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

In many practical applications we are asked to compute a nonblocking supervisor that not only complies with some prescribed safety and liveness requirements but also achieve a certain time optimal performance such as throughput. In this paper we first introduce the concept of supremal minimum-time controllable sublanguage and define a minimumtime supervisory control problem, where the plant is modeled as a finite collection of finite-state automata, whose events are associated with weights, which represent their respective execution time. Then we show that the supremal minimum-time controllable sublanguage can be obtained by a terminable algorithm, where the execution time of each string is computed by using a technique extended from the theory of heaps-of-pieces.