Codiagnosability and coobservability under dynamic observations: Transformation and verification

We investigate the relationship between decentralized fault diagnosis and decentralized control of discrete event systems under dynamic observations. The key system-theoretic properties that arise in these problems are those of codiagnosability and coobservability, respectively. It was shown by Wang et al. (2011) that coobservability is transformable to codiagnosability; however, the transformation for the other direction has remained an open problem. In this paper, we consider a general language-based dynamic observations setting and show how the notion of KK-codiagnosability can be transformed to coobservability. When the observation properties are transition-based, we present a new approach for the verification of transition-based codiagnosability. An upper bound of the diagnosis delay for decentralized diagnosis under transition-based observations is derived. Moreover, we show that transition-based [co]diagnosability is transformable to transition-based [co]observability. Our results thereby complement those in Wang et al. (2011) and provide a thorough characterization of the relationship between the two notions of codiagnosability and coobservability and their verification. In particular, our results allow the leveraging of the large existing literature on decentralized control synthesis to solve corresponding problems of decentralized fault diagnosis.