Table Of ContentCommunications and Control Engineering
Christoforos N. Hadjicostis
Estimation and
Inference in
Discrete Event
Systems
A Model-Based Approach with
Finite Automata
Communications and Control Engineering
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Christoforos N. Hadjicostis
Estimation and Inference
in Discrete Event Systems
A Model-Based Approach with Finite
Automata
123
Christoforos N.Hadjicostis
Department ofElectrical
andComputer Engineering
University of Cyprus
Nicosia, Cyprus
ISSN 0178-5354 ISSN 2197-7119 (electronic)
Communications andControl Engineering
ISBN978-3-030-30820-9 ISBN978-3-030-30821-6 (eBook)
https://doi.org/10.1007/978-3-030-30821-6
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To my family.
Preface
This book addresses the growing need for systematic state estimation and event
inference techniques, as well as efficient verification of related properties, in dis-
crete event systems (DES). Such systems have become prevalent in the past three
decades,primarilyduetotheproliferationofdigitaltechnologies,interconnectivity,
and sensor technology. These developments have led to the emergence of many
highlycomplexsystems,inwhichasignificantportionoftheactivityisdetermined
byrulesdesignedbyhumanengineers.Examplesincludeautomatedmanufacturing
systems, communication networks and transmission protocols, traffic control and
transportationsystems,autonomousvehicles,digitalcontrollersforautomotiveand
printing devices,andothers. The dynamics of such systems aredriven by possibly
asynchronous occurrences of discrete events, some of which are controlled (e.g.,
consciousdecisionsbythesystemcontrollerorthesystemuser)andsomeofwhich
areuncontrolled(e.g.,unexpecteddisturbancesbytheenvironmentorunauthorized
users). As a result, when DES are coupled with dynamic equations, they can
capture, completely or at some level of abstraction, many human-designed tech-
nological systems including several emerging cyber-physical systems.
The above applications span a number of disciplines (e.g., systems and control,
communications,computerscienceandengineering,manufacturingengineering,to
name a few), but a common denominator in all of the above examples is that an
accuratemodeloftheunderlyingsystem(atleastforpartofitsactivity)isavailable
to the engineers that built it. The model-based techniques for state estimation and
event inference inDESthat aredescribedinthisbookhavebeenbrewingoverthe
past three decades. Pieces of them can be found in research papers and existing
DESbooks,butasinglereferencethatincludessuchdiscussionswaslargelyabsent.
ThebookissuitableforprovidingabasicintroductiontoDEStoundergraduate
and graduate student audiences, as well as practitioners, who are interested in
learning more about these systems, and related techniques for state estimation,
event inference, and the verification of properties of interest, such as detectability,
diagnosability, or opacity. The book could certainly be used as a textbook for a
first-year graduate course in (state estimation and event inference in) DES. Parts
vii
viii Preface
ofthebookcouldalsobeusedforasenior-levelundergraduatecourse(forexample,
by excluding the later material on decentralized and distributed estimation/
inference).
One of the objectives in writing this book was to provide a comprehensive, yet
relativelyconcise,treatmentofthesubjectsofstateestimationandeventinference.
Thisisoneofthereasonsforfocusingthediscussionsonsystemsthataremodeled
asdeterministicornondeterministicfiniteautomata,whichallowsthereaderwhois
interested in these topics (e.g., a graduate student or researcher) to quickly obtain
sufficientbackgroundtopursuetheseissuesfurther, perhapsinothertypesofDES
(e.g., Petri nets) where similar techniques can be used. Therefore, despite the fact
that the primary purpose of writing the book was to provide a self-sufficient
exposition of the material, discussions, and pointers to related work in other types
of DES are provided at the end of each chapter for the reader’s benefit. The
intention was not to provide a comprehensive list of the relevant literature, as this
would be a formidable task given the large and continuously growing literature in
the field. Clearly, the references provided at the end of each chapter are rather
focusedandbynomeanscomplete,andweapologizeinadvanceforanyomissions.
Contents of the Book and Organization of the Material
ThebookfocusesonestimationandinferencetechniquesforDESthataremodeled
as deterministic or nondeterministic finite automata. The organization of the
material in the book follows a linear structure, starting from some motivating
discussions,movingontoonlinestateestimation,thenexploringofflineverification
of several properties of interest, and finally concluding with more advanced topics
on decentralized/distributed state estimation.
