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Lecture Notes in Control and Information Sciences 482
Elena Zattoni
Anna Maria Perdon
Giuseppe Conte Editors
Structural
Methods in the
Study of Complex
Systems

Lecture Notes in Control and Information
Sciences
Volume 482
Series Editors
Frank Allgöwer, Institute for Systems Theory and Automatic Control,
Universität Stuttgart, Stuttgart, Germany
Manfred Morari, Department of Electrical and Systems Engineering,
University of Pennsylvania, Philadelphia, USA
Advisory Editors
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P. Kokotovic, University of California, Santa Barbara, CA, USA
A. B. Kurzhanski, Moscow State University, Moscow, Russia
H. Kwakernaak, University of Twente, Enschede, The Netherlands
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Elena Zattoni • Anna Maria Perdon •
Giuseppe Conte
Editors
Structural Methods
in the Study of Complex
Systems
123

Editors
Elena Zattoni
Department of Electrical, Electronic and
Information Engineering “G. Marconi”
Alma Mater Studiorum Università di
Bologna
Bologna, Italy
Anna Maria Perdon
Dipartimento di Ingegneria
dell’Informazione
Università Politecnica delle Marche
Ancona, Italy
Giuseppe Conte
Dipartimento di Ingegneria
dell’Informazione
Università Politecnica delle Marche
Ancona, Italy
ISSN 0170-8643 ISSN 1610-7411 (electronic)
Lecture Notes in Control and Information Sciences
ISBN 978-3-030-18571-8 ISBN 978-3-030-18572-5 (eBook)
https://doi.org/10.1007/978-3-030-18572-5
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Preface
Complex dynamical systems emerge in a variety of disciplines and domains,
ranging from those that deal with physical processes (biology, genetics, environ-
mental sciences, etc.) to those that concern man-made systems (engineering,
energy, finance, etc.). Indeed, in these fields, it is becoming more and more com-
mon to refer to dynamical structures such as systems of systems, hybrid systems
and multimodal systems. In brief, the former ones consist of many interconnected
dynamical systems with various topological patterns and hierarchical relations; the
second ones are dynamical systems that exhibit dynamics of a different nature, both
continuous and discrete; the third ones are dynamical systems whose behaviour
may vary during their life cycle owing to different operating conditions or
depending on the occurrence of some events. The dynamical structures with these
characteristics are currently modelled as multi-agent systems, hybrid impulsive
systems, switching systems, implicit switching systems and so on.
Consequently, control design techniques have changed to adapt to the
ever-increasing system complexity. In this scenario, structural methodologies (i.e.,
those methods which have evolved from original graph theories, differential alge-
braic techniques and geometric approaches) have proven to be particularly powerful
for several reasons. Beforehand, the structural approaches privilege the essential
features of dynamical systems and their interconnections, thus yielding abstractions
that can fit a wide variety of situations. Meanwhile, the geometric perspective,
which is often at the basis of the structural approaches, introduces a relevant visual
and intuitive component which fosters research advancements. Nevertheless, the
formalization of structural and geometric concepts is rendered with algebraic tools,
which, in turn, have a direct correspondence with computational algorithms, thus
paving the way to actual implementation in engineering applications.
In the latest years, relevant theoretical achievements have been obtained within
the scope of each methodology encompassed in the sphere of the structural
approaches (i.e., graph-theoretic methods, differential algebraic methods and geo-
metric methods) in relation to fundamental control and observation problems stated
for complex systems (e.g., multi-agent systems, hybrid impulsive systems, switching
systems, implicit switching systems). Moreover, computational algorithms and case
v

studies have been developed together with the theoretical accomplishments. Thus,
the corpus of consolidated results (both theoretical and practical/computational ones)
presently available motivates this book, whose primary aim is to illustrate the state
of the art on the use of methodological approaches, grounded on structural views, to
investigate and solve paradigmatic analysis and synthesis problems formulated for
complex dynamical systems. In particular, the different perspectives emerging from
the various contributions have the purpose of developing new sensibilities towards
the selection of the most suitable tools to handle the specific problems. Furthermore,
the thorough discussions of specific topics are expected to outline new directions for
solving open problems both in the theory and in the applications.
The book starts with a general description of complexity and structural
approaches to it, then it focuses on some fundamental problems and, finally, it
dwells on applications. In more detail, an overview on the complex systems arising
in the various fields, on the new challenges of engineering design and on how these
can be mastered by means of the structural approaches is provided first. A novel
geometric view, based on transformations which maintain the invariance of global
properties, such as stability or H1 norm, is described and shown to provide new
tools to investigate stability and to parameterize the set of the stabilizing controllers.
A graph-theoretic based approach and the original notion of zero forcing set are the
tools used to analyse controllability, fault detectability and identifiability of system
networks and, more generally, of systems defined over graphs. How solvability
of the output regulation problem in hybrid linear systems with periodic state jumps
can be investigated by structural methods is then illustrated. A mixed digraph
theory and geometric approach is exploited to introduce the novel concept of
subspace arrangement and solve the problem of right-inversion for over-actuated
linear switching systems. Furthermore, the synthesis of unknown-input state
observers with minimum complexity is tackled by structural tools in the context of
linear impulsive systems: necessary and sufficient solvability conditions are derived
once a set of essential requirements has been disentangled. The disturbance
decoupling problem is investigated for a class of implicit switching systems through
geometric considerations inspired to the behavioural approach. In particular, the
theoretical results are applied to the synthesis of a Beard–Jones filter. Finally, a
structural perspective is adopted to analyse Huygens synchronization over dis-
tributed media and it reveals a complex, but structured behaviour behind a seem-
ingly chaotic one.
The book is intended for systems and control scientists interested in developing
theoretical and computational tools to solve analysis and synthesis problems
involving complex dynamical systems. The different contributions aim at giving a
comprehensive picture of the available results together with a stimulating view of
possible new directions of investigation in the field. Since the presentations
emphasize methodologies supported by a solid computational background and
often by specific engineering applications, researchers either focussed on theoretical
issues or mainly committed to applications may equally find interesting hints.
vi Preface

The idea of this book has stemmed from the workshop which the editors have
organized at the European Control Conference 2018 and its realization has been
made possible thanks to the strong and enthusiastic support of the invited speakers
and their co-authors, who have contributed their original work and latest achieve-
ments in the various chapters.
Bologna, Ancona Elena Zattoni
March 2019 Anna Maria Perdon
Giuseppe Conte
Preface vii

Contents
Part I Structure of Complex Dynamical Systems
1 Complex Systems and Control: The Paradigms of Structure
Evolving Systems and System of Systems . . . . . . . . . . . . . . . . . . . . . 3
Nicos Karcanias and Maria Livada
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 The Notion of the System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3 Integrated Design and Operations . . . . . . . . . . . . . . . . . . . . . . . . 9
1.4 Integrated System Design and Model Complexity Evolution . . . . . 12
1.4.1 Integrated Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.4.2 Early–Late Design Models: The Family of Fixed-Order
Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.4.3 Early–Late Design: Model Complexity Evolution . . . . . . . 16
1.5 Cascade Design System Evolution . . . . . . . . . . . . . . . . . . . . . . . . 21
1.5.1 Systems Composition and Complexity . . . . . . . . . . . . . . . 22
1.5.2 Systems Instrumentation and Forms of Evolution . . . . . . . 25
1.6 Integrated Operations and Emergent Properties. . . . . . . . . . . . . . . 32
1.6.1 The Multi-modelling and Hierarchical Structure
of Integrated Operations . . . . . . . . . . . . . . . . . . . . . . . . . . 32
1.7 The Notion of System of Systems . . . . . . . . . . . . . . . . . . . . . . . . 40
1.7.1 The Empirical Deﬁnition of System of Systems . . . . . . . . 41
1.7.2 Composite Systems and SoS: The Integrated Autonomous
and Intelligent System . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
1.7.3 The Systemic Deﬁnition of System of Systems . . . . . . . . . 45
1.7.4 Methods for the Characterization of Systems Play . . . . . . . 47
1.8 Conclusions and Future Research . . . . . . . . . . . . . . . . . . . . . . . . 49
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
ix

