Supervisor Localization: A Top-Down Approach to Distributed Control of Discrete-Event Systems

203 Pages·2016·6.418 MB·English

by  Kai Cai, W. Murray Wonham (auth.)

Lecture Notes in Control and Information Sciences 459
Kai Cai
W. Murray Wonham
Supervisor
Localization
A Top-Down Approach to Distributed
Control of Discrete-Event Systems
Lecture Notes in Control and Information
Sciences
Volume 459
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Kai Cai W. Murray Wonham
(cid:129)
Supervisor Localization
A Top-Down Approach to Distributed
Control of Discrete-Event Systems
123
KaiCai W.Murray Wonham
Urban Research Plaza Department ofElectrical andComputer
Department of Electrical andInformation Engineering
Engineering University of Toronto
Osaka City University Toronto, ON
Osaka Canada
Japan
ISSN 0170-8643 ISSN 1610-7411 (electronic)
Lecture Notesin Control andInformation Sciences
ISBN978-3-319-20495-6 ISBN978-3-319-20496-3 (eBook)
DOI 10.1007/978-3-319-20496-3
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To Akiko
and
Anne
Preface
Inwritingthismonographourgoalhasbeentopresentathoroughtreatmentofthe
supervisor localization approach to distributed control synthesis of discrete-event
dynamicsystems. The monographisintendedfor graduate students specializing in
control of discrete-event systems, researchers involved in distributed control over
networked multi-agent systems, and computer scientists (particularly in distributed
algorithms, artificial intelligence) interested in control-theoretic methods.
In this monograph a single distributed control problem is solved: given a
discrete-event system comprised of multiple agents and some imposed control
specifications, synthesize local controllers for each individual agent such that the
resultingcollectivecontrolledbehaviorsatisfiesthespecificationsandisoptimal(in
the sense of maximally permissive behavior) and nonblocking (i.e., distinguished
target states remain reachable). Our solution to this problem is a top-down proce-
dure that we call supervisor localization: first, synthesize a monolithic supervisor
(or a heterarchical array of modular supervisors) that satisfies the imposed speci-
ficationsandisoptimalandnonblocking;then,decomposethesupervisorintolocal
controllers for individual agents while preserving the optimal and nonblocking
controlled behavior. The distributed control problem is formulated in several dif-
ferent settings: language-based, state-based, and timed; in each case, a corre-
sponding localization solution is provided. The underlying mathematical idea is to
exploitaquotientstructure of thesynthesized supervisor, bymeans of aggregating
its dynamics according to the control information of each individual agent. The
discrete nature of the dynamics plays an essential role in enabling a clear-cut
separation of the control logics of individual agents.
The top-down style of supervisor localization is in sharp contrast with the
bottom-upapproachesmorefrequentlyusedtoaddressdistributedcontrol,notonly
in discrete-event but in other types of dynamic systems. Indeed, by adopting the
top-down direction we seek a method that always synthesizes correct and optimal
distributed control strategies for whatever control specifications are imposed, as
opposedtodesigninganadhocdistributedcontrolruletoperformonlyaparticular
task. Supervisor localization is thus a general method for distributed control syn-
thesis, independent of the imposed control specifications.
vii
viii Preface
The book is organized as follows. Chapter 1 introduces the background,
including a review of the literature and existing control architectures. Chapter 2
presents thefundamental results: thedistributed control problem is formulated and
supervisorlocalizationproposedasthesolution.Moreover,alocalizationalgorithm
is designed for computing local controllers, and properties of localization are
analyzed. Chapter 3 introduces an alternative localization scheme which allows
more flexible allocation of local controllers. This scheme is demonstrated with
examples in multi-robot formations, manufacturing workcells, and distributed
algorithms.Chapters4–6deal withlocalization inlarge-scalesystems.InChaps. 4
and5,localizationiscombined withanefficientheterarchicalsupervisorsynthesis,
resulting in a heterarchical localization procedure; this procedure is successfully
applied to synthesize distributed control of a benchmark case study, Production
Cell. In Chap. 6, an efficient state-based framework for supervisor synthesis called
state tree structures is adopted for supervisor localization. This leads to a more
efficient symbolic localization algorithm, which is demonstrated with a large-scale
example,ClusterTool.InChap.7,thedistributedcontrolproblemisformulatedfor
timed discrete-event systems; timed supervisor localization is presented as a solu-
tion that addresses temporal specifications in addition to logical ones. Finally in
Chap. 8, we state our conclusions and suggest future topics in supervisor locali-
zation that have emerged from this research. The framework that supervisor
localizationisbasedonissupervisorycontroltheory:specifically,inChaps.2–5the
Ramadge-Wonham language model, in Chap. 6 the Ma-Wonham state model, and
in Chap. 7 the Brandin-Wonham timed model.
Supervisor localization originated with the first author’s Master’s research
during2006–2008;theresultsofChaps.2and4–6appearedinhisMaster’sthesis.
Further developments (Chaps. 3 and 7) were completed during the first author’s
postdoctoral research, 2011–2013. The monograph organizes the results of super-
