HN-Models in Control

SOME MODERN TRENDS
IN CONTROL THEORY
Dmitry A. Novikov
dan@ipu.ru, www.ipu.ru, www.mtas.ru
Institute of Control Sciences RAS
Moscow
Institute of Physics and Technology
Moscow

1. HISTORY AND TRENDS OF CONTROL THEORY
2. HIERARCHICAL AND NETWORKED MODELS
3. INTERDISCIPLINARY CONTROL MODELS
4. EMPHASIS OF RECENT CONFERENCES
5. MULTIAGENT SYSTEMS: SPECIFICITY AND ARCHITECTURE OF AN
AGENT
6. HIERARCHICAL MODELS (EXAMLES):
- Diffusive bomb
- Social networks
- Combat modeling
7. SOME TRENDS IN NETWORKED AND HIERARCHICAL MODELING
8. CONTROL THEORY: ANTI-INTUITIVE RESULTS (EXAMPLES)
- Optimization of hierarchies
- Labor supply
- Ecology VS Economy
- Is truthtelling profitable?
- Hierarchical automatization
9. PAST, PRESENT AND FUTURE OF CONTROL THEORY
PLAN

STRUCTURE OF CONTROL SYSTEM
…
Control is “the process of checking to make certain that
rules or standards being applied” (Macmillan Dictionary).
Control is “the act or activity of looking after and making
decisions about something” (Merriam-Webster Dictionary).
Control is “an influence on a controlled system with the
aim of providing the required behavior of the latter” (Theory of
Organizations Control)
CONTROL SYSTEM
CONTROLLED OBJECT
State
of
controlled
object
Control
External disturbances

OBJECTS, METHODS AND MEANS OF CONTROL
CONTROL
OBJECTS METHODS
MEANS
Measuring,
transformative,
actuating
Informational,
computational
…
Control is “the process of checking to make certain that
rules or standards being applied” (Macmillan Dictionary).
Control is “the act or activity of looking after and making
decisions about something” (Merriam-Webster Dictionary).
Control is “an influence on a controlled system with the
aim of providing the required behavior of the latter” (Theory of
Organizations Control)

Scientific knowledge
about the object of control
Control theory
Applications
Technologies of control …
…
t
Typical time of development
CYCLE OF THEORY DEVELOPMENT

t
1860-е 1900 1930 1940 1950 1960 1970 1980 1990 2000 2010
Конец
XVIII
века
150 YEARS OF CONTROL THEORY (Technics)
Scientific knowledge
about the object of control
Control theory
Applications
Technologies of control …
…
t
Typical time of development

Institute of Control Sciences (ICS RAS, Moscow):
- System Theory and General Control Theory;
- Techniques of Control in Complicated Engineering and Man-Machine
Systems;
- Theory of Control in Inter-Disciplinary Models of Organizational, Social,
Economic, Medical and Biological and Environment Protection Systems;
- Theory and Techniques in Development of Software-and-Hardware and
Engineering Tools of Control and Complicated Data Processing and Control
Systems;
- Scientific Fundamentals of Technologies in Vehicle Control and Navigation;
- Scientific Fundamentals of Integrated Control Systems and Automation of
Technological Industrial Processes.
USA: CalTech, Harvard Univ., MIT, Stanford Univ.,
Univ. of California, etc.
UK: Imperial College, Oxford Univ., Cambridge
Univ., etc.
Germany: Univ. of Stutgard, Techn. Univ. of
Darmstadt , etc.
Italy: University of Rome, Politecnico di Torino,
Politecnico di Milano, etc.
France: SUPELEC Paris, Univ. of Grenoble, LAAS-
SNRS Toulose,etc.
Australia: Univ. of New-castle, Australian Nat. Univ., etc.
Sweden: University of Linkoping, Lund University.
Japan: Japan Advanced Inst. of Science and Techn.,
Kyoto Univ., etc.
CONTROL THEORY IN RUSSIA
… and in the World
…

SCIENTIFIC RESEARCHES
AND APPLIED PROJECTS OF ICS RAS. I
Classical linear
control theory
Control of
mechanical
systems
Nonlinear
systems
Control in quantum
systems
Control of
systems with
distributed
parameters
Theory of stability
and stabilization
Control of moving
objects
Robust and
adaptive
control
General
control
theory
)(),,(
.
twtuxfx +=

Study of control problems for a multi-
mode submarine in the case of
emergency. The intelligent control level
is based on production rules for
current and predicted situations
Full-scale multi-mode computer
training complex for Russian Navy
General view of the training complex
AND APPLIED PROJECTS OF ICS RAS. II

