Optimal Control of Timed Petri Nets Under Temporal Logic Constraints with Generalized Mutual Exclusion

Abstract

This paper presents a novel method for optimal control of timed Petri nets, introducing a novel temporal logic based constraint called a generalized mutual exclusion temporal constraint (GMETC). The GMETC is described by an metric temporal logic (MTL) formula where each atomic proposition represents a generalized mutual exclusion constraint (GMEC). We formulate an optimal control problem of the timed Petri nets under a given GMETC and solve the problem by transforming it into an integer linear programming problem where the MTL formula is encoded by linear inequalities. We show the effectiveness of the proposed approach by a numerical simulation.