Supervisory control of state-tree structures with partial observation

Abstract

Supervisory control of discrete-event systems (SCDES) is well developed to find a maximally permissive supervisor. As an extension to supervisory control theory, a new framework, state-tree structures (STS), has been deployed to manage the state explosion problem of SCDES. This paper aims to address this notorious issue of supervisory control with partial observation in the STS framework by state feedback control that calculates the controllers of the controllable-observable events only, which is realized by the following two steps. First, for a specification represented as a predicate, a supremal normal subpredicate that requires only the controllable-observable events enabled/disabled, is computed. Second, according to the new transition function constructed by the natural projection of the given STS, the supremal nonblocking, weakly controllable subpredicate is obtained from the supremal normal subpredicate. The proposed approach based on STS provides the possibility to supervise controllable events under partial observation in large-scale systems with the state explosion problem managed. An example with state size over 107 that leads to program crashes in SCDES can be solved in this paper. Moreover, in order to demonstrate the industrial applications of the contribution of this research, three examples are addressed.