Integrated solutions for upper level control systems in nuclear power
engineering with application in Russia and abroad
ØProgramming language
ØOperating system
ØEngineering equipment (in
cooperation with the Nizhny Novgorod
Scientific Research Institute for
Engineering Systems)
ØApplied software
AND APPLIED PROJECTS OF ICS RAS. III

Equipment for automation devices and computers
New effects in nanostructures
Modern jet devices
(operable up to 500˚ C, in vibration and
radiation environment)
Multi-channel sensors
AND APPLIED PROJECTS OF ICS RAS. IV

Aviation maps
Navigation maps
Digital topographic mapsLarge-scale plans
Digital relief matrix
3D-modeling
3D-modeling
Map making by field survey
Map updating by air survey
Map updating by space survey
Geographic Information Systems
AND APPLIED PROJECTS OF ICS RAS. V

3D-Modeling in control
AND APPLIED PROJECTS OF ICS RAS. VI

APPLICATIONS OF CONTROL THEORY

USA (NSF) priorities:
Group control. Combat control. Control
in financial and economic systems.
Control in biological and ecological
systems. Man and team in a control loop.
Unified theory of control, computation
and communication (С3). …
European priorities:
Man-machine symbiosis (modeling a man
in a control loop and as a controlled
subject).
Distributed and networked systems.
Production, safety and strategies of
heterogeneous control. New principles
of interdisciplinary coordination and
control. …
Russian Academy of Sciences:
Methods and means of communicational and networked
control of multi-level and distributed dynamic systems
under uncertainty; intellectual control.
HETEROGENEOUS =
DIVERSIVE(NETWORKED)
+ DISTRIBUTED
+ HIERARCHICAL
(controlled object, control system and communications).
HETEROGENEOUS CONTROL MODELS

HIERARCHIES AND NETWORKES:
CONTROLLED OBLECT, CONTROL SYSTEM
AND COMMUNICATIONS
(example: Project Management)
FROM NETWORKES AND HIERARCHIES
TO HIERARCHIES OF NETWORKES
AND NETWORKES OF HIERARCHIES
Пакет работ
Уровень
WBS
Уровень
WBS
Уровень
WBS
Пакет
работ
Пакет
работ
Пакет
работ
Пакет
работ
Пакет
работ
Пакет
работ
. . . . . .
Центр
Центр
Центр
OBS
Руководство проекта
Пакет
работ
План
y * A'Î
Результат
деятельности
z A0Î
Действие)
y А'Î
ЦентрЦентр Центр
АЭ АЭ АЭ АЭ АЭ АЭ
RBS
Функциональная структура предприятия
Стимулирующее воздействие
Группа
проектов
ПроектПроектПроект
Уровень проектов
NETWORK
SHEDULE
WBS OBS
RBS
Responsibility
allocation
Resources
allocation
Authority
allocation
Степеньдостиженияпоставленныхцелей
Время реализации
Исходное
состояние
Целевое
состояние
Оценка
состояния
Планируемое
состояние
Реальное
состояние
Плановая
траектория
Реализуемая
Прогноз
реализуемой
Возможная
траектория в рамках
существующей
стратегии (работа над
ошибками)
Оценка затрат для
возврата на плановую
траекторию развития

200019501940 1960 1970 1980 1990
Theory of automatic control
Game theory, operations research
Cybernetics
Decision-making, ;public choice theory
Mechanism design (MD)
Multiagent systems(DAI)
Discrete optimization, optimal control
2010
Network structures (С3
)
Organizational
systems
(MAN)
Social
systems
(SOCIETY)
Ecological
systems
(NATURE)
Technico-organizational
and man-machine
systems Ecologo-
economical
systems
Economical
systems
PRODUCTION
Regulatory-
axiological
systems
Noospheric
systems
Socio-ecological
systems
Technical
systems
Socio-
economical
systems
INTERDISCIPLINARY SYSTEMS

Optimization of hierarchical
and network structures
Territory
Government
Industry
Enterprise
Coordination of interaction and
decision-making in multiagent systems
Interests concordance in ecologo-
economical systems
Reflexive control
Mechanisms of organizations control
Temporal network
organization
А
Б В
Г
2 12 121А В ВА ВАВ
EXAMPLES OF INTERDISCIPLINARY SYSTEMS
Confrontation
Hierarchies
Collective
Decision-making
Cooperative
Control
Interaction.
Distributed
Optimization (e.g.
Task Assignment)
Mission Planning
“Implementation”.
Formation Control
Stabilization.
Consensus Problem
Operational level
Action
Tactical level
Strategic level
(decision-making,
adaptation, learning,
reflexion)
Level of goal-setting and
choice of functioning
mechanisms
Externalinformation
Dynamicsystems
Artificial
Intelligence
Modelsof
CollectiveBehavior
GameTheory

