A parity-based architecture for decentralized discrete-event control

Abstract

Abstract-We introduce a new architecture that extends the class of problems that can be solved in decentralized DES control in the absence of communication. In this architecture, unlike previous architectures that use either conjunction(∧) or disjunction (∨) to fuse local control decisions, the fusion rule is exclusive or (⊕). We also characterize the new architecture, where controllers take a single decision, with respect to the recently-proposed multidecision framework of Chakib and Khoumsi. Unlike previous architectures, parity-based controllers cannot predetermine their local control decision based solely on their local observations. Instead, the local control decisions are calculated a priori.

A Uniform Treatment of Architectures in Decentralized Discrete-Event System

“…Unlike the C&P∧D&A architecture, now we have a morphism g from the conjunctive architecture: red/singly-bordered nodes are mapped by reversing h, where the only green/doubly-bordered node (1, 1) is mapped to (cd, cd). That is, in the C&P architecture, the decision 1 can be interpreted as a conditional decision, which aligns with the interpretation in [ER22], and contrasts to that in [RM13].…”

Inferencing and beyond: further adventures with parity-based architectures for decentralized discrete-event systems

“…We extend our results of Ricker and Marchand (2013) by providing language-based characterizations for when a parity-based architecture exists. In particular, we examine XOR as a fusion rule for…”

“…In Ricker and Marchand (2013) we noted a necessary condition for solving Problem 1: we cast the control problem as an instance of XOR-SAT (Biere et al, 2009) and if the resulting system of linear equations yielded a solution to XOR-SAT, we had a solution to Problem 1. Here, we introduce a language-based characterization of a necessary and sufficient condition to solve Problem 1.…”

“…We previously introduced the idea of incorporating XOR as a fusion rule for decentralized discrete-event systems (Ricker and Marchand, 2013). The problem of finding a correct control solution was reduced to that of solving XORSAT (Biere et al, 2009), although this only provided a necessary condition for the existence of an XOR solution.…”

“…As noted in Ricker and Marchand (2013), the family of distributed-observable languages lies between the family of inference-observable languages and the family of observable languages (i.e., n = 1). (2004)):…”