Progressive time optimal control of reactive systems

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. Previous time optimal synthesis methods have had the significant drawback of only being able to deal with acyclic behavior. In this paper we propose a time optimal synthesis method which can deal with potentially infinite behavior. This is accomplished by dividing a system into progressive behaviors with which the system must be capable of finishing it task within a finite amount of time, and nonprogressive behaviors which can lead to the system having more tasks to complete, and potentially infinite behavior. We also proposed an algorithm with pseudo polynomial time complexity for computing such a supervisor.