GENERAL TOPICS
ACC-2011***
*CDC – Conference on Decision and Control
ECC – European Control Conference
12-15 December 2011
Organized by IEEE, Orlando, Florida
> 1500 papers
**IFAC World Congress
28 Aug – 2 Sept., 2011
> 1500 papers
***ACC – American Control Conference
29-30 June 2011
Organized by IEEE, San Francisco, USA
> 900 papers
CDC-ECC-2011*
Математи-
ческая
теория
9%
Приложения
19%
"Cредства"
4%
"Классика"
49%
"Сетевизм"
19%
Applications
19%
Mathematical
theory
9%
Technical means
4% “Networks”
19%
Classic
49%
"Сетевизм"
11%
"Классика"
32%
Cредства
5%
44%
Математи-
ческая теория
9%
IFAC-2011**
Applications
44%
“Networks”
11%
Classic
32%
Mathematical
theory
9%
Technical means
5%
Математи-
ческая теория
5%
33%
Cредства
5%
"Классика"
42%
"Сетевизм"
14%
Technical means
5%
Applications
33%
Mathematical
theory
5%
Classic
42%
“Networks”
14%

МАС и
консенсус
35%
Кооператив-
ное
управление
21%
Коммуникации
в МАС
35%
Верхние
уровни
управления
4%
Другое
4%
Highest
control levels
4%
Communi-
cations in MAS
35%
Cooperative
control
21%
Consensus
problems
35%
Others
4%
Другое
8%Верхние
уровни
10%
Коммуникации
в МАС
26%
Кооператив-
ное
10%
МАС и
консенсус
46%
Highest
control levels
10%
Communi-
cations in MAS
26%
Cooperative
control
10%
Consensus
problems
46%
Others
8%
МАС и
консенсус
33%
Кооперативное
15%
Коммуникации в
МАС
31%
Верхние уровни
13%
Другое
8%
Highest
control levels
13%
Communications
in MAS
31%
Cooperative
control
15%
Consensus
problems
31%
Others
8%
«NETWORKS»
II
I III
IV
ACC-2011
СDС-ECCC-2011 IFAC-2011
II
I
III
IV
I
II
III
IV

Другие
19%
Морские
подвижные
объекты
2%
Автомобили и
автотрафик
11%
Биология и
медицина
13%
Мехатроника и
роботы
11%
Производство
2%
Авиация и
космос
9%
Энергетика
33%
Others
19%
Energetics
33%
Aero-Space
9%
Production
2%Mechatronics
and robots
11%
Maritime
mobile
objects
2%
Avto-vehicles
and traffic
11%
Bio-Med
13%
17%
Авиация и
космос
7%
18%
роботы
13%
Биология и
медицина
13%
13%
Морские
подвижные
объекты
3%
Другие
16%
Others
16%
Energetics
17%
Aero-Space
7%
Production
18%
Mechatronics
and robots
13%
Bio-Med
13%
Avto-vehicles
and traffic
13%
Maritime
mobile
objects
3%
Другие
8%Морские
подвижные
объекты
11%
8%
Биология и
медицина
17%
роботы
18%
8%
Авиация и
космос
8%
22%
Others
8% Energetics
22%
Aero-Space
8%
Production
8%
Mechatronics
and robots
18%
Bio-Med
17%
Avto-vehicles
and traffic
8%
Maritime
mobile
objects
11%
APPLICATIONS
ACC-2011
СDС-ECCC-2011 IFAC-2011

MULTIAGENT SYSTEMS (MAS)
«… a rat or individual locusts
are not too clever, and almost
harmless. However, flocks of
rats or swarms of locusts can
have a devastating impact».
Modern trends:
- decentralization
- miniaturization
- intellectualization

Centralized control
Decentralized (group) control
NETWORK
MAS
Material MAS
Virtual MAS
(softbots)
Wheeled UAVs AUVs…
Specificity of MAS:
üMultiple components;
üDistributed, networked
communications;
üHierarchy;
üIntelligence (autonomy):
• rationality (decision-making under
uncertainty and cognitive restrictions);
• autonomous goal-setting, goal-
oriented behavior;
• reflection;
• cooperative and/or competitive
interactions (the formation of
coalitions, information, and other
confrontation).
MULTIAGENT SYSTEMS: SPECIFICITY

MULTIAGENT SYSTEMS: ARCHITECTURE OF AN AGENT
Confrontation
Hierarchies
Collective
Decision-making
Cooperative
Control
Interaction.
Distributed
Optimization (e.g.
Task Assignment)
Mission Planning
Formation Control
Stabilization.
Consensus Problem
Operational level
Action
Tactical level
Strategic level
(decision-making,
reflexion)
mechanisms
Externalinformation
Dynamicsystems
Artificial
Intelligence
Modelsof
CollectiveBehavior
GameTheory

