Supervisory Control of Fuzzy Discrete Event Systems: A Formal Approach

Fuzzy {\it discrete event systems} (DESs) were proposed recently by Lin and Ying [19], which may better cope with the real-world problems with fuzziness, impreciseness, and subjectivity such as those in biomedicine. As a continuation of [19], in this paper we further develop fuzzy DESs by dealing with supervisory control of fuzzy DESs. More specifically, (i) we reformulate the parallel composition of crisp DESs, and then define the parallel composition of fuzzy DESs that is equivalent to that in [19]; {\it max-product} and {\it max-min} automata for modeling fuzzy DESs are considered; (ii) we deal with a number of fundamental problems regarding supervisory control of fuzzy DESs, particularly demonstrate controllability theorem and nonblocking controllability theorem of fuzzy DESs, and thus present the conditions for the existence of supervisors in fuzzy DESs; (iii) we analyze the complexity for presenting a uniform criterion to test the fuzzy controllability condition of fuzzy DESs modeled by max-product automata; in particular, we present in detail a general computing method for checking whether or not the fuzzy controllability condition holds, if max-min automata are used to model fuzzy DESs, and by means of this method we can search for all possible fuzzy states reachable from initial fuzzy state in max-min automata; also, we introduce the fuzzy $n$-controllability condition for some practical problems; (iv) a number of examples serving to illustrate the applications of the derived results and methods are described; some basic properties related to supervisory control of fuzzy DESs are investigated. To conclude, some related issues are raised for further consideration

Petri net controllers for Generalized Mutual Exclusion Constraints with floor operators

In this paper a special type of nonlinear marking specifications called stair generalized mutual exclusion constraints (stair-GMECs) is defined. A stair-GMEC can be represented by an inequality whose left-hand is a linear combination of floor functions. Stair-GMECs have higher modeling power than classical GMECs and can model legal marking sets that cannot be defined by OR–AND GMECs. We propose two algorithms to enforce a stair-GMEC as a closed-loop net, in which the control structure is composed by a residue counter, remainder counters, and duplicate transitions. We also show that the proposed control structure is maximally permissive since it prevents all and only the illegal trajectories of a plant net. This approach can be applied to both bounded and unbounded nets. Several examples are proposed to illustrate the approach

Discrete events: Perspectives from system theory

Systems Theory;differentiaal/ integraal-vergelijkingen

Modular supervisory controller for complex systems

Automation for the oil and gas industry is driven by the need to improve efficiency, productivity, consistency, and personnel safety, while reducing cost. Fully automated systems alleviate the physical toll on human operators and allow them to focus on monitoring unsafe well events and machinery maintenance. Complex systems like drilling rigs and snubbing units require supervisory controllers that can safely coordinate equipment and processes, overcome interoperability challenges and allow for functional scalability without sacrificing safety, security, and consistency of operations. The primary objective of this report is to explore the feasibility of developing a modular supervisory controller architecture which addresses these concerns by modifying and extending existing architectures. Such modifications include the use of non-homogeneous models in sub-system modules, including discrete event models for control and physics-based models for collision avoidance, addition of a system compilation module (Meta Module) to identify simple design errors, and implementation of an algorithm for synthesis of modules and filters to replace missing sub-systems. This report discusses the implementation results of the modular supervisory control architecture (modMFSM) on a simplified two-machine drilling system for assessment of design practices. Simulations for three test cases were executed to assess the ability of the controller to correctly perform error-free operations, detect and react to possible collisions, and adapt to missing equipment. The report then discusses the possibilities of extending the modMFSM architecture to control large complex systems such as drilling rigs, using snubbing operations as an example.Mechanical Engineerin

Optimal Supervisory Control Synthesis

The place invariant method is well known as an elegant way to construct a Petri net controller. It is possible to use the constraint for preventing forbidden states. But in general case, the number forbidden states can be very large giving a great number of control places. In this paper is presented a systematic method to reduce the size and the number of constraints. This method is applicable for safe and conservative Petri nets giving a maximally permissive controller.Comment: Journ\'ee sur l'Instrumentation Industrielle J2I, ORAN : Alg\'erie (2009