visor localization in the past 8 years into a self-contained volume. Supplementary
materials such as software and examples are available on the Internet at:
https://sites.google.com/site/supervisorlocalization
We would like to thank Dr. Renyuan Zhang for programming several key
procedures without which the examples in this monograph would not have been
possible. Financial support from the Program to Disseminate Tenure Tracking
System (Japan Society for the Promotion of Science) and the Discovery Grants
Program (Natural Sciences and Engineering Research Council of Canada) is
gratefully acknowledged. Finally we are deeply indebted to our wives, Akiko and
Anne, for their care and encouragement throughout the writing of this book.
Toronto Kai Cai
December 2014 W. Murray Wonham
Contents
1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Background on Distributed Control . . . . . . . . . . . . . . . . . . . . . 1
1.2 Control Architectures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2.1 Centralized Architecture. . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.2 Heterarchical Architecture. . . . . . . . . . . . . . . . . . . . . . . 5
1.2.3 Distributed Architecture . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3 Supervisor Localization Approach . . . . . . . . . . . . . . . . . . . . . . 7
2 Localization: Fundamental Results . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1 Supervisory Control Theory . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 Distributed Control Problem . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3 Control Covers and Localization Procedure. . . . . . . . . . . . . . . . 20
2.4 Necessity of Control Covers . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.5 Localization Algorithm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.6 Language Interpretation of Localization . . . . . . . . . . . . . . . . . . 33
2.7 Boundary Cases of Localization. . . . . . . . . . . . . . . . . . . . . . . . 35
2.7.1 Fully-Localizable. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.7.2 Non-Localizable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3 Localization: Further Results and Examples . . . . . . . . . . . . . . . . . 39
3.1 Extended Localization Theory. . . . . . . . . . . . . . . . . . . . . . . . . 39
3.1.1 Control Localization. . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.1.2 Marking Localization. . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.1.3 Main Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.2 Multi-Robot Formations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.2.1 Formulation of Multi-Robot Formation. . . . . . . . . . . . . . 47
3.2.2 Convergence to Formation . . . . . . . . . . . . . . . . . . . . . . 49
3.2.3 Shortest Paths to Formation . . . . . . . . . . . . . . . . . . . . . 51
ix
x Contents
3.3 Smart Machines in Manufacturing Workcells. . . . . . . . . . . . . . . 53
3.3.1 Workcell 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.3.2 Workcell 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.3.3 Workcell 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.4 Distributed Algorithms in Computer Science. . . . . . . . . . . . . . . 62
3.4.1 Mutual Exclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.4.2 Dining Philosophers. . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.4.3 Cigarette Smokers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4 Localization for Large-Scale Systems . . . . . . . . . . . . . . . . . . . . . . 73
4.1 Heterarchical Supervisor Synthesis. . . . . . . . . . . . . . . . . . . . . . 74
4.1.1 Natural Observer and Local Control Consistency. . . . . . . 78
4.2 Heterarchical Localization. . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.3 Case Study: Automated Guided Vehicles . . . . . . . . . . . . . . . . . 91
5 Case Study: Production Cell. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.1 System Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.2 Distributed Control by Heterarchical Localization. . . . . . . . . . . . 112
5.3 Control Architecture Comparisons . . . . . . . . . . . . . . . . . . . . . . 123
6 Localization Based on State Tree Structures . . . . . . . . . . . . . . . . . 127
6.1 Preliminaries on State Tree Structures. . . . . . . . . . . . . . . . . . . . 127
6.2 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
6.3 Localization Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
6.3.1 Necessary Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
6.4 Symbolic Localization Algorithm. . . . . . . . . . . . . . . . . . . . . . . 141
6.5 Case Study: Cluster Tool . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
7 Localization of Timed Discrete-Event Systems. . . . . . . . . . . . . . . . 153
7.1 Preliminaries on Timed Discrete-Event Systems. . . . . . . . . . . . . 154
7.2 Timed Localization Problem . . . . . . . . . . . . . . . . . . . . . . . . . . 158
7.3 Timed Localization Procedure . . . . . . . . . . . . . . . . . . . . . . . . . 160
7.3.1 Localization of Preemptive Action. . . . . . . . . . . . . . . . . 161
7.3.2 Localization of Disabling Action. . . . . . . . . . . . . . . . . . 163
7.3.3 Main Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
7.4 Case Study: Manufacturing Cell. . . . . . . . . . . . . . . . . . . . . . . . 167
8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
Appendix A: Nerode Equivalence and Canonical Recognizer. . . . . . . . 179
Appendix B: NP-Hardness of Minimal-State Localization . . . . . . . . . . 183