2 Stability and the Kleinian View of Geometry . . . . . . . . . . . . . . . . . . 57
Zoltán Szabó and József Bokor
2.1 Introduction and Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
2.1.1 Invariants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
2.1.2 A Projective View . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
2.2 A Glimpse on Modern Geometry—The Kleinian View . . . . . . . . . 62
2.2.1 Elements of Projective Geometry . . . . . . . . . . . . . . . . . . . 63
2.2.2 Projective Transformations . . . . . . . . . . . . . . . . . . . . . . . . 67
2.2.3 A Trapezoidal Addition . . . . . . . . . . . . . . . . . . . . . . . . . . 68
2.3 The Standard Feedback Loop . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
2.3.1 Youla Parametrization . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
2.4 Group of Controllers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
2.4.1 Indirect Blending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
2.4.2 Direct Blending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
2.4.3 Strong Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
2.4.4 Example: State Feedback . . . . . . . . . . . . . . . . . . . . . . . . . 80
2.5 A Geometry Based Controller Parametrization . . . . . . . . . . . . . . . 82
2.5.1 A Coordinate Free Parametrization . . . . . . . . . . . . . . . . . . 83
2.5.2 Geometric Description of the Parameters. . . . . . . . . . . . . . 85
2.6 From Geometry to Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
2.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
3 Strong Structural Controllability and Zero Forcing . . . . . . . . . . . . . 91
Henk J. van Waarde, Nima Monshizadeh, Harry L. Trentelman
and M. Kanat Camlibel
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
3.2 Zero Forcing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
3.3 Zero Forcing and Structural Controllability . . . . . . . . . . . . . . . . . 94
3.3.1 Strong Structural Controllability . . . . . . . . . . . . . . . . . . . . 95
3.3.2 Leader Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
3.3.3 Qualitative Subclasses . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
3.4 Targeted Controllability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
3.4.1 Output Controllability . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
3.4.2 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
3.4.3 Targeted Controllability for QðGÞ . . . . . . . . . . . . . . . . . . . 101
3.4.4 Targeted Controllability for QdðGÞ . . . . . . . . . . . . . . . . . . 105
3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
x Contents

Part II Control and Observation of Complex Dynamical Systems
4 Output Regulation of Hybrid Linear Systems: Solvability
Conditions and Structural Implications . . . . . . . . . . . . . . . . . . . . . . 115
Sergio Galeani and Mario Sassano
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
4.2 Notations, Preliminaries and Assumptions . . . . . . . . . . . . . . . . . . 117
4.3 Solvability Conditions, Without a Structural Approach . . . . . . . . . 122
4.3.1 Full Information Case . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
4.3.2 Error Feedback Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
4.4 Some Structural Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
4.4.1 A Decomposition of the Flow Dynamics . . . . . . . . . . . . . 126
4.4.2 On the Solution of an Integral Equation . . . . . . . . . . . . . . 128
4.5 Solvability Conditions, Untangled: A Structural
Interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
4.5.1 Structural Formulation and Solution of the hybrid
regulator equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
4.5.2 The Heart of the Hybrid Regulator . . . . . . . . . . . . . . . . . . 134
4.5.3 The Flow Zero Dynamics Internal Model Principle . . . . . . 135
4.6 On Well-Posedness, Universal and Generic Solvability . . . . . . . . . 138
4.6.1 The Classic (Non-hybrid) Case . . . . . . . . . . . . . . . . . . . . . 139
4.6.2 The Hybrid Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
4.7 Semi-classical Solution to Hybrid Output Regulation . . . . . . . . . . 141
4.7.1 The Classic (Non-hybrid) Case . . . . . . . . . . . . . . . . . . . . . 142
4.7.2 The Hybrid Case: Periodic Semi-classical Solutions. . . . . . 143
4.7.3 The Hybrid Case: Constant Semi-classical
Solutions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
4.8 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
4.9 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
5 A Stratiﬁed Geometric Approach to the Disturbance Decoupling
Problem with Stability for Switched Systems Over Digraphs . . . . . . 153
Junqiang Zhou and Andrea Serrani
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
5.2 Background and Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
5.3 Switched Discrete-time Linear Systems . . . . . . . . . . . . . . . . . . . . 156
5.4 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
5.5 Invariant Subspace Arrangements . . . . . . . . . . . . . . . . . . . . . . . . 158
5.5.1 Invariant Subspace Arrangements . . . . . . . . . . . . . . . . . . . 158
5.5.2 Controlled Invariant Subspace Arrangements. . . . . . . . . . . 158
5.6 Disturbance Decoupling Problem with Stability . . . . . . . . . . . . . . 160
Contents xi

5.6.1 Stabilization of Switched Discrete-Time
Linear Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
5.6.2 Solution to DDP with Stability . . . . . . . . . . . . . . . . . . . . . 162
5.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
6 Unknown-Input State Observers for Hybrid Dynamical
Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
Giuseppe Conte, Anna Maria Perdon and Elena Zattoni
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
6.2 Preliminaries and Problem Statement . . . . . . . . . . . . . . . . . . . . . . 170
6.3 A Structural Approach to the MOUIO Problem . . . . . . . . . . . . . . 173
6.3.1 Hybrid Conditioned Invariance . . . . . . . . . . . . . . . . . . . . . 173
6.3.2 Synthesis of the Observer . . . . . . . . . . . . . . . . . . . . . . . . 175
6.3.3 Parametrization of the Induced Dynamics . . . . . . . . . . . . . 178
6.3.4 Stabilizability of Conditioned Invariant Subspaces . . . . . . . 181
6.3.5 Hybrid Controlled Invariance . . . . . . . . . . . . . . . . . . . . . . 183
6.3.6 The Maximal Hybrid Conditioned Invariant Subspace . . . . 184
6.4 Problem Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
6.4.1 Necessary and Sufﬁcient Conditions for the Existence
of Asymptotic Observers . . . . . . . . . . . . . . . . . . . . . . . . . 188
6.4.2 Order Minimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
6.5 A Checkable Necessary and Sufﬁcient Condition . . . . . . . . . . . . . 194
6.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
7 Advances of Implicit Description Techniques in Modelling
and Control of Switched Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
Moisés Bonilla Estrada, Michel Malabre and Vadim Azhmyakov
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
7.2 Time-Dependent Autonomous Switched Systems . . . . . . . . . . . . . 205
7.2.1 Example (Part 1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
7.3 Implicit Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
7.3.1 Existence of Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
7.3.2 Proper Implicit Representations . . . . . . . . . . . . . . . . . . . . 213
7.3.3 Switched Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
7.3.4 Example (Part 2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
7.4 Reachability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
7.4.1 R
Xd
: Reachable Subspace . . . . . . . . . . . . . . . . . . . . . . . . 221
7.4.2 External Reachability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
7.4.3 Externally Assignable Output Dynamics . . . . . . . . . . . . . . 224
7.4.4 Example (Part 3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
xii Contents

7.5 Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
7.5.1 Decoupling of the Variable Structure . . . . . . . . . . . . . . . . 226
7.5.2 Example (Part 4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
7.5.3 Rejection of the Variable Structure . . . . . . . . . . . . . . . . . . 230
7.5.4 Example (Part 5) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
7.6 Numerical Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
7.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238
Part III Applications of Complex Dynamical Systems
8 Huygens Synchronization Over Distributed Media—Structure
Versus Complex Behavior. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
Vladimir Răsvan
8.1 Introduction and Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
8.2 Basic Mathematical Models—The “Toy” Application . . . . . . . . . . 246
8.3 Two Electronic Oscillators on a LC Transmission Line. . . . . . . . . 249
8.4 The Single Oscillator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
8.5 The Functional Differential Equations of the Coupled
Oscillators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256
8.6 Stability and Forced Oscillations of the System of Functional
Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
8.7 Two Mechanical Oscillators on the String . . . . . . . . . . . . . . . . . . 266
8.8 Challenges and Existing Results . . . . . . . . . . . . . . . . . . . . . . . . . 270
8.9 Conclusions and Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275
Contents xiii

