On the relationship between codiagnosability and coobservability under dynamic observations

We investigate the relationship between the problem of decentralized fault diagnosis and the problem of 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. in [1] 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 K-codiagnosability can be transformed to coobservability. Moreover, we show that, when the observation map is static, the standard notion of centralized diagnosability is transformable to observability. Our results thereby complement those in [1] and provide a better understanding of the relationship between the notions of codiagnosability and coobservability. In particular, our new results allow the leveraging of the large existing literature on decentralized control synthesis to solve problems of decentralized fault diagnosis.