The synthesis of time optimal supervisors by using heaps-of-pieces

In many practical applications we need to compute a nonblocking supervisor that not only complies with pre-specified safety requirements but also achieves a certain time optimal performance such as maximum throughput. In this paper we first present a minimum-makespan supervisor synthesis problem. Then we show that the problem can be solved by a terminable algorithm, where the execution time of each string is computable by the theory of heaps-of-pieces. We also provide a timed supervisory control map that can implement the synthesized minimum-makespan sublanguage.