Contributors
Vadim Azhmyakov Department of Mathematical Science, Universidad EAFIT,
Medellin, Colombia
József Bokor Institute for Computer Science and Control, Hungarian Academy of
Sciences, Budapest, Hungary
Moisés Bonilla Estrada CINVESTAV-IPN, Control Automático, UMI 3175
CINVESTAV -CNRS, A.P. 14-740, México City, México
M. Kanat Camlibel Johann Bernoulli Institute for Mathematics and Computer
Science, University of Groningen, Groningen, The Netherlands
Giuseppe Conte Dipartimento di Ingegneria dell’Informazione, Università
Politecnica delle Marche, Ancona, Italy
Sergio Galeani Department of Civil Engineering and Computer Science,
University of Rome Tor Vergata, Rome, Italy
Nicos Karcanias School of Engineering and Mathematical Sciences, Systems and
Control Research Centre, City, University of London, London, UK
Maria Livada School of Engineering and Mathematical Sciences, Systems and
Control Research Centre, City, University of London, London, UK
Michel Malabre CNRS, LS2N (Laboratoire des Sciences du Numérique de
Nantes) UMR 6004, B.P. 92101, Cedex 03, France
Nima Monshizadeh Engineering and Technology Institute Groningen, University
of Groningen, Groningen, The Netherlands
Anna Maria Perdon Dipartimento di Ingegneria dell’Informazione, Università
Politecnica delle Marche, Ancona, Italy
Vladimir Răsvan Department of Automatic Control, University of Craiova,
Craiova, Romania
xv

Mario Sassano Department of Civil Engineering and Computer Science,
University of Rome Tor Vergata, Rome, Italy
Andrea Serrani Department of Electrical and Computer Engineering, The Ohio
State University, 412 Dreese Laboratories, Columbus, OH, USA
Zoltán Szabó Institute for Computer Science and Control, Hungarian Academy of
Sciences, Budapest, Hungary
Harry L. Trentelman Johann Bernoulli Institute for Mathematics and Computer
Henk J. van Waarde Johann Bernoulli Institute for Mathematics and Computer
Elena Zattoni Department of Electrical, Electronic and Information Engineering
“G. Marconi”, Alma Mater Studiorum Università di Bologna, Bologna, Italy
Junqiang Zhou GE Global Research Center, Niskayuna, NY, USA
xvi Contributors

List of Figures
Fig. 1.1 The notion of the system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Fig. 1.2 The notion of the system with the basic variables . . . . . . . . . . . 8
Fig. 1.3 System and its operational hierarchy Ó [2011] IEEE.
Reprinted, with permission, from [22] . . . . . . . . . . . . . . . . . . . . 11
Fig. 1.4 Engineering design process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Fig. 1.5 Partial Realization as feedback interconnection of linear
systems. Reprinted from [3], Copyright 1987, with permission
from Elsevier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Fig. 1.6 Example of graph dimensional variability. . . . . . . . . . . . . . . . . . 20
Fig. 1.7 Example of Structural Graph Growth problem. Reprinted from
[32], Copyright 2008, with permission from Elsevier . . . . . . . . . 21
Fig. 1.8 Globally well-formed composite system . . . . . . . . . . . . . . . . . . . 24
Fig. 1.9 Effective and progenitor system model . . . . . . . . . . . . . . . . . . . . 24
Fig. 1.10 Model projection problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Fig. 1.11 Input–output problems reduction. . . . . . . . . . . . . . . . . . . . . . . . . 29
Fig. 1.12 Hierarchy of system operations. . . . . . . . . . . . . . . . . . . . . . . . . . 34
Fig. 1.13 Functional representation of the integrated system . . . . . . . . . . . 36
Fig. 1.14 System and emergent properties . . . . . . . . . . . . . . . . . . . . . . . . . 37
Fig. 1.15 A functional model for a general process . . . . . . . . . . . . . . . . . . 37
Fig. 1.16 Nesting of models in the hierarchy . . . . . . . . . . . . . . . . . . . . . . . 38
Fig. 1.17 Dynamical nesting in the hierarchy. . . . . . . . . . . . . . . . . . . . . . . 40
Fig. 1.18 Simpliﬁed description of the system . . . . . . . . . . . . . . . . . . . . . . 43
Fig. 1.19 Integrated and autonomous system Ó [2013]
IEEE. Reprinted, with permission, from [33] . . . . . . . . . . . . . . . 44
xvii

Fig. 2.1 Euclidean constructions Klein proposed group theory as a
mean of formulating and understanding geometrical
constructions. The idea of constructions comes from a need to
create certain objects in the proofs. Geometric constructions
were restricted to the use of only a straightedge and compass
and are related to Euclid’s first three axioms: to draw a straight
line from any point to any point, to produce a finite straight
line continuously in a straight line and to draw a circle with
any center and radius. The idealized ruler, known as a
straightedge, is assumed to be infinite in length, and has no
markings on it because none of the postulates provides us with
the ability to measure lengths. While modern geometry has
advanced well beyond the graphical constructions that can be
performed with ruler and compass, it is important to stress that
visualization might facilitate our understanding and might
open the door for our intuition even on fields where, due to an
increased complexity, a direct approach would be
less appropriate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
Fig. 2.2 Interplay: geometry, algebra and control. . . . . . . . . . . . . . . . . . . 61
Fig. 2.3 Fano plane: the corresponding projective geometry consists of
exactly seven points and seven lines with the incidence relation
described by the attached figure. The circle together with the
six segments represent the seven lines . . . . . . . . . . . . . . . . . . . . 64
Fig. 2.4 Projective addition: for the addition of two points let us fix the
points P0 and P1. Then a fixed line m0 through P0 meets the
two distinct fixed lines m1 and m0
1 in the points R and S0
,
respectively, while the lines PaR and PbS0
meet m0
1 and m1 at
R0
and S. The line R0
S meets m at Pa þ Pb ¼ Pa þ b. By
reversing the latter steps, subtraction can be analogously
constructed, e.g., Pa ¼ Pa þ b Pb. Observe that by sending
point P1 to infinity we obtain the special configuration based
on the “Euclidean” parallels and the common addition on the
real line. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
Fig. 2.5 Projective coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
Fig. 2.6 Parallel addition: set the origin to the point Y and let mx and mz
the directions determined by the points X and Z. If the points
1x, 1y are set to infinity we obtain a usual setting for parallel
vector addition: the coordinates of the point W are constructed
by taking parallels to mx and mz through W. For a “projective”
vector addition we can set the points 1x, 1y on a given line
a of R2
intersecting mx and mz. The point W is provided as
W ¼
h
ðX _ YÞ ^ a

_ Z
i
^
h
ðZ _ YÞ ^ a

_ X
i
. . . . . . . . . . . . 70
xviii List of Figures

Fig. 2.7 While the quadrangle XYZW is not a parallelogram, its
construction has something in common with the one of a
parallelogram: the picture illustrates the fundamental process
of passing from a commutative, associative law—vector
addition, corresponding to usual parallelograms—to a
non-commutative law:
W ¼

ðX _ YÞ ^ b

_ Z

^

ðZ _ YÞ ^ a

_ X

.
Trapezoidal addition, i.e., b ¼ i, the point W is provided as
W ¼

ðX _ YÞ ^ i

_ Z

^

ðZ _ YÞ ^ a

_ X

. . . . . . . . . . . 72
Fig. 2.8 Afﬁne parametrization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
Fig. 2.9 Feedback connection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
Fig. 2.10 Youla parametrization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
Fig. 2.11 Youla based blending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
Fig. 3.1 The graph G ¼ ðV; EÞ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
Fig. 3.2 The subgraph G0
¼ ðV; E0
Þ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
Fig. 3.3 Graph G with VL ¼ f1; 2g . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
Fig. 3.4 DðVLÞ ¼ f1; 2; 3g . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
Fig. 3.5 Graph G1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
Fig. 3.6 Graph G2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
Fig. 3.7 Graph G3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
Fig. 3.8 Example showing that Theorem 3.5 not necessary . . . . . . . . . . . 110
Fig. 4.1 The hybrid time domain T . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
Fig. 4.2 Schematics of the RC circuit; the switches are closed
periodically at integer multiples of sM . . . . . . . . . . . . . . . . . . . . 145
Fig. 4.3 Time history of the output regulation error e(t). . . . . . . . . . . . . . 146
Fig. 4.4 Input evolution for the subvectors u1 (solid line) and u2
(dashed line) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
Fig. 4.5 Time histories of the state components: hybrid steady-state
response (dashed gray) and state response to the semi-classical
steady-state input uss ¼ Cw from xð0; 0Þ ¼ 0 (solid black) . . . . . 147
Fig. 4.6 Time histories of the state components: classic steady-state
response xss;c ¼ Pw (dashed) and state response to the
semi-classical steady-state input uss ¼ Cw
from xð0; 0Þ ¼ 0 (solid) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
Fig. 5.1 The digraph G ¼ ðV; EÞ of a switched discrete-time linear
system: The vertex set V ¼ f1; 2; 3g deﬁnes three switched
modes; only transitions in the directed edge set
E ¼ fð1; 1Þ; ð1; 2Þ; ð2; 2Þ; ð2; 3Þ; ð3; 3Þ; ð3; 1Þg are admissible . . . 156
List of Figures xix

