Table Of ContentQuantitative Measure for
Discrete Event Supervisory Control
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edited by
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The Pennsylvania State University
University Park, PA, USA
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Louisiana Tech University
Ruston, LA, U.S.A.
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N.I.S.T. –Information Technology Laboratory
Gaithersburg, MD, USA
Asok Ray Vir V. Phoha N.I.S.T.
The Pennsylvania State Louisiana Tech Univ. Information
Univ. Ruston, LA Technology Lab.
University Park, PA Gaithersburg, MD
20899
Shashi P. Phoha
Library of Congress Cataloging-in-Publication Data
A C.I.P. Catalogue record for this book is available from the
Library of Congress.
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SSSSuuuuppppeeeerrrrvvvviiiissssoooorrrryyyy CCCCoooonnnnttttrrrroooollll //// Edited by Asok Ray, Vir V.
Phoha, Shashi P. Phoha
p.cm
Includes bibliographical references and index.
ISBN 0-387-02108-6 (HC) -ISBN 0-387-23903 -0 (eBook) Printed
on acid-free paper.
1. Supervisory control systems. 2. Discrete-time systems. I. Ray,
Asok, 1946- II. Phoha, Vir V. III. Phoha, Shashi, 1948-
TJ222.Q36 2005
629.8—dc22
2004059173
2005 Springer Science+Business Media, Inc.
All rights reserved. This work may not be translated or copied in
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Contents
Preface ix
About the Editors xix
Part I Theory of Language Measure and Supervisory Control
1 Signed Real Measure of Regular Languages
Asok Ray, Xi Wang 3
2 Optimal Supervisory Control of Regular Languages
Asok Ray, Jinbo Fu, Constantino Lagoa 39
3 Robust Optimal Control of Regular Languages
Constantino Lagoa, Jinbo Fu, Asok Ray 71
4 Advanced Topics in Supervisory Control
Ishanu Chattopadhyay, Asok Ray 95
Part II Engineering and Software Applications of Language
Measure and Supervisory Control
5 Discrete Event Supervisory Control of a Mobile Robotic
System
Xi Wang, Peter Lee, Asok Ray, Shashi Phoha 133
6 Optimal Control of Robot Behavior Using Language
Measure
Xi Wang, Asok Ray, Peter Lee, Jinbo Fu 157
7 Optimal Discrete Event Control of Gas Turbine Engines
Murat Yasar, Jinbo Fu, Asok Ray 183
vi Contents
8 Supervisory Control of Software Systems
Vir Phoha, Amit Nadgar, Asok Ray, Shashi Phoha 207
9 Supervisory Control of Malicious Executables in Software
Processes
Xin Xu, Vir V. Phoha, Asok Ray, Shashi Phoha 239
Index 261
Asok Ray dedicates this monograph to his students, teachers,
and colleagues
Vir Phoha dedicates this monograph to his parents and his
brother Rajesh
Shashi Phoha dedicates this monograph to her parents
Preface
Discrete event systems belong to a special class of dynamical systems. The
states of a discrete event system may take discrete (or symbolic) values and
change only at (possibly asynchronous) discrete instants of time, in contrast
to the familiar continuously varying dynamical systems of the physical world,
which can be modelled by differential or difference equations. The dynamics
of many human-engineered systems evolve asynchronously in time via com
plex interactions of various discrete-valued events with continuously varying
physical processes. The relatively young discipline of discrete event systems
has undergone rapid growth over the last three decades with the evolution of
human engineered complex systems, such as integrated control and communi
cation systems, distributed sensing and monitoring of large-scale engineering
systems, manufacturing and production systems, software fault management,
and military Command, Control, Computer, Communication, Intelligence,
Surveillance, and Reconnaissance {C^ISR) systems.
