Supervisory Control of Fuzzy Discrete Event Systems

In order to cope with situations in which a plant's dynamics are not precisely known, we consider the problem of supervisory control for a class of discrete event systems modelled by fuzzy automata. The behavior of such discrete event systems is described by fuzzy languages; the supervisors are event feedback and can disable only controllable events with any degree. The concept of discrete event system controllability is thus extended by incorporating fuzziness. In this new sense, we present a necessary and sufficient condition for a fuzzy language to be controllable. We also study the supremal controllable fuzzy sublanguage and the infimal controllable fuzzy superlanguage when a given pre-specified desired fuzzy language is uncontrollable. Our framework generalizes that of Ramadge-Wonham and reduces to Ramadge-Wonham framework when membership grades in all fuzzy languages must be either 0 or 1. The theoretical development is accompanied by illustrative numerical examples.Comment: 12 pages, 2 figure

Similarity-Based Supervisory Control of Discrete Event Systems

Due to the appearance of uncontrollable events in discrete event systems, one may wish to replace the behavior leading to the uncontrollability of pre-specified language by some quite similar one. To capture this similarity, we introduce metric to traditional supervisory control theory and generalize the concept of original controllability to \ld-controllability, where \ld indicates the similarity degree of two languages. A necessary and sufficient condition for a language to be \ld-controllable is provided. We then examine some properties of \ld-controllable languages and present an approach to optimizing a realization.Comment: 22 pages, 5 figure

State-Based Control of Fuzzy Discrete Event Systems

To effectively represent possibility arising from states and dynamics of a system, fuzzy discrete event systems as a generalization of conventional discrete event systems have been introduced recently. Supervisory control theory based on event feedback has been well established for such systems. Noting that the system state description, from the viewpoint of specification, seems more convenient, we investigate the state-based control of fuzzy discrete event systems in this paper. We first present an approach to finding all fuzzy states that are reachable by controlling the system. After introducing the notion of controllability for fuzzy states, we then provide a necessary and sufficient condition for a set of fuzzy states to be controllable. We also find that event-based control and state-based control are not equivalent and further discuss the relationship between them. Finally, we examine the possibility of driving a fuzzy discrete event system under control from a given initial state to a prescribed set of fuzzy states and then keeping it there indefinitely.Comment: 14 double column pages; 4 figures; to be published in the IEEE Transactions on Systems, Man, and Cybernetics--Part B: Cybernetic

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

DESIGN OF OPTIMAL PROCEDURAL CONTROLLERS FOR CHEMICAL PROCESSES MODELLED AS STOCHASTIC DISCRETE EVENT SYSTEMS

This thesis presents a formal method for the the design of optimal and provably correct procedural controllers for chemical processes modelled as Stochastic Discrete Event Systems (SDESs). The thesis extends previous work on Procedural Control Theory (PCT) [1], which used formal techniques for the design of automation Discrete Event Systems (DESs). Many dynamic processes for example, batch operations and the start-up and shut down of continuous plants, can be modelled as DESs. Controllers for these systems are typically of the sequential type. Most prior work on characterizing the behaviour of DESs has been restricted to deterministic systems. However, DESs consisting of concurrent interacting processes present a broad spectrum of uncertainty such as uncertainty in the occurrence of events. The formalism of weighted probabilistic Finite State Machine (wp-FSM) is introduced for modelling SDESs and pre-de ned failure models are embedded in wp-FSM to describe and control the abnormal behaviour of systems. The thesis presents e cient algorithms and procedures for synthesising optimal procedural controllers for such SDESs. The synthesised optimal controllers for such stochastic systems will take into consideration probabilities of events occurrence, operation costs and failure costs of events in making optimal choices in the design of control sequences. The controllers will force the system from an initial state to one or more goal states with an optimal expected cost and when feasible drive the system from any state reached after a failure to goal states. On the practical side, recognising the importance of the needs of the target end user, the design of a suitable software implementation is completed. The potential of both the approach and the supporting software are demonstrated by two industry case studies. Furthermore, the simulation environment gPROMS was used to test whether the operating speci cations thus designed were met in a combined discrete/continuous environment