Fig. 7.1 Structural properties of the state-space representation
Rstate
ðAqi
; B; Cqi
Þ with matrices (7.5). The characteristic
polynomial is detðs I Aqi
Þ ¼ ðs þ 1Þ

s ð1 þ a þ bÞ

, the
uncontrollable and unobservable modes, C and O, are
and
,
respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
Fig. 7.2 Connexions between the notions of existence of solution.
a, b Conditions of existence of at least one solution for all
admissible inputs of Lebret [25]. c Condition of viable solution
of Aubin and Frankowska [2] or smooth solution (without any
jump) of Özçaldiran and Haliločlu [36]. d Condition of Geerts
[18] guaranteeing that the set of consistent initial conditions
equals the whole space. e Condition of C-solvability in the
function sense of Geerts [18] or the condition of Przyluski and
Sosnowski [38] guaranteeing that the set of initial conditions
of smooth solutions (with possible jumps) equals the whole
space, or the impulse controllability condition of Ishihara and
Terra [23], or the impulse-mode controllability with arbitrary
initial conditions of Hou [22] . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
Fig. 7.3 Maps induced by AF
p
and EF
d
. U and P are canonical
projections. The map E is invertible and E
ð1Þ
is
its inverse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
Fig. 7.4 Simulation results of Control with observation of the descriptor
variable. a Output, y. b and c Model matching error,
yðtÞ y
ðtÞ
j j. d and e Control input, u. f and g Observation
error, ^
x x
k k2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
Fig. 8.1 The original setting of Huygens . . . . . . . . . . . . . . . . . . . . . . . . . 245
Fig. 8.2 Mechanical oscillators on a string. . . . . . . . . . . . . . . . . . . . . . . . 246
Fig. 8.3 Two van der Pol oscillators on the elastic rod . . . . . . . . . . . . . . 246
Fig. 8.4 Two electronic oscillators on the inﬁnite LC line . . . . . . . . . . . . 253
Fig. 8.5 Nonlinear characteristic of the tunnel diode . . . . . . . . . . . . . . . . 254
xx List of Figures

Part I
Structure of Complex Dynamical Systems

Chapter 1
Complex Systems and Control:
The Paradigms of Structure Evolving
Systems and System of Systems
Nicos Karcanias and Maria Livada
Abstract This chapter deals with two rather new notions of complexity emerging
in Engineering Systems, reviews existing approaches and results and introduces a
number of open problems defining a research agenda in the field. We examine these
notions based on the fundamentals of a systemic framework and from the perspective
of Systems and Control Theory. The two new major paradigms expressing forms
of engineering complexity which have recently emerged are the new paradigms of
Structure Evolving Systems (SES) and Systems of Systems (SoS). The origin and types
of complexity linked to each one of these families are considered, and an effort is
made to relate these new types of complexity to engineering problems and link the
emerging open issues to problems and techniques from Systems and Control Theory.
The engineering areas introducing these new types of complexity are linked to the
problems of Integrated System Design and Integrated System Operations.
1.1 Introduction
Complex Systems is a term that emerges in many disciplines and domains [9] and
has many interpretations, implications and problems associated with it. The spe-
cific domain provides dominant features and characterizes the nature of problems
to be considered. A major classification of such systems is to those linked with
physical processes (physics, biology, genetics, ecosystems, social, etc.) and the arti-
ficial, which are man-made (engineering, technology, energy, transport, software,
management and finance, etc.). We are dealing with man-made systems and we are
interested in identifying generic types of system complexity among the different
problem domains and then identify the relevant concepts and tools that can handle
N. Karcanias (B) · M. Livada
School of Engineering and Mathematical Sciences, Systems and Control Research Centre, City,
University of London, Northampton Square, London EC1V 0HB, UK
e-mail: N.Karcanias@city.ac.uk
M. Livada
e-mail: Maria.Livada@city.ac.uk
© Springer Nature Switzerland AG 2020
E. Zattoni et al. (eds.), Structural Methods in the Study of Complex
Systems, Lecture Notes in Control and Information Sciences 482,
https://doi.org/10.1007/978-3-030-18572-5_1
3

4 N. Karcanias and M. Livada
the different types of complexity and then enable the design or redesign of complex
systems–processes. There is a need to develop generic methodologies and tools that
can be applied across the different problem domains. This research aims to identify
Systems and Control concepts and tools which are important in the development
of methodologies for the Management of Complexity of engineering-type complex
systems.
Existing methods in Systems and Control deal predominantly with fixed systems,
where components, interconnection topology, measurement–actuation schemes and
control structures are specified. Two new major paradigms expressing forms of engi-
neering complexity which have recently emerged are the new paradigms of
• Structure Evolving Systems (SES) [32]
• Systems of Systems (SoS) [23, 37, 50]
Using the traditional view of the meaning of the system (components, intercon-
nection topology, environment), the common element between the first two new
paradigms is that the interconnection topology may vary and evolve in the case
of SES, whereas in the case of SoS the interconnection rule is generalized to a new
notion of “systems play” [33] defined on the individual system goals. The paper deals
with the fundamentals regarding representation, structure and properties of those two
challenging classes, demonstrates the significance of traditional systems and control
theory, and introduces a new research agenda for control theory defined by:
Structure Evolving Systems [32]: Such a class of systems emerges in natural
processes such as Biology, Genetics, Crystallography [24], etc. The area of man-
made processes includes Engineering Design, Power Systems under de-regulation,
Integrated Design and Redesign of Engineering Systems (Process Systems, Flexible
Space Structures, etc.), Systems Instrumentation, Design over the Life Cycle of pro-
cesses, Control of Communication Networks, Supply Chain Management, Business
Process Re-engineering, etc. This family deviates from the traditional assumption
that the system is fixed and its dominant features, introducing types of system com-
plexity related to the following:
• The topology of interconnections is not fixed but may vary through the life cycle
of the system (Variability of Interconnection Topology Complexity).
• The overall system may evolve through the early–late stages of the design process
(Design Time Evolution).
• There may be variability and/or uncertainty on the system’s environment dur-
ing the life cycle requiring flexibility in organization and operability (Life Cycle
Complexity).
• The system may be large scale and multicomponent, and this may impact on
methodologies and computations (Large Scale—Multicomponent Complexity).
• There may be variability in the Organizational Structures of the information and
decision-making (control) in response to changes in goals and operational require-
ments (Organizational Complexity Variability).
The above features characterize a new paradigm in systems theory and introduce
major challenges for Control Theory and Design and Systems Engineering. There

1 Complex Systems and Control: The Paradigms of Structure Evolving Systems … 5
are different forms of structure evolution. Integrated System Design has been an area
that has motivated some of the early studies on SES. The integration of traditional
design stages [28], such as Process Synthesis (PS), Global Instrumentation (GS) and
finallyControlDesign(CD),isanevolutionaryprocessasfarmodelsystemformation
and two typical forms of evolution are the structural design evolution, the early–late
design evolution and the interconnection topology evolution [32]. Methodologies
and tools developed for Fixed Structure Systems (FES) cannot meet the challenges
of the SES class and new developments on the level of concepts, modelling, analysis
and synthesis methodologies are needed. The research is influenced by the need to
address life cycle and redesign issues, and such problems have a strong technological
and economic dimension.
System of Systems: The notion of “System of Systems” (SoS) has emerged in many
fields of applications from air traffic control to constellations of satellites, integrated
operations of industrial systems in an extended enterprise to future combat systems
[23, 50]. Such systems introduce a new systems paradigm with main characteris-
tic the interaction of many independent, autonomous systems, frequently of large
dimensions, which are brought together in order to satisfy a global goal and under
certain rules of engagement. These complex multisystems are very interdependent,
but exhibit features well beyond the standard notion of system composition. They
represent a synthesis of systems which themselves have a degree of autonomy, but
this composition is subject to a central task and related rules defined as “system plays”
[33] expressing the subjection of subsystems to a central task. This generalization
of the interconnection topology notion introduces special features and challenging
problems, which are different than those linked to the design of traditional systems
in engineering. The distinguishing features of this new form of complexity are as
follows [32]:
• The role of “objects” or “subsystems” of the traditional system definition is taken
by the notion of the autonomous agent, and it is characterized by some form of
intelligence. This is linked to the notion of “integrated intelligent system” defining
an autonomous intelligent agent.
• The notion of “interconnection topology” of traditional systems is generalized to
that of “systems play” which is expressed at the level of goals of autonomous
intelligent agents [71].
• Decision-making and control are linked to the nature of the “systems play” which
among other fields may be linked to cooperative control, game among the subsys-
tems, etc.
• System organization (Hierarchical-Multilevel, Holonic [67], etc.) defines an inter-
nal form of system structure and this plays a central role in the characterization of
the notion of emergent properties.
The problem of Systems Redesign has been only partially addressed in engineering
as redesign of control structure in response to faults, and it has been an active area
in business [65]. This problem may be considered within the framework of Inte-
grated Systems Design and leads to problems in the SES area [32]. Understanding
the issues linked to SES and SoS is critical in addressing the problem in its entirety

