On Conditional Decomposability

The requirement of a language to be conditionally decomposable is imposed on a specification language in the coordination supervisory control framework of discrete-event systems. In this paper, we present a polynomial-time algorithm for the verification whether a language is conditionally decomposable with respect to given alphabets. Moreover, we also present a polynomial-time algorithm to extend the common alphabet so that the language becomes conditionally decomposable. A relationship of conditional decomposability to nonblockingness of modular discrete-event systems is also discussed in this paper in the general settings. It is shown that conditional decomposability is a weaker condition than nonblockingness.Comment: A few minor correction

Supervisory Control Synthesis of Discrete-Event Systems using Coordination Scheme

Supervisory control of discrete-event systems with a global safety specification and with only local supervisors is a difficult problem. For global specifications the equivalent conditions for local control synthesis to equal global control synthesis may not be met. This paper formulates and solves a control synthesis problem for a generator with a global specification and with a combination of a coordinator and local controllers. Conditional controllability is proven to be an equivalent condition for the existence of such a coordinated controller. A procedure to compute the least restrictive solution is also provided in this paper and conditions are stated under which the result of our procedure coincides with the supremal controllable sublanguage.Comment: 29 pages, 11 figure

Conditions for Hierarchical Supervisory Control under Partial Observation

The fundamental problem in hierarchical supervisory control under partial observation is to find conditions preserving observability between the original (low-level) and the abstracted (high-level) plants. Two conditions for observable specifications were identified in the literature -- observation consistency (OC) and local observation consistency (LOC). However, the decidability of OC and LOC were left open. We show that both OC and LOC are decidable for regular systems. We further show that these conditions do not guarantee that supremal (normal or relatively observable) sublanguages computed on the low level and on the high level always coincide. To solve the issue, we suggest a new condition -- modified observation consistency -- and show that under this condition, the supremal normal sublanguages are preserved between the levels, while the supremal relatively observable high-level sublanguage is at least as good as the supremal relatively observable low-level sublanguage, i.e., the high-level solution may be even better than the low-level solution