The discipline of discrete event systems was initiated with simulation of
human-engineered processes about four decades ago in the middle of nineteen
sixties. The art of discrete event simulation emerged with the development
of a simulation software package, called GPSS, that was followed by numer
ous other software simulation tools, such as SIMSCRIPT II.5, SLAM II, and
SIMAN [10]. Shortly thereafter, computer scientists and control theorists en
tered the field and brought in theoretical concepts of languages and automata
in modelling discrete event systems. In the late nineteen sixties, Arbib [8]
showed how algebraic methods could be used to explore the structure of finite
automata to model dynamical systems. Around that time, computer scientists
focused on formal languages, automata theory, and computational complexity
for application of language-theoretic concepts (e.g., regular expressions and
context-free grammars) in software development including design of compil
ers and text processors [7]. In the late nineteen seventies and early nineteen
eighties, Ho and co-workers introduced the concept of finite perturbation in
discrete event systems for modelling and analysis of human-engineered sys-
X Preface
terns [5]. So far, no concrete theoretical concept and mathematical tools had
been available for analysis and synthesis of discrete event control systems.
The concept of discrete event supervisory (DES) control was first intro
duced in the seminal paper of Ramadge and Wonham [12] and this important
paradigm has been subsequently extended by other researchers (for example,
see citations in [9] [1], and the October 2000 issue of Part B of IEEE Trans
actions on Systems, Man, and Cybernetics). These efforts have led to the
evolution of a new discipline in decision and Control, called Supervisory Con
trol Theory (SCT), that requires partitioning the discrete-event behavior of a
physical process, called the plant, into legal and illegal categories. The legal
behavior of the plant dynamics is modelled by a deterministic finite-state au
tomaton, abbreviated as DFSA in the sequel. The DFSA model is equivalent
to a regular language that is built upon an alphabet of finitely many events;
the event alphabet is partitioned into subsets of controllable events (that can
be disabled) and uncontrollable events (that cannot be disabled). Based on the
regular language of an unsupervised plant, SCT synthesizes a DES controller
as another regular language, having the common alphabet with the plant lan
guage, that guarantees restricted legal behavior of the controlled plant based
on the desired specifications. Instead of continuously handling numerical data,
DES controllers are designed to process event strings to disable certain con
trollable events in the physical plant. A number of algorithms for DES control
synthesis have evolved based on the automata theory and formal languages re
lying on the disciplines of Computer Science and Control Science. In general, a
supervised plant DFSA is synthesized as a parallel composition of the unsuper
vised plant DFSA and a supervisor DFSA. The supervised plant DFSA yields
a sublanguage of the unsupervised plant language, which enables restricted
legal behavior of the supervised plant [12] [9] [1]. These concepts have been
extended to several practical applications, including hierarchical Command,
Control, Communications, and Intelligence (C^/) systems [11]. Apparently,
there have been no quantitative methods for evaluating the performance of
supervisory controllers and establishing thresholds for their performance.
The concept of permissiveness has been used in DES control litera
ture [1] [9] to facilitate qualitative comparison of DES controllers under the
language controllability condition. Design of maximally permissive DES con
trollers has been proposed by many researchers based on different conditions.
However, maximal permissiveness does not necessarily imply best performance
of the supervised plant from the perspectives of plant operational objectives.
For example, in the travelling salesman problem, a maximally permissive su
pervisor would not usually yield the least expensive way of visiting the sched
uled cities and returning to the starting point because no quantitative measure
of performance is addressed in this type of supervisor design. Hence, permis
siveness is not an adequate measure of performance.
Preface xi
The controlled behavior of a given plant DFSA under different supervisors
could vary if they are designed to meet different control specifications. As such
the respective controlled sublanguages of the plant language form a partially
ordered set that is not necessarily totally ordered. Since the literature on DES
control does not apparently provide a language measure, it may not be possible
to quantitatively evaluate the performance of a DES controller. Therefore,
it is necessary to formulate a mathematically rigorous concept of language
measure(s) to quantify performance of individual supervisors such that the
measures of controlled plant behavior, described by a partially ordered set of
controlled sublanguages, can be structured to form a totally ordered set. From
this perspective, it is necessary to formulate a signed real measure /J, that can
be assigned to sublanguages of the regular language of the unsupervised plant
to achieve the following objective [16] [15] [13]:
Given that the relation C induces a partial ordering on a set of con
trolled sublanguages {L{S^/G),j — 1,...,N} of the plant language
L{G) under supervisors whose languages are {L(S^)J — 1,...^N},
the language measure /j, induces a total ordering < on {/j,{L{S^/G))}.