from an engineering perspective. Addressing the issues of SES and SoS has important
implications for the underpinning Control Theory and related Design methodologies.
Control Theory and Design has developed considerably in the last 40 years. How-
ever, the underlying assumption has always been that the system has been already
designed and thus control has been viewed as the final stage of the design process
on a system that has been formed. The new paradigms deviating from the “fixed sys-
tem structure assumption” introduce new challenges for Control Theory and Control
Design. These force us to reconsider some of the fundamentals (viewing Control as
the final design stage on a formed system) and create the need for new developments
where Control provides the concept and tools intervening in the overall design pro-
cess, even at stages where the system is not fixed but may vary, and may be under
some evolution. Traditional Control has been capable to deal with uncertainty at the
unit process level, but now has to develop to a new stage where it has to handle issues
of structural, dynamic evolution of the system as well as control in the context of
a “systems play”. The paper aims to provide an overview of these new areas, deal
with issues of representation, examine different forms of system evolution, define
the relevant concepts and tools, provide a systems based characterization of SoS, and
introduce a research agenda for these new paradigms. Integral part of the effort is the
linking of these new challenges to well-defined systems and control concepts and
methodologies.
The paper is structured as follows: Section 1.2 reviews the notions of the system
and summarizes the emergent forms of complexity. In Sect. 1.3, we review the three
major engineering problems which introduce types of complexity, that is, the prob-
lems of Integrated Design, Integrated Operations and Re-engineering, and identify
the different types of systems complexity which will be the main subject of the sub-
sequent sections. Section 1.4 deals with the evolution of models from the early to late
design stages, different types of system evolution are considered and the problems
associated with them are specified. We consider external and then internal system
representations. We examine the notion of a Progenitor model and the derivation of
models for control design. This is linked to a form of evolution where the input and
output system dimensions are reduced and considered in Sect. 1.5. An alternative
formulation based on internal descriptions, where a process graph is defined with
fixed nodal cardinality and subsystem models of variable complexity, and or fixed
dynamics of subsystems and variable nodal cardinality. The evolution of systems
linked to the cascade design process is considered in Sect. 1.5. We consider an evo-
lution type linked to system composition by design of the interconnection graph, and
then additional types of evolution associated with the selection of sets of inputs and
outputs, referred to here as “systems instrumentation”. Within the latter category,
we distinguish two distinct forms of evolution, the introduction of orientation in
implicit models and the model projection problems. Section 1.6 deals with multidi-
mensional system view linked to an integrated hierarchical structure and introduces
system aspects related to the variable complexity and a different nature of subsys-
tem models. We also provide a characterization of system and emergent properties
for the system. The notion of System of Systems (SoS) is considered in Sect. 1.7.
We review first the relative literature which provides an empirical definition of this

notion. We then introduce the notion of the Integrated Autonomous System which
is integral part of the new systemic definition for SoS. The crucial element of the
new definition is the notion of the “systems play” and its characterization in terms of
standard systems and control concepts and methods is considered. Finally, Sect. 1.8
provides the conclusions, which are in the form of a research agenda for such new
families of complex systems.
1.2 The Notion of the System
The development of a systems framework for general systems is not a new activity
[52]. Such developments have been influenced predominantly by the standard engi-
neering paradigm. Addressing the variety of new paradigms emerging in man-made
systems requires a further development of the standard notion [31]. We will recon-
sider existing concepts and notions from the general systems area, detach them from
the influences of specific paradigms and generalize them appropriately to make them
relevant for the new challenges. We use the following standard systems definition.
Definition 1.1 A system is an interconnection and organization of objects that is
embedded in a given environment.
This definition is very general and uses as fundamental elements the primitive notions
of objects, connectivities–relations (topology), and environment, and for man-made
systems involves the notion of system purpose, goal. It can be symbolically denoted
as in Fig.1.1.
Fig. 1.1 The notion of the system

The notion of the object is considered to be the most primitive element, or a system
and this allows us to use it in any domain. We define the notion of the object as:
Definition 1.2 An object, B, is a general unit (abstract, or physical) defined in terms
of its attributes and the possible relations between them.
Remark 1.1 This definition of a system is suitable for the study of “soft”, as well
as “hard” systems and it is based on a variety of paradigms coming from many and
diverse disciplines. It refers essentially to simple systems since issues of internal
organization are reduced only to the interconnection topology. Systems with internal
organization will be referred to as integrated systems and they will be considered in
the following section. These definitions do not make use of notions such as causality,
input–output orientation, definition of goal, behaviour, and so on. Quite a few systems
do not involve these features, and thus they have to be introduced as additional
properties of certain families.
A more explicit description of the notion of the system that involves some form
of orientation and which also describes the basic signals is given in Fig. 1.2 where
the basic variables are also included. These are the control inputs u, the outputs y,
the internal variables z, the input connections e and output connections w. Note that
input and output influences are the result of the given system being embedded in a
larger system; v may also represent disturbances. For composite systems having μ
subsystems Sa, j we denote by dv, j , dq, j the dimensions of the input and output influ-
ences of Sa, j ; then μ will be referred to as the order and

dv, j , dq, j

, j = 1, ..., μ

as the cardinality of the order composite system.
Issues of complexity are naturally connected with the above description and they
may be classified in the following categories:
• Objects, Subsystems nature and their variability
Fig. 1.2 The notion of the system with the basic variables

• Interconnection topology variability (variability of order and cardinality)
• Internal System Organization (non-simple systems)
• Embedding the system to a larger system
• System Design and Redesign
• System Operations
• System Dimensionality
• Support activities related to Data, Information and Computations
• Uncertainty in system description
Central to all above categories of system complexity are issues of system variabil-
ity due to different types of evolution. The paper is considering the different types
of evolutionary processes described above.
1.3 Integrated Design and Operations
The problem of system integration in engineering systems is a technological chal-
lenge, and it is perceived by different communities from different viewpoints. Sys-
tems Integration means linking the different stages of systems design in the shaping
of the system, relating the functions of system operations and establishing a frame-
work where operational targets are translated to design tasks. This problem has been
treated mostly as a software problem, and the multidisciplinary nature of the problem
(apart from software and data) has been neglected. The significance of integration
has created some urgency in working out solutions to difficult problems and this has
led to the development of interdisciplinary teams empowered with the task to create
such solutions. The key issue here is the lack of methodology that bridges disci-
plines and provides a framework for studying problems in the interface of particular
tasks. The problem of integrating design has been considered in [22, 28, 63]. Recent
developments in the area of hybrid systems [5], new developments in the area of
organization and overall architectures [67] contribute to the emergence of elements
for the integration of system operations. There are, however, many more aspects
of the effort to develop a framework of integration which are currently missing. A
general view of manufacturing systems involves the following [22]:
1. System Design Issues
2. Operational Issues–Signals and Operations
3. Business Activities
4. Vertical Activities–Data, IT, Software
The diagram indicates a natural nesting of problem areas, where design issues provide
the core, linked with the formation of the physical process that realizes production.
Production-levelactivitiestakeplaceonagivensystem,theyaremostlyorganizedina
hierarchical manner and they realize the higher level strategies decided at the business
level. Vertical activities are issues going through the Business–Operations–Design
hierarchy and they have different interpretations at the corresponding level. The

