Local Modular Control with Distinguishers applied to a Manufacturing System Marcelo Teixeira, Jos´ e E. R. Cury and Max H. de Queiroz ∗ Universidade Federal de Santa Catarina, Florian´ opolis, Brasil (e-mail: {mt,cury,max}@das.ufsc.br) Abstract: Local Modular Control (LMC) is a decentralized method to synthesize supervisors for Discrete Event Systems (DES) and distinguishers define a design-oriented concept that allows to simplify specifications modeling. When associated with approximations, distinguishers can also reduce synthesis effort. In this paper, we show how to combine advantages from LMC, distinguishers and approximations, to solve DES control problems. The approach preserves controllability, nonblocking and least restrictiveness of supervisors, while providing important computational gains. Our contributions are applied to the control of a manufacturing system with material feedback. Keywords: Discrete Event Systems, Local Modular Control, Distinguishers, Approximations. 1. INTRODUCTION Supervisory Control Theory (SCT) (Ramadge and Won- ham [1989]) describes the synthesis of supervisors for Dis- crete Event Systems (DES), mathematically grounded on Finite-state Automata formalism. Two major concerns in SCT are the computational cost to synthesize supervisors and the difficulty to model control specifications. The first problem arises as a result of the exponential growth in the number of states of a DES as a function of the number of its components. With regard to the second problem, the ability for structuring modeling tasks with automata is limited to a few dozens of states, while some control specifications may require hundreds of states to be represented. For example, consider controlling the number of workcycles performed on workpieces in a manufacturing system. Depending on the number of cycles to be allowed and the number of subsystems within the cycle, modeling this control specification may involve a large and intricate combination of events. Local Modular Control (LMC) (Queiroz and Cury [2000]) proposes a way to conduct the synthesis of supervisors in a decentralized manner. In LMC, each specification defines a local problem, which is then solved by using a local plant, composed by an appropriate subset of sub-systems. The modularization brought by the LMC allows to reduce the computational cost of synthesis, although in general it does not simplify modeling tasks. In this sense, the use of distinguishers (Bouzon et al. [2009], Cury et al. [2012]) can be considered. This approach consists in refining instances of the occurrence of a same event in the system, in a way to simplify the modeling of control specifications. Parallel advantages from LMC and distinguishers can be obtained by combining them to solve a same control prob- lem (Teixeira et al. [2011]). In this approach, each local supervisor can be computed either using the distinguishers ⋆ We would like to thank CNPq for supporting this research. or not, whenever appropriate. It has been shown, however, that achieving the same global controlled behavior as in the original LMC, requires also the same computational effort as when resolving the original problem. In this paper, we extend the above cited combined ap- proach with the use of approximated models for the plant. Approximations have shown to be suitable to simplify monolithic synthesis (Cury et al. [2012]), although they can lead to suboptimal results. Moreover, using approx- imations in the LMC may interfere on conflicting condi- tions. In the paper, we first show how to construct ap- proximated local plants. Then, we derive conditions under which using them in synthesis leads to computational gains, while preserving controllability, nonblocking and least restrictiveness of both local and global solutions. We apply our approach to control a small manufacturing system. In this example, distinguishers are used to make viable the model of the closed-loop specification. After- wards, using the LMC we compute approximations to the local plants, which lead first to a suboptimal control. Then, we show how to refine the approximations in a way to achieve the least restrictive controlled behavior. Although simple, the example is illustrative and the results can be naturally extended to large scale DES. The remainder of this document is structured as follows: section 2 recalls the SCT, LMC, distinguishers and their combination. The use of approximations is presented in section 3; section 4 applies the results to the manufac- turing system example. Finally, section 5 discusses some conclusions and perspectives. 2. PRELIMINARIES 2.1 Supervisory Control Theory of DES Supervisory Control Theory formally describes the syn- thesis of supervisors for DES. In this approach, the plant of a DES is modeled by a finite-state automaton G =