Confrontation
Hierarchies
Collective
Decision-making
Cooperative
Control
Interaction.
Distributed
Optimization (e.g.
Task Assignment)
Mission Planning
Formation Control
Stabilization.
Consensus Problem
Operational level
Action
Tactical level
Strategic level
(decision-making,
reflexion)
mechanisms
Externalinformation
Dynamicsystems
Artificial
Intelligence
Modelsof
CollectiveBehavior
GameTheory
MULTIAGENT SYSTEMS: CONSENSUS

Multi-agent system
( ) nitxtxatx
n
j
jiiji ...,,1,)()()(
1
=--= å
=
& – characteristic of agent i,)(txi,
),()( txLtx -=& ( ) ,)(...,),()(
T
1 txtxtx n=
[ ] ,ij n nL ´= l
ïî
ï
í
ì
=
¹-
=
å¹
.,
,,
)( ija
ija
t
ik
ik
ij
ijl
Theorem*
Consensus is reachable iff the communication graph is “connected”.
CONSENSUS PROBLEM
*Agaev R., Chebotarev P. (A&RC. 9. 2000)

Confrontation
Hierarchies
Collective
Decision-making
Cooperative
Control
Interaction.
Distributed
Optimization (e.g.
Task Assignment)
Mission Planning
Formation Control
Stabilization.
Consensus Problem
Operational level
Action
Tactical level
Strategic level
(decision-making,
reflexion)
mechanisms
Externalinformation
Dynamicsystems
Artificial
Intelligence
Modelsof
CollectiveBehavior
GameTheory
MULTIAGENT SYSTEMS: FORMATION CONTROL

С3 & FORMATIONS CONTROL
Basic consensus problem
( )ix t& =
1
( ( ) ( ))
n
ij j i
j
a x t x t
=
-å
Communications & computations
( )ix t& =
1
( )( ( ) ( ))
n
c
ij j ij i ij
j
a t x t x tt t
=
- - -å
Model of the controlled object
Autonomous Underwater Vehicles. Edited by N. Cruz. – Rijeka: InTech, 2011.
+ nonlinearity
+ observability
+ adaptivity
+ switching communication matrix
…
Formation control
( )ix t& = vi(t),
( )iv t& =
1
( ( ) ( ))
n
ij j i
j
b x t x t
=
-å +
1
( ( ) ( ))
n
ij j i
j
b v t v t
=
-å + ci(V(t) – vi(t))
x(t), v(t)V(t)

Confrontation
Hierarchies
Collective
Decision-making
Cooperative
Control
Interaction.
Distributed
Optimization (e.g.
Task Assignment)
Mission Planning
Formation Control
Stabilization.
Consensus Problem
Operational level
Action
Tactical level
Strategic level
(decision-making,
reflexion)
mechanisms
Externalinformation
Dynamicsystems
Artificial
Intelligence
Modelsof
CollectiveBehavior
GameTheory
MULTIAGENT SYSTEMS: PLANNING

Confrontation
Hierarchies
Collective
Decision-making
Cooperative
Control
Interaction.
Distributed
Optimization (e.g.
Task Assignment)
Mission Planning
Formation Control
Stabilization.
Consensus Problem
Operational level
Action
Tactical level
Strategic level
(decision-making,
reflexion)
mechanisms
Externalinformation
Dynamicsystems
Artificial
Intelligence
Modelsof
CollectiveBehavior
GameTheory
MULTIAGENT SYSTEMS: COOPERATIVE CONTROL

).,...,,,,...,,(maxArg *
,
*
1,
*
1,
*
1
*
niiiiiiiii
Xx
i xxxxxfx
ii
ssssss q +-
Î
Î
Informational equilibrium
Information control problem
.max),(min
)(
¾¾®¾F ÁÎYÎ IIx
Ix
X
YX (I) Í X' – the set of real agents
actions, which are stable under
information structure I;
F(x, I) – control efficiency criterion;
Á – set of feasible information
structures.
Taking into account the nontrivial mutual beliefs
of agents allows:
1. (normative point of view) to enlarge the set of
game’s outcomes, which in its turn increases
the efficiency of information control;
2. (descriptive point of view) to describe many
practically observed situations, which can not
be interpreted as a Nash equilibrium under
common knowledge, as informational
equilibriums under proper information
structure.
ГI = {N, (Xi)i Î N, (fi(×))i Î N, W, I} – reflexive game;
W – set of feasible states of nature;
I – information structure;
N – set of players (agents);
fi: W ´ X’ ® Â1
– goal function of the i-th agent.
Information (beliefs) structure
q1 qi qn
qi1 qij qin
… …
… …
I1
Ii1
Real agent
Phantom
agent
Reflexion
. . . . . .
. . .
. . .
INFORMATIONAL REFLEXION AND CONTROL