Physical Process Dimension deals with issues of design–redesign of the Engineering
Process and here the issues are those related to integrated design [8, 22, 28, 49,
57, 58]. The Signals, Operations Dimension is concerned with the study of the
different operations, functions based on the Physical Process and it is thus closely
related to operations for production. In this area, signals, information extracted from
the process are the fundamentals and the problem of integration is concerned with
understanding the connectivities between the alternative operations, functionalities
and having some means to regulate the overall behaviour. Both design, operations
and business generate and rely on data and deploy software tools, and such issues are
considered as vertical activities. Compatibility and consistency of the corresponding
data structures and software tools express the problem of software integration.
The operation of production of the types frequently found in the Process Industries
relies on the functionalities, which are illustrated in Fig.1.3. Such general activities
may be grouped as [22] (i) Enterprise Organization Layers, (ii) Monitoring functions
providinginformationtoupperlayersand(iii)Controlfunctionssettinggoalstolower
layers. The process unit with its associated Instrumentation are the primary sources
of information. However, processing of information can take place at the higher layer.
Control actions of different nature are distributed along the different layers of the
hierarchy.
The main layer of technical supervisory control functions involves [22, 58]: Qual-
ity Analysis and Control; State Assessment, Off Normal Handling and Maintenance;
Supervisory control and Optimization; and Identification, Parameter Estimation,
Data Reconciliation. These are of supervisory nature activities and refer to the pro-
cess operator. The automated part of the physical process refers to Process control
and involves [22, 58] Regulation, End Point and Sequence Control; Emergency Pro-
tection; and Process Instrumentation and Information System.
It is apparent that the complexity of operating the production system is very
high. A dominant approach as far as organizing such activities is through a Hierar-
chical Structuring [53] considered here. However, other forms of organization have
emerged [67], but their full potential has not yet been explored. The study of Industrial
Processes requires models of different types. The borderlines between the families
of Operational Models (OM) and Design Models (DM) are not always very clear
and frequently the same model may be used for some functions. Handling the high
complexity of the overall system is through aggregation, modularization and hierar-
chization [8], and this is what characterizes the overall OPPCP structure described in
Fig.1.3. The production system may be viewed as an information system, and thus
notions of complexity are naturally associated with it [49].
It is clear that for engineering-type problems the notion of the system emerging is
moreelaboratethanthenotionof the simplesystem introducedintheprevious section.
Systems produced as results of design with operations expressing the functionalities
related to the system goal may be referred to as integrated systems. Such systems
have the design process linked to the physical (engineering) process and an internal
organization referred to the different operational functionalities, and all these are
supported by signals and data. The integrated system has forms of complexity which
may be classified as

Fig. 1.3 System and its operational hierarchy © [2011] IEEE. Reprinted, with permission,
from [22]
1. Integrated Design types of complexity
2. System organization types of complexity
3. System of Systems type of complexity
4. System Re-engineering types of complexity
Note that engineering design is an iterative process and we may distinguish early
stages of design and late stages of design [32]. The transition from early to late design
is expressed by models of variable complexity, and this introduces a notion of model

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*** START OF THE PROJECT GUTENBERG EBOOK WARREN
COMMISSION (09 OF 26): HEARINGS VOL. IX (OF 15) ***

INVESTIGATION OF
THE ASSASSINATION OF PRESIDENT JOHN F.
KENNEDY

HEARINGS
Before the President's Commission
on the Assassination
of President Kennedy
Pursuant To Executive Order 11130, an Executive order creating a
Commission to ascertain, evaluate, and report upon the facts
relating to the assassination of the late President John F. Kennedy
and the subsequent violent death of the man charged with the
assassination and S.J. Res. 137, 88th Congress, a concurrent
resolution conferring upon the Commission the power to administer
oaths and affirmations, examine witnesses, receive evidence, and
issue subpenas
Volume
IX
UNITED STATES GOVERNMENT PRINTING OFFICE

WASHINGTON, D.C.
U.S. GOVERNMENT PRINTING OFFICE, WASHINGTON: 1964
For sale in complete sets by the Superintendent of Documents, U.S. Government
Printing Office Washington, D.C., 20402

PRESIDENT'S COMMISSION
ON THE
ASSASSINATION OF PRESIDENT
KENNEDY
Chief Justice Earl Warren, Chairman

Senator Richard B. Russell
Senator John Sherman Cooper
Representative Hale Boggs
Representative Gerald R. Ford
Mr. Allen W. Dulles
Mr. John J. McCloy
J. Lee Rankin, General Counsel
Assistant Counsel
Francis W. H. Adams
Joseph A. Ball
David W. Belin
William T. Coleman, Jr.
Melvin Aron Eisenberg
Burt W. Griffin
Leon D. Hubert, Jr.
Albert E. Jenner, Jr.
Wesley J. Liebeler
Norman Redlich
W. David Slawson
Arlen Specter
Samuel A. Stern
Howard P. Willens
A
Staff Members
Phillip Barson
Edward A. Conroy
John Hart Ely
Alfred Goldberg
Murray J. Laulicht

Arthur Marmor
Richard M. Mosk
John J. O'Brien
Stuart Pollak
Alfredda Scobey
Charles N. Shaffer, Jr.
Biographical information on the Commissioners and the staff can
be found in the Commission's Report.
A
Mr. Willens also acted as liaison between the Commission and
the Department of Justice.

Preface
The testimony of the following witnesses is contained in volume
IX: Paul M. Raigorodsky, Natalie Ray, Thomas M. Ray, Samuel B.
Ballen, Lydia Dymitruk, Gary E. Taylor, Ilya A. Mamantov, Dorothy
Gravitis, Paul Roderick Gregory, Helen Leslie, George S. De
Mohrenschildt, Jeanne De Mohrenschildt and Ruth Hyde Paine, all of
whom became acquainted with Lee Harvey Oswald and/or his wife
after their return to Texas in 1962; John Joe Howlett, a special agent
of the U.S. Secret Service; Michael R. Paine, and Raymond Franklin
Krystinik, who became acquainted with Lee Harvey Oswald and/or
his wife after their return to Texas in 1962.

Contents
Page
Preface v
Testimony of—
Paul M. Raigorodsky 1
Mrs. Thomas M. Ray (Natalie) 27
Thomas M. Ray 38
Samuel B. Ballen 45
Lydia Dymitruk 60
Gary E. Taylor 73
Ilya A. Mamantov 102
Dorothy Gravitis 131
Paul Roderick Gregory 141
Helen Leslie 160
George S. De Mohrenschildt 166
Jeanne De Mohrenschildt 285
Ruth Hyde Paine 331, 426
John Joe Howlett 425
Michael R. Paine 434
Raymond Franklin Krystinik 461
EXHIBITS INTRODUCED
Page

Commission Exhibit
No. 364 93
De Mohrenschildt
Exhibit No.:
1 277
2 278
3 279
4 279
5 279
6 279
7 279
8 279
9 279
10 279
11 279
12 282
13 282
14 282
15 282
16 26
Paine (Michael)
Exhibit No.:
1 437
2 441
Paine (Ruth) Exhibit
No.:
270 408
271 408
272 411
273 411
274 411
275 424
276 424

277 426
277-A 429
277-B 430
278 432
278-A 432
461 347
469 390
Raigorodsky Exhibit
No.:
9 25
10 25
10-A 25
10-B 25
11 26
11-A 26
14 26
14-A 26

Hearings Before the President's
Commission on the Assassination of
President Kennedy

