State Estimation and Detectability of Networked Discrete Event Systems With Multi-Channel Communication Networks

Abstract

In this paper, we extend existing results on detectability of Discrete Event Systems (DES) to Networked Discrete Event Systems (NDES), a class of DES whose communication between the plant and the agent (supervisor, diagnoser, prognoser, etc) is carried out through a network that can have several channels. We assume that each channel is subject to different communication delays, which may cause changes in the order of the event observations with respect to their actual occurrences in the system automaton, and also that event transmission may be lost in the communication channels causing loss of observations. We follow a previously presented approach to construct an equivalent nondeterministic untimed automaton, and, based on this model, we present a method for the state estimation of NDES. We extend existing D-detectability definitions of DES to NDES subject to delays and loss of observation, referred here to as strong networked D-detectability, weak networked D-detectability, strong periodic networked D-detectability, weak periodic networked D-detectability. Finally, necessary and sufficient conditions for the networked D-detectability notions proposed here are proposed and algorithms for their verification are developed. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —State estimation is an important problem that appear in several practical applications, e.g. industrial systems, aircraft control and business management. Of current interest is the problem of distinguishing in real time if the system is not in pairs of states, the so-called D-detectability. In practical terms, it is not necessary to actually know the current state of the system but if the system may not be in two or more conflicting states. With the use of communication networks, additional features such as communication delay must also be taken into account in the process of performing D-detectability. In this paper we consider discrete event systems, a class of systems used to model a wide class of practical engineering problems whose dynamic evolution is driven by event occurrences, that are embedded in a communication network; we will refer to these systems as networked discrete event systems. In this regard, we generalize existing notions of D-detectability, and we call them networked D-detectability. Algorithms for networked D-detectability verification and a method to perform online state estimation are given in the paper.