State feedback stabilizing controller for the failure recovery of timed discrete event systems

While being placed resolutely within the reactive systems framework, this article approaches two techniques of failure recovery making it possible to characterize the essential properties of a safe controller but also to be able to generate its expression formally. The system, modeled as a timed discrete event system (TDES), will be characterized by two operating modes: nominal and degraded. When a failure occurs, the system continues its service on the basis of controllers that provide switching from the nominal to the degraded operating mode. In this spirit, concepts of controllability and stability may arise and we propose to investigate them within TDES. On the basis of these concepts, an algorithm is proposed for the synthesis of controllers able to carry out the system from its state of breakdown towards one of these operating modes.