On a generalization of robust supervisory control of discrete event systems

In this paper we consider a generalization of the robust supervisory control problem introduced by Lin (Lin. 1993), improved by Takai (Takai. 2000; Takai, 2002), Park and Lim (Park and Lim, 2000; Park and Lin, 2002) and Cury and Krogh (Cury and Krogh, 1999). Following the formalism in (Lin, 1993), we suppose tbe plant language L(G) ⊆ Σ belongs to a finite collection of non-empty, prefix-closed languages L(G) € {L1,L-2,.. .,Ln}, where L,(0) ⊆ Σ,1 € {1,2,...,n). The event-set Σ is partitioned into controllable (Σ_c) and uncontrollable (Σu) subsets respectively. We assume all events are observable, and the supervisor has no prior knowledge as to the vakie of L(G) € {Li.Z,2....,L_n}. For each Li ⊆ Σ we suppose there exists a prefix-closed language Ki ⊆ Li We present three conditions that are necessary and sufficient for the existence of a supervisor that enforces K, if the plant language L(G) - Li. It is possible that for a given choice of the sets {L1.L2 Ln} and {K1, K2, ..., Kn}, the conditions identified in this paper are not satisfied. This calls for finding a {K1, K2, -, K_n}, such that i € {1,2,_n}.Ki ⊆ K1 that meets the required conditions, and each Ki satisfies some property that we might be interested in. Tbe search for a satisfactory {K1,K2_,Kn} using the notion of monotone properties is also presented.