Redundant Tasks in Multitasking Control of Discrete Event Systems

This paper addresses the control of multitasking DES that allow for dealing with liveness properties in the case where multiple classes of tasks have to be independently completed by the system. Colored marking generators (CMG) have been previously introduced as a model to consider multitasking control. The computational cost of the supervisor synthesis for multitasking DES grows with the number of classes of tasks. In this paper we investigate conditions under which removing tasks of the DES model does not affect the result of supervisory control in the sense that their completion is guaranteed as a consequence of the completion of the other tasks in the DES model. Conditions are derived under which tasks of a class or a set of classes can be removed from the model, and the results are extended to the case of abstracted models in a hierarchical and decentralized control architecture. Those conditions, which can be verified in polynomial time, are stated as properties of strongly connected components of the automata models in different levels of the control hierarchy. The results of the paper are illustrated by a manufacturing system example, showing the potential gains of the approach.