Supervisor Synthesis for Approximating Maximally-allowable Behaviors

We present three algorithms for supervisor synthesis in discrete-event systems. In all cases the desired language is not both controllable and observable. To allow supervisor synthesis, we approximate the desired language with languages that are controllable and observable. These languages are contained in the desired language, and are ‘large’ in some sense. We note that there exists algorithms for calculating ‘maximal’ sublanguages of this kind, but in general they are nonunique as well as computationally prohibitive. On the other hand, there exist algorithms that synthesize unique ‘normal’ sublanguages, but these often are poor approximations to the desired language (i.e. they are very small sublanguages). The first algorithm, proposed by Kumar, realizes a controllable and observable language that he denoted CO(K). CO(K) represents a conservative attempt to extend normal sublanguages, by disabling events that potentially lead to ‘illegal’ strings (strings that result in non-observability). The second and third algorithms represent attempts to increase the approximating language beyond CO(K). They accomplish this task by better keeping track of the system state and by allowing a reduction of the number of disabled events at any particular time. The second algorithm was developed independently by Heymann and Lin and by us. The third algorithm is the new contribution of the present paper.