Modular Antipermissive Control of Discrete-Event Systems

Recently it has been shown that under very general conditions closed-loop languages under permissivecontrol policy (introduced by coinduction as a new operation called supervised product) distribute with synchronous (parallel) product.This paper is focused on the study of distributivity between synchronousproduct and closed-loop languages with respect to antipermissivecontrol policy. It is guaranteed that under the conditions derivedin the paper antipermissive control synthesis can be done locally and the local antipermissive control synthesis yields the same solution as the global control synthesis. An example illustrates that antipermissive control synthesis yields in general larger observable sublanguages than the supremal normal sublanguages are and that the mutual observability as a structural condition is not necessary for distributivity of closed-loop languages under the antipermissive control policy with the synchronous product.