Optimal directed control of discrete event systems with linear temporal logic constraints

We consider a quantitative discrete event system modeled by a weighted automaton, where a weight assigned to each transition represents a cost by the occurrence of the transition. An optimal directed controller selects at most one controllable event at each state to optimize director´s cost of the controlled discrete event system. On the other hand, linear temporal logic is often used to specify the qualitatively desired behavior of a discrete event system. In this paper, we formulate a novel optimal directed control problem where the selection of the controllable event at each state is determined so as to maximize the worst-case value of the mean payoffs of controlled behaviors subject to a given linear temporal logic control specification. We propose a design method using a two-player game automaton whose players are the director and the product automaton. The former aims to maximize the worst-case value of the generated behaviors while the latter wants to minimize it. Under this situation, we use the concept of a best response and provide an algorithm to compute an optimal director. Then, we apply the proposed algorithm to a control problem of an AGV.