Decentralized Control of Discrete-Event Systems When Supervisors Observe Particular Event Occurrences

Abstract

Abstract-Work on decentralized discrete-event control systems is extended to handle the case when, instead of always observing or never observing an event, a supervisor may observe only some occurrences of a particular event. Results include a necessary and sufficient condition for solving this version of the decentralized problem (which is analogous to the co-observability property used in the standard version of the problem) and a method for checking when this condition holds. In this paper, whether an event is observed by a given agent is dependent on that agent's state (or the string of events that agent has seen so far). This model of event observation is applicable to problems where a supervisor communicates observations of event occurrences to another supervisor to help the other one make control decisions.

On Codiagnosability and Coobservability With Dynamic Observations

“…The dynamic versions of the properties of observability and coobservability also have been considered in [24] in the context of sensor activation. Polynomial testing methods for transition-based dynamic observations are developed in [34] for observability and in [35] for coobservability of two-agent systems.…”

Codiagnosability and coobservability under dynamic observations: Transformation and verification

“…For instance, Ref. Huang et al (2008) presents a verification algorithm of complexity of O(|X | 6 |E|) for transition-based coobservability with two agents (|X | is the number of states and |E| is the number of events of the system); however, the extension of this algorithm to the case of n agents is not available in the literature (Sears & Rudie, 2015). However, by applying the transformation algorithm in Wang et al (2011) and the verification algorithm in Section 4, the verification of transition-based coobservability can be…”

“…|E| 2 ), which may improve the computational complexity over the algorithm in Huang et al (2008), since |E| is usually much smaller than |X|. Moreover, this approach is applicable to the case of n agents.…”

“…It is well known that coobservability together with controllability provide the necessary and sufficient conditions for the existence of a set of decentralized supervisors that together achieve a given language. Formally, we recall the definition of coobservability under dynamic observations from Huang et al (2008) and Wang et al (2011). Let…”

“…In the context of dynamic observations, the observability properties of an event are not fixed but may vary along each system trajectory. In Huang, Rudie, and Lin (2008), the authors studied the property of coobservability under dynamic observations. The fault diagnosis problem under dynamic observations has also been investigated in several works, such as Cassez and Tripakis (2008) and Thorsley and Teneketzis (2007) for the centralized case and Wang, Girard, Lafortune, and Lin (2011) for the decentralized case.…”