TESTIMONY OF PAUL M.
RAIGORODSKY
The testimony of Paul M. Raigorodsky was taken at 11:15 a.m.,
on March 31, 1964, in his office, First National Bank Building, Dallas,
Tex., by Mr. Albert E. Jenner, Jr., assistant counsel of the President's
Commission.
Mr. Jenner. Mr. Raigorodsky, do you swear that in the testimony
you are about to give, you will tell the truth, and nothing but the
truth?
Mr. Raigorodsky. I do.
Mr. Jenner. Miss Oliver, this is Paul M. Raigorodsky, whose office
is in the First National Bank Building, Dallas, room 522, and who
resides in Dallas.
Mr. Raigorodsky. At the Stoneleigh Hotel.
Mr. Jenner. Who resides at the Stoneleigh Hotel in Dallas.
Mr. Raigorodsky, I am Albert E. Jenner, Jr., of the legal staff of
the Warren Commission, and Mr. Robert T. Davis, who is also
present, is the assistant attorney general of the State of Texas and is
serving on the staff of the Texas Court of Inquiry. The Commission
and the attorney general's office of Texas are cooperating in their
respective investigations.
The Commission was authorized by Senate Joint Resolution 137
of the U.S. Congress and was then created by President Lyndon B.
Johnson by Executive Order 11130 and its members appointed by

him. The Commission has adopted rules and regulations regarding
the taking of depositions. The Commission to investigate all the
circumstances of the assassination of President Kennedy.
We have some information that you are particularly well
acquainted with the overall so-called Russian emigre community in
Dallas, and you are an old time Dallasite, and while frankly we do
not expect you to have any direct information as to the
assassination, today, we think you do have some information that
might help us with respect to—using the vernacular—cast of
characters, people who touched the lives of Lee Harvey Oswald and
Marina Oswald, as the case might be, and as I understand it you
appear voluntarily to assist us?
Mr. Raigorodsky. Oh, sure.
Mr. Jenner. Helping out in any fashion your information may
assist us in that regard?
Mr. Raigorodsky. Sure.
Mr. Jenner. I think it will be well if you, in your own words, gave
us your general background, just give us your general background—
when you came to Texas and in general what your business
experience has been.
Mr. Raigorodsky. My background?
Mr. Jenner. Yes.
Mr. Raigorodsky. Well, commencing—I don't know where to start,
please?
Mr. Jenner. Well, where were you born?
Mr. Raigorodsky. I was born in Russia, I lived in Russia until I
was, oh, let's see, I escaped from Russia in 1919, went to
Czechoslovakia to the university there.
Mr. Jenner. You did what, sir?

Mr. Raigorodsky. I went to the university there and I am escaping
from Russia—I fought against the Bolsheviks in two different armies
and then came to the United States with the help of the American
Red Cross and the YMCA.
Mr. Jenner. When was that?
Mr. Raigorodsky. In December—the 28th, 1920.
Mr. Jenner. 1940?
Mr. Raigorodsky. 1920.
Mr. Jenner. How old are you, by the way?
Mr. Raigorodsky. Sixty-five—exactly.
May I have this not on the record?
Mr. Jenner. All right.
(Discussion between Counsel Jenner and the witness off the
record at this point.)
Mr. Jenner. All right, go ahead.
Mr. Raigorodsky. Well, I came to this country.
Mr. Jenner. In 1920?
Mr. Raigorodsky. Yes; and they told me that for the money that
they advanced for me to travel, that we only have to serve in the
United States for some capacity, so when I came in, I enlisted in the
Air Force and was sent to Camp Travis, Texas, and then in 1922 I
received an honorable discharge, and because it was I enlisted in
time of war, I became full-fledged citizen in 4 months after I arrived
to this country. We still were at war with Germany, the peace hadn't
been signed. And then I went to the University of Texas in 1922 and
graduated in 1924.
Mr. Jenner. What degree?
Mr. Raigorodsky. Civil Engineering. That's all they were giving,
even though my specialty is petroleum engineering, but I took

courses in different subjects.
By the way, first, I speak with accent and second, I speak with
colds, and you can stop me any time and I will be glad to repeat.
And, that was in 1924—then I went to work in Los Angeles, Calif.
I simultaneously married and that was in 1924. I married Ethel
Margaret McCaleb, whose father was with Federal Reserve Bank—a
Governor or whatever you call it.
Mr. Jenner. Federal Reserve Bank?
Mr. Raigorodsky. It was here in Dallas under Wilson in 1918—he
was appointed. At that time he was a banker and was organizing
banks. Then, I stayed in California for some—from 1924 until more
or less—until 1928. I worked as an engineer with E. Forrest Gilmore
Co.
Mr. Jenner. Is that a Dallas concern?
Mr. Raigorodsky. No; that was a California concern, specializing in
the building of gasoline plants and refineries. Then, I worked for
Newton Process Manufacturing Co. and for Signal Oil and Gas Co.—
just, that is, progressive—you see, it was going from one to another,
getting higher pay and things like that, and then in 1928 the Newton
Process Manufacturing Co. was sold out and three of us, I was at
that time chief process engineer, and the other man was chief
construction engineer, and the third one was chief operational
engineer—we organized a company called Engineering Research and
Equipment Co., and we started to build gasoline plants and
refineries. Then, I was sent to Dallas because our business was good
—I was sent to Dallas.
Mr. Jenner. Your business was growing?
Mr. Raigorodsky. Oh, yes; growing. I was sent to Dallas and I
organized an office here. Then, we moved the company from Dallas
and made the Los Angeles office a branch office. Then, I went to
Tulsa and opened an office of our company there, and that way we
were building lots of plants in Louisiana, in Texas, in Oklahoma.

Then, I sold out my third in 1929. It was a good time to sell out, and
I organized the Petroleum Engineering Co., which company I have
had ever since, until just now—it is inoperative.
Then, I continued to—I opened an office in Houston and
continued to build gasoline plants and refineries under the name of
Petroleum Engineering Co. and built about 250 of them all over the
world and in the United States—lots of them—even in Russia,
though I never went there, we had a protocol (I believe No. 4),
under which we were supposed to have given them some refineries
and gasoline plants—you know the chickens and the eggs
situation. The fact is I had an order from the Treasury Department
and one of them was sunk. Maybe this should be off the record?
Mr. Raigorodsky. Let's see, now, Pearl Harbor was in 1939?
Mr. Jenner. 1941; December of 1941.
Mr. Raigorodsky. 1941?
Mr. Davis. 1941.
Mr. Jenner. December 8th.
Mr. Davis. The war started in 1939.
Mr. Raigorodsky. Yes.
Mr. Jenner. The Germans invaded Poland in September 1939.
Mr. Raigorodsky. Already then we had the War Production Board,
though to begin with it was the Defense Board, and then War
Production Board, but I was asked to come to Washington. Now,
let's see, which year was it? Probably 1941—before the war.
Mr. Jenner. Before the war with Japan, you mean?
Mr. Raigorodsky. Before Pearl Harbor.

Mr. Raigorodsky. I was asked to come to Washington to organize
the Department of Natural Gas and Natural Gasoline Industries for
the United States, which I did, and then I had to open—I worked
under DeGolyer. I organized the Department from nothing until I had
five offices. We had districts in California and Tulsa and Chicago,
Houston and New York, and then in 1943 I resigned, and in the
meantime I got ulcer, you know, working like you do, until 11:30
nights, so in 1943 I resigned and came back to my business.
Mr. Jenner. Here in Dallas?
Mr. Raigorodsky. No, in Houston. At that time I officed in
Houston. By the way, while I was building plants for others, I also
built plants for myself for the production of motor fuel, L.P.G. and
other pipeline products, and the first plant was built in 1936—the
Glen Rose Gasoline Co. The second one was built in 1943—the
Claiborne Gasoline Co. Then, I lived in Houston until about 1949 or
1950 and I got sick with my back. You know, I have a very bad
back. They wanted to operate on me there but Jake Hamon here, a
friend of mine, told me that he wouldn't speak to me unless I come
to Dallas, so believe or not, they brought me to Dallas.
That's very interesting what I am going to tell you—in an
ambulance from Houston—and there was a Dr. Paul Williams—he
told me that without operation he would put me on my feet. I never
went back to Houston, even to close my apartment or to close my
office, but I moved my apartment and my offices here to Dallas and
I offered people that worked with me, that I would pay them for
whatever loss they had, because in selling their houses and moving
here, lock, stock and barrel, I never went back. I was so mad, and I
have lived here ever since with one exception. I believe it was in
1952—in 1952 I was asked by—you know General Anderson, by any
chance?
Mr. Jenner. No.
Mr. Raigorodsky. He was what we call—there was an organization
in Europe called SRE, Special Representatives to Europe. There was

an Ambassador Draper at the head of it, and Ambassador Anderson
is a Deputy, and in 1952 Ambassador Anderson asked me to come to
Europe and help them with production, so I went to Europe to
improve the production of tanks, planes, ammunition, et cetera for
all the NATO countries.
I was Deputy Director of Production. Now, I think I was getting
along all right and again I got sick in my neck this time, so they flew
me—they flew me to Johns Hopkins and found out that I had bad
neck. By the way, I'm not supposed to have this, but here is my
card.
(Handed instrument to Counsel Jenner.)
I left in such a hurry, they flew me under such pain, that I didn't
return anything, and I had to start to destroy most of the things,
and I didn't destroy this one. I stayed there for several months and
then I came back here and I have been here ever since, living here,
going to different places, going to Europe and I made trips to
Europe, Tahiti, Jamaica, and finally bought a plantation in Jamaica
together with some other friends here and we organized a club
called Tryall, T-r-y-a-l-l [spelling] Golf Club, and I go there every year
now. That's about all. My wife divorced me in 1943 for the primary
reason that I wouldn't retire. I have two daughters, one is Mrs.
Harry Bridges. That has nothing to do with the——
Mr. Jenner. With the Longshoremen?
Mr. Raigorodsky. That has nothing to do with the Longshoremen.
And off the record now.
record.)
Mr. Raigorodsky. In fact, I just came from the wedding. That's the
second marriage. Then, I have another daughter—maybe you know
my son-in-law, Howard Norris?
Mr. Davis. Where is he—in Washington?

