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Modular supervisory control of composed systems is investigated. Composed systems are discrete event systems represented by the composition of smaller subsystems. This paper refines the modular control by exploiting aspects of modularity of specifications and of plant, aiming to incorporate the least necessary number of subsystems in each control module. Then, a more eficient approach to veri& modularity and synthesize modular controllers for composed systems is formulated and illustrated by an example. IntroductionA discrete-event system (DES) is a dynamical system whose state changes occur in discrete points of time, due to specific isolated events. Composed systems are DESs formed by the composition of several smaller subsystems. This is often the case of large scale systems, since modeling the several involved parts is generally an intermediate step in the representation of the whole behavior of the system.One of the main problems in the project of discrete-event systems is the synthesis of supervisors that, while controlling the system, restrict its operation to a specified behavior. The theory of Ramadge-Wonham [RW89] has been a quite powerful tool for that task. In this theory, the most important step in the supervisors' synthesis is the calculation of the suprema1 controllable language contained in a language that represents the desired behavior. The complexity of this calculation, although polynomial in the number of states of the plant model and of the specification, is an obstacle in applications because the number of states that represent the system increases exponentially with the number of component elements of the system. This restricting factor has been considered by several authors that attempt to overcome these computationalThis paper is about the modular control of composed systems, defined by local specifications. Local specifications are requirements referring to a specific part of the system to control, i.e., described on a subset of the events that affect the plant, as it is for example very often the case for manufacturing systems. The modularity property [WR88] assures the solution of the control problem through the synthesis of separate supervisors for each specification, without harming the global operation of the plant.However, the process of modularity verification found in the literature doesn't consider the properties of composed systems and it demands a single modeling that characterizes the open loop behavior of the whole system. For large scale systems, that process can demand a very high computational effort. This paper presents a more efficient approach for the verification of modularity, taking into account the concurrent structure of composed systems.When the modular control is applicable, the approach presented in this paper explores, besides the modularity of the specifications, aspects of modularity of the open loop behavior of composed systems, aiming to incorporate the least necessary number of subsystems in each control module. Hence, a supervisor for each local specifi...

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.

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