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

Abstract

A coloured Petri net (CPN) is widely used to model discrete event systems due to its compact representation of the system by colour sets associated with places, transitions and I/O arcs. For real-world systems such as manufacturing systems, transportation systems, and communication protocols, a coloured timed Petri net (CTPN) is proposed to model timed behaviours. To control a discrete event system with a desired control specification, it is important to describe the control specification formally. For the CPN, a class of specification called coloured generalized mutual exclusion constraints (cGMEC) is utilized to specify the behaviours. However, cGMEC can only represent safety constraints and not temporal constraints. Therefore, in this paper, we propose a novel temporal logic based constraint called a coloured generalized mutual exclusion temporal constraint (cGMETC). The cGMETC is described by a signal temporal logic (STL) formula where each atomic predicate represents a cGMEC. We propose a method for optimal control of the CTPN under a given cGMETC. In particular, we formulate an optimal control problem and solve the problem by transforming it into an integer linear programming problem. Through a simulation of an optimal control problem of a manufacturing system, we demonstrate the effectiveness of the proposed approach.INDEX TERMS Petri nets, coloured timed Petri nets, temporal logic, generalized mutual exclusion constraints, integer linear programming. I. INTRODUCTIONA Petri net is an appropriate tool for modelling of discrete event systems [1], [2]. In particular, it has been applied to resource allocation problems including scheduling in manufacturing systems because it provides representation of systems with a large state space [3], [4], [5]. For real-world systems, however, the size of the systems increases, and the systems contain structures that are similar but not exactly the same. To model such systems, a coloured Petri net (CPN), which is an extension of Petri nets, has been studied [6], [7]. The CPN has colour sets that are associated with places, transitions and I/O arcs, and it provides a more compact representation for complex and large systems than ordinary Petri nets. There have been many studies utilizing the CPN,The associate editor coordinating the review of this manuscript and approving it for publication was Zhiwu Li .

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