Marked-String Accepting Observers for the Hierarchical and Decentralized Control of Discrete Event Systems

The paper extends previous work, where we develop a control theory for nonblocking hierarchical control of decentralized discrete event systems (DES). The results are based on two technical conditions for the hierarchical abstraction: it has to be (i) locally nonblocking and (ii) marked string accepting. In this paper, we investigate the systematic construction of the hierarchical abstraction. Starting from an initial natural projection which need not fulfil (i) and (ii), we provide an algorithm to compute the hierarchical abstraction with the coarsest equivalence kernel finer than that of the initial natural projection, and such that (i) and (ii) hold. Our approach extends the work in (K. Wong and W.M. Wonham, 2004), where the authors compute observers for the hierarchical control of DES