Mr. Raigorodsky. Howard Lee Norris, he graduated, I think, in
1951 or 1952.
Mr. Davis. No, I don't think so. What business is he in?
Mr. Raigorodsky. Lawyer of the University of Texas.
Mr. Davis. No, I don't think so.
Mr. Raigorodsky. I am very proud of that. That's my child.
(At this point the witness exhibited wedding pictures to Counsel
Jenner.)
Mr. Jenner. This is your daughter on the left?
Mr. Raigorodsky. Yes. And, I will answer anything else you want
to now.
Mr. Jenner. All right. While living in the Dallas area, and I listened
to your splendid career, I assume that—and if this assumption is
wrong, please correct me—that the people of Russian descent who
came into this area of Texas would tend to seek your advice or
assistance, that you in turn voluntarily, on your own part, had an
interest in those people in the community and that in any event you
became acquainted with a good many people from Europe who
settled in this general area—in the Dallas metropolitan area and
even up into Houston?
Mr. Raigorodsky. Yes—Louise, will you get me my church file?
(Addressing his secretary, Mrs. Louise Meek.)
Mr. Jenner. Will you be good enough to tell me first, and Mr.
Davis, in general of the usual—if there is a usual pattern of someone
coming in here? How they become acquainted? What is the
community of people of Russian descent, and I do want to tell you in
advance that the thought I have in mind in this connection is trying
to follow the Oswalds.
Mr. Raigorodsky. That's right.

Mr. Jenner. What would be the common manner and fashion in
which the Oswalds would become acquainted, or others would
become acquainted with them, and before you get to that, that's
kind of a specific, I want you to give me from your fund of
knowledge and your interests—tell me what your interests have
been, what the expected pattern would be of people coming—like
Marina Oswald, for example, into this community?
Let's not make it Marina Oswald—I don't want to get into a
specific, but let's take a hypothetical couple?
Mr. Raigorodsky. All right. I can just summarize what happened in
the many years that I have been both in Houston and in Dallas.
There are methods of, I would say, of immigration into the
communities in Dallas of the Russians I'm talking about. One is via
friendship, acquaintanceship somewhere in Europe or in China or
somewhere else, but with different Russians and the order by the
Tolstoy Foundation—you are acquainted with the Tolstoy Fund?
Mr. Jenner. I think for the purposes of the record, since the
reader may not be acquainted with it, that you might help a little bit
on the Tolstoy Foundation.
Mr. Raigorodsky. Well, Miss Alexandra Tolstoy is a daughter of our
great novelist, Leo Tolstoy, and I guess you know him, and she came
to this country and she organized a Tolstoy Foundation, which takes
care of Russian refugees throughout the world wherever they may
be. They process them, which means that they know all about them
before they come into here through their own organization or your
different organizations. Like, you have a church in the United States
—you have a church organization or all kinds of benevolent
organizations that want to help refugees and they don't know who to
help so they go to the Tolstoy Foundation and therefore the Tolstoy
Foundation is able to place many, many Russians in this country, not
only in this country but—I am on the Board of Directors of the
Tolstoy Foundation—but also in European countries. Sometimes they
cannot bring them to the United States, not enough money perhaps.

Now, anybody who comes to the Tolstoy Foundation, you know right
off of the bat they have been checked, rechecked and double
checked. There is no question about them. I mean, that's the No. 1
stamp.
Mr. Jenner. That's the No. 1 stamp of an approval or of their
genuineness?
Mr. Raigorodsky. Of approval—in fact, the U.S. Government
recognized that and has been up until about a year or two ago
giving the Tolstoy Foundation as much as $400,000 a year subsidy
for this kind of work.
Now, of the other Russians that come here, as I said, they come
in through acquaintanceship—most of them.
Mr. Jenner. They come because of prior acquaintanceship?
Mr. Raigorodsky. With some.
Mr. Jenner. With some people who are here?
Mr. Raigorodsky. That's right—correspondence you see. Like we
have in Houston—we had a bunch of people coming from Serbia,
you know, Yugoslavia—the few we have that left Russia and went to
Yugoslavia and then they had to escape Yugoslavia, and there was
quite a Russian colony there and some of them drifted to the United
States and settled in Houston, and of course they start
correspondence and working and lots of other people came to
Houston and to Dallas through that channel.
Mr. Jenner. They followed?
Mr. Raigorodsky. Then, there is a small bunch of Russians that
appear from nowhere. I mean, they don't come with any approval
from Tolstoy Foundation or do they come through the
acquaintanceship of people here. They just drift and there's no
place, believe me, in the world where you cannot find one Russian.
Now, I would like this off the record.
Mr. Jenner. All right. Off the record.

Mr. Jenner. All right. Now, let's have this on the record.
Mr. Raigorodsky. Now, because of my—I always believe that even
though I am, myself, not much of a churchgoing man, but I believe
that the only way to unite Russians, and I think they should be
united in this country, was through a church, so, for many years we
had a church in Texas—at Galveston—but that church—we didn't like
because the Serbian priest, they were coming over there. We
couldn't figure it out, whether they were one side of the fence or the
other.
Mr. Jenner. One side of what fence or the other?
Mr. Raigorodsky. Well, the only fence I know of is between the
communism and the anticommunism.
Mr. Jenner. All right. You are on the anticommunistic side of the
fence?
Mr. Raigorodsky. Oh; of course.
Mr. Jenner. I want that to appear on record is why I asked.
Mr. Raigorodsky. Oh, yes; I have been all my life. So, let's see,
maybe in 1949 or thereabouts—I have donated quite a bit of money
to the Russian colony in Houston there with the understanding that
if they would secure at least 50 percent of additional money from
the rest of the people of the Russian colony, that they buy or build a
church there, which they did.
Mr. Jenner. What religion is that—the name of the church?
Mr. Raigorodsky. Russian—Greek Orthodox. You may call it also
Eastern Greek Orthodox. It's the same religion as Greek Catholics
have with two main differences—one is the language in which the
service is performed is the old Slavic languages against Greek, and
then, of course, we have our own Patriarch at the head of our own
church.

Mr. Jenner. In Houston?
Mr. Raigorodsky. Oh, no, no; we have in New York—it's
Metropolitan Anastasia, who is the head of our church of this
country.
Mr. Jenner. Who was the pastor over in Houston?
Mr. Raigorodsky. Well, I will come to that.
Mr. Raigorodsky. Then, when we got to—when I came to Dallas
we had Father Royster here of the church, I mean, he is a convert.
He is an American convert to the Greek Orthodox religion and he
approached me because he wanted to build the Church of St.
Seraphim in Dallas.
Mr. Jenner. You must be acquainted with Father Royster?
Mr. Raigorodsky. He knows me very well, but anyhow, here it is
about the church here——
Mr. Jenner. The full name is Dimitri Robert Royster—go right
ahead.
Mr. Raigorodsky. (Handed instrument to Counsel Jenner.) That
gives us the history of the situation here, but then we had a split
here between the Russians who came to this country escaping the
Communists or Bolsheviks, at that time we called them—they called
themselves the Guard.
Mr. Jenner. The original church that you helped organize, that is
referred to as the Old Guard?
Mr. Raigorodsky. That's right, and St. Seraphim you see, because
we both occupy the same premises and I was the head of both of
them.
Mr. Jenner. You were the head of both churches?
Mr. Raigorodsky. Oh, yes; I belong to both churches. In fact I
belong to three churches.

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