Control of Parameterized Discrete Event Systems

Abstract

This paper investigates the control of parameterized discrete event systems when specifications are given in terms of predicates and satisfy a similarity assumption. This study is motivated by a weakness in current synthesis methods that do not scale well to huge systems. For systems consisting of similar processes under total or partial observation, conditions are given to deduce properties of a system of n processes (arbitrary size) from properties of a system of n 0 processes (bounded size), with n ≥ n 0 . Furthermore, it is shown how to infer a control policy for the former from the latter's, while taking into account interconnections between processes.

A reachability graph construction technique for supervisor synthesis with parameters

“…For instance, when the cases handled by a workflow process are similar, they can be considered as instances of a replicated structure in order to exploit a control theory for PDESs [4]. On one hand, replicated structures can be restrained to nbounded state graphs.…”

“…The index i denotes the identity of a process and it is used to specify interconnections between processes [1], [4]. In this paper, the concept of identity is irrelevant and a non-indexed replicated structure S (Q, Σ s ∪ Σ, δ, Q m ) is regarded as a labeled state graph with an initial marking (see Fig.…”

Weak invariant simulation: Properties and algorithms

“…In many instances, such systems can be modeled conveniently as collections of isomorphic interacting processes such that the model of each process in the network is obtained by appropriate relabeling of a given template process. Such networks are examples of 'parameterized systems,' where the system parameter of interest is the size of the network, as characterized by the number of processes [2]. Parameterized modeling is particularly useful when the number of processes is unknown, timevarying or very large.…”

“…Within the control literature, Behrer et. al have considered control synthesis for parameterized systems [2]; however their synthesis method and does not address blocking issues. In fact, checking the nonblocking property in these networks is undecidable [3].…”

On Distributed and Parameterized Supervisor Synthesis Problems

“…As a potential tool for dealing with parameterized supervisor synthesis problems, the notion of weak invariant simulation is recently proposed in [29] for the analysis of parameterized discrete event systems. A decidable fragment of state based parameterized supervisor synthesis problem, without considering the non-blocking property, is reported in [30].…”