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2019 | Buch

Algebraic Preliminaries Kapitel lesen Erstes Kapitel lesen

Supervisory Control of Discrete-Event Systems

verfasst von: Prof. W. Murray Wonham, Prof. Kai Cai

Verlag: Springer International Publishing

Buchreihe : Communications and Control Engineering

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

This book shows how supervisory control theory (SCT) supports the formulation of various control problems of standard types, like the synthesis of controlled dynamic invariants by state feedback, and the resolution of such problems in terms of naturally definable control-theoretic concepts and properties, like reachability, controllability and observability. It exploits a simple, abstract model of controlled discrete-event systems (DES) that has proved to be tractable, appealing to control specialists, and expressive of a range of control-theoretic ideas. It allows readers to choose between automaton-based and dually language-based forms of SCT, depending on whether their preference is for an internal-structural or external-behavioral description of the problem.

The monograph begins with two chapters on algebraic and linguistic preliminaries and the fundamental concepts and results of SCT are introduced. To handle complexity caused by system scale, architectural approaches—the horizontal modularity of decentralized and distributed supervision and the vertical modularity of hierarchical supervision—are introduced. Supervisory control under partial observation and state-based supervisory control are also addressed; in the latter, a vector DES model that exploits internal regularity of algebraic structure is proposed. Finally SCT is generalized to deal with timed DES by incorporating temporal features in addition to logical ones.

Researchers and graduate students working with the control of discrete-event systems or who are interested in the development of supervisory control methods will find this book an invaluable aid in their studies. The text will also be of assistance to researchers in manufacturing, logistics, communications and transportation, areas which provide plentiful examples of the class of systems being discussed.

Inhaltsverzeichnis

Frontmatter
Chapter 1. Algebraic Preliminaries
Abstract
This chapter provides a brief introduction to partially ordered sets (posets), lattices, the lattice of equivalence relations, and derived concepts such as the factorization of a function through its equivalence kernel. These ideas capture, in a primitive but useful way, the general notion of ‘information’ in a feedback control loop together with that of ‘dynamic observer’ by which such information is extracted. An application is sketched to the Internal Model Principle of regulation theory, in a relatively unstructured setting of plain sets and functions.
W. Murray Wonham, Kai Cai
Chapter 2. Linguistic Preliminaries
Abstract
In supervisory control, formal languages provide a level of abstraction at which control concepts can be formulated in a way that is independent of any specific concrete implementation of the plant and controller. Some basic definitions are presented, leading to the Nerode equivalence relation as the bridge from a language to its dynamical state description. Emphasis is placed on regular (finite-state) languages as the class that is simplest and most directly applicable in the control context.
W. Murray Wonham, Kai Cai
Chapter 3. Supervision of Discrete-Event Systems: Basics
Abstract
We introduce the concept of controlled discrete-event system, by adjoining to the structure of a language generator a control technology. This amounts to partitioning the set of events into controllable events and uncontrollable, the former being amenable to disablement by an external controller or supervisor. Starting from the fundamental definition of a controllable language, it is shown how to formulate and solve a basic problem of optimal supervision. The formulation is extended to treat event forcing, reconfiguration, mutual state exclusion, and forbidden state subsets. Computation is illustrated using the software package TCT.
W. Murray Wonham, Kai Cai
Chapter 4. Decentralized and Distributed Supervision of Discrete-Event Systems
Abstract
In applications of supervisory control, especially to large systems made up of several component subsystems and with several individual specifications, it is generally advantageous to decompose the monolithic supervisor accordingly, both for greater computational feasibility and for enhanced transparency of control action. A risk, however, is that component modular supervisors may conflict and result in blocking, leading to the often difficult requirement of effective coordination. This chapter introduces the formal issues involved.
W. Murray Wonham, Kai Cai
Chapter 5. Hierarchical Supervision of Discrete-Event Systems
Abstract
Hierarchy is a layered architecture in which control authority is structured according to scope, as measured by temporal horizon and logical depth of command. The fundamental problem with hierarchy is to guarantee that each layer faithfully executes the commands received from the next higher, as confirmed by the corresponding feedback loop. Such hierarchical consistency is addressed in the framework of controlled DES already introduced; it is achieved by suitable refinement of the information transmitted from a given layer to the next higher.
W. Murray Wonham, Kai Cai
Chapter 6. Supervisory Control with Partial Observations
Abstract
A natural generalization of the control paradigm explored so far allows for feedback in which information may be lost in the channel linking plant to controller. It will be assumed that the channel behaves like a natural (zero-memory) projection, transmitting observable and erasing unobservable events symbol by symbol. A concept of language observability is introduced to express that control decisions based on such partial feedback information are always correct. It is shown that control synthesis of a given language is possible just when the language is controllable and observable; constructive procedures are provided to design and implement the resultant feasible controller. It is then effectively computable how control performance depends on the information available to the supervisor, as parametrized by the subset of observable events.
W. Murray Wonham, Kai Cai
Chapter 7. State-Based Control of Discrete-Event Systems
Abstract
In certain contexts it is convenient to employ directly a state space model combined with a simple logic formalism, in preference to the linguistic basis adopted so far. To retain flexibility, we indicate how the two approaches are conceptually dual. This chapter provides the background for vector discrete-event systems, to be introduced in Chap. 8. Two illustrations of discrete state models are adapted from the literature on industrial process control.
W. Murray Wonham, Kai Cai
Chapter 8. Supervision of Vector Discrete-Event Systems
Abstract
The state-based approach to DES supervisory control of Chap. 7 will be applied to a class of models known as vector addition systems, which when endowed with our standard control technology we call vector discrete-event systems (VDES). VDES offer a modeling option especially for systems incorporating groups of similar entities (e.g. machines in a workcell) which for control purposes need not be individually distinguished; often in practice such systems are equivalent to a synchronous product of buffers. VDES may be represented graphically as Petri nets (PN); results from the extensive PN literature will be exploited to advantage. We further consider problem restrictions under which an optimal supervisor itself admits a VDES representation, providing examples when this is or respectively is not the case.
W. Murray Wonham, Kai Cai
Chapter 9. Supervisory Control of Timed Discrete-Event Systems
Abstract
This chapter provides a framework for the study of theoretical issues in the design of supervisory controls for timed discrete-event systems. The model incorporates both time delays and hard deadlines, and admits both forcing and disablement as means of control. In addition it supports composition of modular subsystems and systematic synthesis.
W. Murray Wonham, Kai Cai
Backmatter
Metadaten
Titel
Supervisory Control of Discrete-Event Systems
verfasst von
Prof. W. Murray Wonham
Prof. Kai Cai
Copyright-Jahr
2019
Electronic ISBN
978-3-319-77452-7
Print ISBN
978-3-319-77451-0
DOI
https://doi.org/10.1007/978-3-319-77452-7

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