Multitasking Supervisory Control of Discrete-Event Systems MAX H. DE QUEIROZ* maxqueiroz@cefetsc.edu.br LAHPYGEMMYCEFET/SC, Floriano ´polis, SC 88020-301, Brazil JOSE ´ E. R. CURY cury@das.ufsc.br DASYCTC-Federal University of Santa Catarina, Floriano ´polis, SC 88040-900, Brazil W. M. WONHAM wonham@control.utoronto.ca Systems Control Group, Department of Electrical and Computer Engineering, University of Toronto, Toronto, ON M5S 3G4, Canada Abstract. This paper presents an approach for functionally dealing with multiple tasks in the supervisory control of discrete-event systems (DES). The colored marking generator (CMG), a special type of Moore automaton, is introduced as a model that distinguishes classes of tasks in DES. The main results of supervisory control theory are extended to this model, allowing the synthesis of minimally restrictive supervisors, which respect the safety specifications and ensure coreachability of multiple control objectives. Reversibility is also investigated as an alternative way of ensuring liveness of multiple tasks. Two examples illustrate the convenience of this approach. Keywords: supervisory control, discrete-event systems, tasks, control system synthesis, automata 1. Introduction Supervisory control theory (SCT) as initiated by Ramadge and Wonham (1987) has been developed in recent decades as an expressive framework for the synthesis of control for discrete-event systems (DES). In SCT, the open-loop behavior of a DES, called plant, is modeled by a generator (Wonham, 2004), whose marked states represent completion of some task. The restrictions to be imposed on the plant can be expressed in terms of a language representing the admissible behavior. The Ramadge-Wonham framework provides computational algorithms for the synthesis of a minimally restrictive supervisor that constrains the behavior of the plant by disabling controllable events in such a way that it respects the admissible language and that it ensures nonblocking, i.e., there is always an event sequence available to reach a marked state. While the admissible language can be viewed as a safety specification (assuring that nothing Bbad^ happens), nonblocking can be interpreted as a liveness specification that ensures that the supervisor will not prevent the completion of a task (something good happens). Other classes of liveness specifications such as stability (Ozveren and Willsky, 1991) and fairness (Gohari-M., 2002) have also been investigated in the literature. Discrete Event Dynamic Systems: Theory and Applications, 15, 375–395, 2005 # 2005 Springer Science + Business Media, Inc. Manufactured in The Netherlands. * Corresponding author.