Reflexive model of group aircraft battle
Strategic behavior in collective decision-making. Suppose, that the
principal is interested in the result x0Î[d;D] of expert examination. Let the
opinions of n experts {riÎ[d;D]}iÎN, be known by the principal only, who is able
to form second-order beliefs of the experts. Collective decision x = p(s),
where s Î [d;D]n is the vector of opinions, revealed by experts. Denote:
x0i(a,ri) is the solution of the following equation:
p(a, …, x0, …, a) = ri , di(ri) = max {d; x0i(D, ri)}, Di(ri) = min {D; x0i(d, ri)},
d(r) = (d1(r1), d2(r2), …, dn(rn)), D(r) = (D1(r1), D2(r2), …, Dn(rn)).
Statement 15. Any result x0Î[p(d(r));p(D(r))] may be implemented as the
collective decision by means of information control with the second rank of
reflexion.
SOME APPLICATIONS OF INFORMATIONAL CONTROL

INFORMATIONAL AND STRATEGIC REFLEXION
«Optimizational models
of collective behavior
Models of games
Game theory
Models of
collective
behavior
Informational
structures
Concept of equilibrium
Informational
equilibrium
Nash
equilibrium
Control problems
Informational
control
MODELS OF STRATEGIC REFLEXION
Reflexive structures
k-level models;
cognitive
hierarchies
models, etc
Models of
reflexion in
bimatrix
games
Informational
reflexion
Strategic
reflexion
Prognostical
Reflexive
equilibrium
Reflexive
control
“Reflexive”
models
Level
Phenomenological
(descriptive)
Normative
Models of reflexive
decision-making
Game theory
(super-intelligent players)
Theory of collective
behavior
(rational agents)
LEVEL OF “INTELLIGENCE”
REFLEXION

«Probability» of target destruction:
ü Direct attack of 40 “simple” agents: 0,125
ü 8 «investigators» + 32 «reflexive» agents: 0,985
ü 40 «investigators»: 0,999
Level of
hierarchy
Modelled processes Modelling tools
6 Choice of agents and
their characteristics
Discrete and
multicriteria
optimization
5 Choice of agents’
trajectories and
velocities
Optimal control
4 Forecasting by the
agent opponents’
behavior
Reflexive games
3 Minimization of the
probability
of detection
Optimization and
heuristics of choosing
the direction of
motion
2 Collision and
obstacle avoidance
Algorithms of “local”
trajectories’ choice
1 Motion toward the
target
Equations of
dynamics
DIFFUSIVE BOMB MODEL: STRATEGIC REFLEXION

Confrontation
Hierarchies
Collective
Decision-making
Cooperative
Control
Interaction.
Distributed
Optimization (e.g.
Task Assignment)
Mission Planning
Formation Control
Stabilization.
Consensus Problem
Operational level
Action
Tactical level
Strategic level
(decision-making,
reflexion)
mechanisms
Externalinformation
Dynamicsystems
Artificial
Intelligence
Modelsof
CollectiveBehavior
GameTheory
MULTIAGENT SYSTEMS: CONFRONTATION

MODELS OF SOCIAL NETWORKS
The set M of
principals
The set of agents
N
…
Problem – find a control vector u, s.t.
F(X, u) = H(X) – c(u) ®
UuÎ
max ,
H(×) – “gain”, с(×) – control costs.
Each principal (from set M) is able to influence on the
initial opinions of the agents uij and is interested in
forming the final opinions XM.
Problem – find equilibrium of the game:
Г = (M, {Uj}j Î M, {Gj(×)}j Î M).
A set N of agents form social network G = (N, E).
x – vector of initial opinions, X – final opinions.
aij ³0 – the trust of i-th agent to j-th,
k-th agent indirectly influences
on i-th agent: xk+1
= A [xk
+ B uk
].
Problem – find total influence
of one agents on another,
find the agents, that form
the final opinions
3. Informational interaction (dynamics)
4. Informational control
5. Information warfare
Facebook
Twitter
Newsvine
Habr
2. Structural analysis
1. «Statistical» analysis

