A Framework for Discrete State attraction of Event systems Under Partial observation

State attraction for discrete event systems (DES) addresses the problem of reaching a desired subset of the plant state space after a bounded number of event occurrences. The problem of state attraction arises for example in fault-tolerant supervisory control or in the control of reconfigurable manufacturing systems, and is also applicable to systems biological problems such as the control of gene regulatory networks. State attraction is investigated with the assumption of full event observation in the existing literature. This paper extends the concept of state attraction to the case of partial observation. The notion of weak attraction under partial observation (WAPO) is introduced and necessary and sufficient conditions for the existence of a supervisor under partial observation that achieves WAPO are derived. Furthermore, a solution algorithm is proposed that finds such supervisor whenever it exists. It is shown that such supervisor can always be realized as a subautomaton of the observer automaton of the DES plant. An application example from systems biology illustrates the obtained results.  2014 Elsevier Inc. All rights reserved. 1. Introduction The supervisory control theory by Ramadge/Wonham [35] is a well-established theory for the control of systems that can be modeled as discrete event systems (DES). In the classical formulation, it addresses the synthesis of a supervisor in order to ensure that a DES plant fulfills a given formal language specification. Various approaches in the literature extend the classical formulation to supervisory control under partial observation [25], decentralized supervisory control [26,32,51], supervisory control with hierarchical abstractions [10,39,48], optimal control [41], state attraction [4,5], real-time scheduling [34], diagnosability [36,50] and supervisory control approaches for fuzzy discrete event systems [17,18,27–29]. The particular supervisory control problem studied in this paper is state attraction as introduced in [4,33]. It amounts to driving the state of a DES plant to a pre-specified desired subset of the state space after a bounded number of event occurrences, and staying in this subset indefinitely. If a supervisor that enforces this behavior exists, the subset is denoted as a week attractor. It is shown in [4] and related works such as [5,22] that, if such supervisor exists, it can be realized as a state-feedback supervisor on the state space of the DES plant. Moreover, the supervisor can be computed with polynomial complexity in the number of plant states. In the recent literature, state attraction is used for the fault-tolerance of DES [23,45] and for the supervisory control of reconfigurable manufacturing systems [12,40]. Moreover, the problem of state attraction is highly relevant in the field of systems biology or, more precisely, the field of modeling and controlling gene http://dx.doi.org/10.1016/j.ins.2014.05.026 0020-0255/ 2014 Elsevier Inc. All rights reserved. ⇑ Corresponding author. Tel.: +90 312 2331311. E-mail addresses: schmidt@cankaya.edu.tr (K.W. Schmidt), christian.breindl@ist.uni-stuttgart.de (C. Breindl). Information Sciences 281 (2014) 265–280 Contents lists available at ScienceDirect Information Sciences journal homepage: www.elsevier.com/locate/ins