising from the dependency between current predictions and the control policy. The key idea is to first borrow information from future instants and then ensure information consistency. This reduces the supervisor synthesis problem to a safety game in the information space. We prove that the proposed algorithm is both sound and complete, and the resulting supervisor is maximally permissive.

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