ANALYSIS AND MODELING
OF INFORMATIONAL PROCESSES IN SOCIAL MEDIA
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0
5000
10000
15000
Суточное количество сообщений : Политики A и B
0 10 20 30 40 50 60 70
?0.4
?0.2
0.0
0.2
0.4
0.6
0.8
1.0
Автокорреляционная функция по сообщениям : Политики A и B
0 20 40 60 80 100 120 140
?0.2
?0.1
0.0
0.1
0.2
0.3
0.4
0.5
Парная корреляционная функция по сообщениям
Политик A Политик B
11.11.11 06.12.11 31.12.11 25.01.12 19.02.12 15.03.12 09.04.12 04.05.12 29.05.12 23.06.12
11
10
9
8
7
6
5
4
3
2
1
Вейвлет скалограмма ?объём сообщений ?: Политик A
11.11.11 06.12.11 31.12.11 25.01.12 19.02.12 15.03.12 09.04.12 04.05.12 29.05.12 23.06.12
11
10
9
8
7
6
5
4
3
2
1
Вейвлет скалограмма ?объём сообщений ?: Политик B
Политическая жизнь России
Политик A Политик B
Общество / Блогосфера / СМИ
Активность
блоггеров
Активность
блоггеров
11.11 .11 06.12 .11 31.12.11 25.01 .12 19.02 .12 15.03 .12 09.04 .12 04.05.12 29.05 .12 23.06.12
0
20
40
60
80
100
Точки статистической разладки: Политик A
11.11.11 06.12 .11 31.12.11 25.01.12 19.02.12 15.03.12 09.04 .12 04.05.12 29.05.12 23.06.12
0
100
200
300
400
Точки статистической разладки: Политик B
Political activity
Person A Person B
Society / Blogoshere / Media
Blogers’ activity Blogers’ activity
Daily mentioned: persons A and B
Autocorrelation by persons
Autocorrelation by messages
Person BPerson A
Statistical discord: person A
Statistical discord: person B
Scalogramma: person B
Scalogramma: person A

Characteristics of maximal component
• Number of agents – 362.000,
• Number of “connections”– 802.000 (12.000.000 comments)
Structure of components
1 – Discussing component (25%).
2 - Un-popular component (45%).
3 – Popular component (8%).
4 - Others (22%).
The structure is time-stable:
• May 2011
• November 2011
• December 2011
45
The rate of information (average) spread
- 5.3 steps to receive information FROM any agent;
- 5.3 steps to transmit information TO any agent.
THE STRUCTURE OF MAXIMAL
WEAKLY CONNECTED COMPONENT
1
2
3
4

Number of removed nodes
Sizeofmaximalcluster(%)
Number of removed nodes
Numberofclasters
CONTROL IN SOCIAL NETWORKS
CONTROL:
- OPINIONS,
- BELIEFS (TRUST),
- REPUTATION,
- …
- MEMBERSHIP and STRUCTURE.
The removal of small number of the most
significant nodes leads to the appearance of a
great number of unconnected groups (А).
But this groups are small, and the largest
group is still connected (B).
ЧислоавторовЧислоавторов
64.000 – cumulative estimate of politically active blogers in
Russian LiveJournal
A
B

BACKGROUND: CONSENSUS PROBLEM
French J.R. A Formal Theory of Social Power // Psychological
Review. 1956. № 63. P. 181 – 194.
Harary F. A Criterion for Unanimity in French’s Theory of Social
Power / Studies in Social Power. – Michigan: Institute of Sociological
Research. 1959. P. 168 – 182.
De Groot M.H. Reaching a Consensus // Journal of American
Statistical Association. 1974. № 69. P. 118 – 121.
Roberts F. Discrete Mathematical Models with Applications to Social,
Biological, and Environmental Problems. – Prentice: Prentice Hall, 1976.
Jackson M. Social and Economic Networks. – Princeton: Princeton
University Press, 2008.

BACKGROUND: GAME THEORY
Network games
Network formation games Network-based games
Networking games
Cognitive games
Social networks games
Games over theproject network-schedules
Network – is a result of game-
theoretical interaction
Network isfixed and determines the
dependence of players gains fromtheir
actions

SOCIAL NETWORKS AND LINEAR DYNAMIC SYSTEMS
xk+1
= A [xk
+ B uk
], k = 0, 1, …
MULTIAGENT
SYSTEMS
SOCIAL NETWORKS COGNITIVE MAPS
PageRank Problem
ui
xi
F(X, u)

Level of
hierarchy
Modeled phenomena
and processes
Technique of modeling
5 Allocation of forces
and means in space
Game theory
(Colonel Blotto game,
etc.)
4 Allocation of forces
and means in time
Optimal control,
repeated games, etc.
3 Number of troops
dynamics
Lanchester’s equations
and its modifications
2 «Local»
interactions
of squads
Markovian and other
stochastic models
1 Interaction
of separate
battle units
Dynamic systems.
Finite state automata.
Simulation.
HIERARCHICAL COMBAT MODELS