The major motivation here is to present a signed real measure of regu
lar languages, which can be used for quantitative analysis and synthesis of
DES control systems for physical plants, instead of relying on permissive
ness as the (qualitative) performance index. Construction of the proposed
language measure follows My hill-Nero de Theorem [6] and Hahn Decompo
sition Theorem [14], where a state-based partitioning of the (unsupervised)
plant language yields equivalence classes of finite-length event strings. Each
marked state is characterized by a signed real value that is chosen based on
the designer's perception of the state's impact on the system performance.
Conceptually similar to the conditional probability, each event is assigned a
cost based on the state at which it is generated. This procedure permits a
string of events, terminating on a good (bad) marked state, to have a positive
(negative) measure; each of the remaining strings of events in the language,
terminating on an unmarked state, is assigned zero measure. In this setting, a
supervisor can be designed with the goal of eliminating bad strings and retain
ing good strings by disabling controllable event(s) at selected states. Different
supervisors may attempt to achieve this goal in different ways and generate a
partially ordered set of controlled languages. The language measure then cre
ates a total ordering on the performance of the controlled languages, which
provides a precise quantitative comparison of the controlled plant behavior
under different supervisors.
The language measure has been used as a performance index for analysis
and synthesis of DES control systems. For example, Fu et al. [4] [3] [2] have
proposed optimal control and robust optimal control of regular languages
where a state-based optimal control policy is obtained by selectively disabling
controllable events to maximize the measure of the controlled plant language.
xii Preface
The concept of DES control has been vahdated by laboratory experimenta
tion on mobile robots as well as on simulation test beds for applications to
gas turbine engines, software fault management, C^I systems, and control of
malicious executables in computers.
Main Features of the Research Monograph
This monograph presents a novel and mathematically rigorous approach to
discrete event supervisory control, and builds on the research work, some of
which is only recently available in conference proceedings, or will be available
in journals within one to two years because of lag time in publication. The new
concepts and their applications are presented for practicing professionals and
graduate students in engineering, computer science, physics, applied mathe
matics as well as in other fields such as economics, life sciences, social sciences,
and political sciences. It is envisioned that the presented inter-disciplinary ma
terial will significantly enhance the science and technology base not only in
engineering and physical sciences but also in other disciphnes such as man
agement sciences, biological sciences, social sciences, and economics.
Starting from the fundamental principles of automata theory and lan
guages, this research monograph presents a quantitative measure of formal
languages^ which lays the theoretical foundations for supervisory decision and
control in complex human-engineered systems with application examples of
anomaly detection and fault handling in robotics, gas turbine engines, and
software systems. It introduces a new paradigm to quantitatively compare
the performance of different automata models of a controlled physical process.
The language measure is well suited to serve as a performance index for opti
mal and robust optimal supervisory decision algorithms in the discrete-event
setting for both military and commercial C^I systems. This approach, which
was first reported in the Proceedings of 2002 American control Conference
and is not available in any existing monographs and textbooks, will help dis
seminate the underlying concepts and spread its use in various disciplines and
applications.
To the best of the editors' knowledge, this monograph is the first com
prehensive, self-contained treatment of a language-theoretic quantitative ap
proach to discrete event supervisory decision and control. It complements the
information contained in other research monographs (e.g., [9]) and text books
(e.g., [1]) on discrete event supervisory control. The main features of this
monograph are summarized below:
• The monograph focuses on quantification of regular languages as a signed
real measure. It provides insight and understanding through rigorous
mathematical foundations and necessary proofs, while avoiding non-essential
mathematical details and emphasizing applications. The concept of signed
