A new method for centralised and modular supervisory control of real-time discrete event systems

Abstract

This article deals with the problem of controlling a plant described as a real-time discrete event system (RTDES). In particular, automata-based supervisory control of RTDES is addressed. The aim of supervisory control is to restrict the behaviour (using a supervisor) of an uncontrolled plant in order to conform to a given specification. First, we propose a centralised method for the synthesis of a supervisor that forces a given plant to conform to a given specification. Then, we extend this centralised method to the modular case, that is, for the synthesis of n supervisors that force the plant to conform to n given specifications, respectively. Timed automata (TA) with invariants is the model used to describe the plant and the specification(s). The synthesis approach is based on the transformation of the control problem into a non-real-time form, using a transformation of TA into equivalent particular finite state automata called Set-Exp-Automata. This transformation allows to adapt the theory of Ramadge and Wonham, and is justified by the fact that it reduces the state space explosion problem compared to other transformation methods such as the transformation of TA into region automata. Moreover, the Set-Exp-Automata model provides a suitable control architecture for implementation. The proposed approach allows to obtain the solution to both the centralised and modular supervisory control problem, by identifying the solvability conditions and giving a step-by-step computation procedure of the solution.