20 40 60 80 100
Номер ИПБ
500
1000
1500
2000
МЦРMRRR
REFLEXIVE COLONEL BLOTTO GAME
Average maximal rational rank of
reflexion (MRRR) ~ 230 (nonsense!)
Denote by N = [1, …, n] the set of objects, x = (x1, …, xn) – first player’s action, y = (y1, …, yn) – second player’s
action, where xi ³ 0 (yi ³ 0) – amount of resources, allocated by the first (second) player to i-th object, i = 1,n .
Resources are limited
(1) i
i N
x
Î
å £ Rx, i
i N
y
Î
å £ Ry.
In probabilistic Colonel Blotto Model (CBM) the probability px(xi, yi) of the first player win on the i-th object
does not depend on other objects and is “proportional” to the amount or resources, allocated on this object.:
(2) px(xi, yi) =
( )
( ) ( )
i
i i
r
i i
r r
i i i
x
x y
a
a +
, py(xi, yi) = 1 – px(xi, yi), где ri Î (0; 1], ai > 0, px(xi = 0, yi = 0) =
1
i
i
a
a +
.
Let BRx(y) = (u1 y1 + e, …, un yn + e) denote the best response of first player, where n-dimentional vector u = (u1,…, un) is a solution of the
following knapsack problem: (3)
{0;1}
1
1
max,
,
i
n
i i
u
i
n
i i x
i
uV
u y R
Î
=
=
ì
®ï
ï
í
ï £
ïî
å
å
, e =
1
1
( )
n
x i i
i
R u y
n =
- å , i.e. let’s assume that the player tries to win on the most valuable set of
objects, and the rest of resources are equally divided among other objects.
Let BRy(x) = (v1 x1 + d, …, vn xn + d) denote the best response of first player, where n-dimentional vector v = (v1,…, vn) is a solution of the
following knapsack problem: (4)
{0;1}
1
1
max,
,
i
n
i i
v
i
n
i i y
i
vV
v x R
Î
=
=
ì
®ï
ï
í
ï £
ïî
å
å
, d =
1
1
( )
n
y i i
i
R u x
n =
- å .
Rank game
exploration
MRRR

1. HISTORY AND TRENDS OF CONTROL THEORY
2. HIERARCHICAL AND NETWORKED MODELS
3. INTERDISCIPLINARY CONTROL MODELS
4. EMPHASIS OF RECENT CONFERENCES
5. MULTIAGENT SYSTEMS: SPECIFICITY AND ARCHITECTURE OF AN
AGENT
6. HIERARCHICAL MODELS (EXAMLES):
- Diffusive bomb
- Social networks
- Combat modeling
7. SOME TRENDS IN NETWORKED AND HIERARCHICAL MODELING
8. CONTROL THEORY: ANTI-INTUITIVE RESULTS (EXAMPLES)
- Optimization of hierarchies
- Labor supply
- Ecology VS Economy
- Is truthtelling profitable?
- Hierarchical automation
9. PAST, PRESENT AND FUTURE OF CONTROL THEORY
PLAN

MODERN TRENDS IN MAS
1) Strategic
decision-making
2) Increasing role
of game-theory
3) Benchmark scenarios
and problems
Confrontation
Hierarchies
Collective
Decision-making
Cooperative
Control
Interaction.
Distributed
Optimization (e.g.
Task Assignment)
Mission Planning
Formation Control
Stabilization.
Consensus Problem
Operational level
Action
Tactical level
Strategic level
(decision-making,
reflexion)
mechanisms
Externalinformation
Dynamicsystems
Artificial
Intelligence
Modelsof
CollectiveBehavior
GameTheory

MAS & STRATEGIC BEHAVIOR: As Is
Game theory
MAS, group
control
Distributed
optimization

Game theory
MAS, group
control
Algorithmic game
theory
Distributed
optimization
Models of collective
behavior, bounded
rationality
MAS & STRATEGIC BEHAVIOR: As Is

Game theory,
mechanism design
MAS, group
control
Algorithmic game
theory
Distributed
optimization
Models of collective
behavior, bounded
rationality
Experimental
economics, Behavioral
Game Theory
MAS & STRATEGIC BEHAVIOR: To Be

«MAXIMAL INTELLECTUALIZATION»
Intention to maximize the
“intellectualization” is limited
not only by “costs”
(computational, cognitive,
economical, etc), but by the
inefficient “over-complexity”.
«Intellectualization»
«Costs»
«Result»
«Effect»

MAS: SOME QUALITATIVE RESULTS
1) The level of MAS’ “intellectualization” should
be adequate to the problem in hand (taking
into account various “costs”).
2) The intention to maximize the
“intellectualization” at the higher levels of
agent’s architecture leads to a centralized
scheme.
3) Trend to the integration of networked
MAS, game theory and artificial intelligence.