(cid:129) Chapter 1 serves as a motivational chapter that situates the discussions in the
book within the more general context of DES research (in state estimation and
event inference, but also in other relevant DES research topics). In particular,
this chapter provides pointers and identifies related literature that the interested
reader can further investigate.
(cid:129) Chapters 2 and 3 introduce some necessary notation for capturing finite auto-
mata models in terms of their input/output behavior and their state transition
functionality. Particular attention is paid to the observation models in these
automata (e.g., the presence of silent or unobservable transitions).
(cid:129) In Chap. 4, we develop state estimation techniques, focusing on three different
typesofstateestimationtasks:current-stateestimation,delayed-stateestimation
(or smoothing), and initial-state estimation. This chapter essentially develops
recursive (online) state estimation algorithms for current-, delayed-, or
initial-stateestimation.Inallcases,adistinctionismadebetweenfiniteautomata
without silent transitions and finite automata with silent transitions.
Preface ix
(cid:129) Chapter 5 is an introduction to the topic of verification of observation-related
properties. It focuses on the analysis of so-called state isolation properties,
which capture our ability to determine, following any feasible sequence of
observations, that the state (current, delayed, or initial) of the given finite
automaton falls within a given set of states of interest.
(cid:129) In the next three chapters, we discuss three important system properties and
ways to verify them. More specifically, Chap. 6 discusses several variants of
detectability, i.e., our ability to be in position to (almost always) determine
exactlythestateofthesystem;Chap.7discussesdiagnosability,i.e.,ourability
toeventually inferthatacertaintype ofeventhasoccurredornot;andChap.8
discusses opacity, i.e., our inability to conclude, based on the observations we
make about a given system, that the system has necessarily executed secret
behavior.
(cid:129) Extensionstodecentralizedanddistributedobservationsettingsareaddressedin
Chaps. 9 and 10, respectively. In these settings, there are multiple observation
points, which may communicate with a coordinator (decentralized setting) or
among themselves (distributed setting). The two chapters discuss and analyze
the implementation and verification of several protocols that can be used for
decentralized/distributed state estimation and event inference.
Therearemanywaysinwhichreaderscanstudythematerial,dependingontheir
interests and their familiarity with DES modeled as finite automata. Below we
discuss some of these possible ways.
1. One should certainly obtain an understanding of the notation by reading (or at
leastskimmingthrough)Chaps.2and3.Theamountoftimeareaderspendson
this material depends on the familiarity of the reader with these concepts.
2. The next two chapters, namely Chaps. 4 and 5, comprise the core of the book:
the former chapter discusses online (recursive) state estimation and event
inference, whereas the latter chapter discusses offline verification of a class of
properties that relate to state estimation.
3. The next three chapters could be read rather independently, depending on the
interests of a reader. For example, a reader who is interested in opacity could
jumpdirectlytoChap.8(skippingChaps.6and7,whichfocusondetectability
and fault diagnosis, respectively). Similarly, a reader who is interested in fault
diagnosis can focus on Chap. 7, and skip the other two chapters.
4. The last two chapters focus on decentralized/distributed state estimation and
event reference. We expect that the reader will first study Chap. 9 and then
Chap. 10, though this is not strictly necessary. A reader can read these two
chapters without explicitly studying detectability, diagnosis, or opacity in
Chaps. 6–8 (though some parts of the discussions in Chaps. 9 and 10 discuss
decentralized/distributed verification of these properties).
The hope is that the readers will find the contents of the book interesting and
inspiring for further work in the exciting area of DES. Clearly, in a project of this
size, there is always room for improvement and comments/suggestions are most
x Preface
welcome. Finally, I would like to take this opportunity to express my gratitude to
numerous persons and organizations, whose help and assistance made the com-
pletion of this book possible. I am grateful to all of them, particularly to Oliver
Jackson of Springer, for his encouragement, patience, support, and enthusiasm
throughout the later stages of the writing of this book.
Nicosia, Cyprus Christoforos N. Hadjicostis
July 2019
