A Polynomial-Time Algorithm for Computing Finite-Makespan Controllable Sublanguages

Recently, a new language-based time-optimal control framework has been proposed. We adopt that new framework in this paper and address the finite-makespan controller synthesis problem. A polynomial-time algorithm is proposed to solve the problem. In order to determine the potential difference between the attained finite makespan and the expected minimum makespan for the sake of evaluating the performance of a synthesized finite-makespan controller, we provide another polynomial-time algorithm to compute a strictly lower bound of the minimum makespan so that explicitly computing the minimum makespan can be avoid, as the latter turns out to be NP-hard. Experimental results are provided to show the effectiveness of our algorithms.