GENERAL TRENDS
1) Inter-disciplinary: control objects, methods and means of control.
2) Network/hierarchical structure of controlled object, control system and
communications.
3) Intra-paradigmal problems: «linearity» of development, desire to reduce the
problem to well-known, i.e. «internal» problems of any subject field. Self-
isolation of different braches of control science. The demand for the creation of
new adequate mathematical technique.
4) «Heuristical» applications: the concept of bounded rationality (under the lack
of time, ability or necessity) – instead of optimal pseudo-optimal solutions are
heuristically searched.
5) Unification:
5C = Control + Computation + Communication + Cost + Cycle.
6) Heterogeneous (hierarchical, complex, integrated) modeling. Problems of
models «coupling», search for common language. Generating and replicating
typical solutions of control problems.

K(rm) =
)(
max
mEy rÎ
f0(y) ®
ÃÎmr
max .
Вертикальные
связи
Горизонтальные
связи
А
Б В
Г
Временная
сетевая
организация
CNetwork
organization
Network organization -
a structure, where temporal
connections between the
elements are actualized for the
period of solving certain problem.
The problem of structural
synthesis: find the number of
levels of hierarchy m and
distribution of agents among the
levels (feasible structure rm), which
maximize the efficiency f0(y), given
that the agents in corresponding
hierarchical game choose their
equilibrium actions:
Examles:
- distributed production;
- IT-projects;
- group control, etc.
HIERARCHICAL AND NETWORK ORGANIZATIONS
Statement. For any technological structure and any
equilibrium x Î E1
N(rm) there exist the set of decision-
making strategies
in a game Г2(rm
0), which guarantees to all the
decision-makers the same levels of utilities, as in the
initial game.

OPTIMIZATION OF HIERARCHIES
Development of the organization
management structure
Data collection and processing
algorithms
Design of assembly plant Task management in network
structures
…
Optimization of
control hierarchy

LABOR SUPPLY (theory)
a
a0
t(a)
0
I = 1
a
a0
t(a)
0
I = 2
a
a0
t(a)
0
I = 3
a
a0
t(a)
0 amax
I = 4
a
a0
t(a)
0 amax
I = 5
t(a) – desired working time (hours/day), a – wage rate

Индекс (1999)
I
25%
II
53%
III
6%
IV
16%
Индекс (2009)
I
25%
II
41%
III
16%
IV
8%
V
10%
Sample volume
> 500
Sample volume
> 5000
LABOR SUPPLY (“practice”)
a
a0
t(a)
0
I = 1
a
a0
t(a)
0
I = 2
a
a0
t(a)
0
I = 3
a
a0
t(a)
0 amax
I = 4
a
a0
t(a)
0 amax
I = 5
t(a) – desired working time (hours/day), a – wage rate

Economic agents
(enterprises)
Environment
(NATURE)
Control Center
(principal)
Interaction with
environment
Results
of
activity
Control
State
of nature
ECOLOGO-ECONOMICAL SYSTEM
Model:
u ³ 0 – production level;
y ³ 0 – security level;
z(u), j(y) – enterprise’s costs;
Hi(u, y) – principal’s income;
si(u¢, u, x, y) =
î
í
ì
¹¹
==
'
'
или,0
,,
uuxy
uuxyVi
;
K = {1, 2, …, k} – the set of principals.
Goal function of i-th principal:
Fi(si(×), u, y) = Hi(u, y) – si(u, y), i Î K,
Goal function of the enterprise:
f({si(×)}, u, y) = c u + å
Î
s
Ki
i yu ),( – z(u) – j(y).
u*
= arg
0
max
³u
[c u – z(u)];
F*
i =
0,
max
³yu
[Hi(u, y) – c (u*
– u) + [z(u*
) – z(u)] – j(y)], i Î K;
S = {u ³ 0, y ³ 0 | $ V Î k
+Â : Hi(u, y) – Vi ³ F*
i, i Î K,
å
ÎKi
iV = c (u*
– u) – [z(u*
) – z(u)] + j(y)};
L = {u ³ 0, y ³ 0, V Î k
+Â | Hi(u, y) – Vi ³ F*
i, i Î K,
å
ÎKi
iV = c (u*
– u) – [z(u*
) – z(u)] + j(y)}.
F*
0 =
0,
max
³yu
[ å
ÎKi
i yuH ),( – c (u*
– u) + [z(u*
) – z(u)] – j(y)].
Theorem. The compromise set is not empty iff
F*
0 ³ å
Î
F
Ki
i
*
.
ECOLOGY VS ECONOMY
Territory
Government
Industry
Enterprise

The problem of project’s duration reduction
Model:
D – the required reduction of project duration;
yi – the required reduction of i-th operation duration;
xi – plan of reduction of i- th operation duration;
ri – «efficiency» of i-th agent;
N – set of agents (operations);
ci (yi, ri) = ri j (yi / ri) – costs function of i-th agent;
l – rate of payment for the reduction of project duration;
fi (yi, ri) = l yi – ci (yi, ri) – agent’s goal function;
s = (s1, s2, ..., sn) – agents’ message;
Theorem. The procedure of decision-making xi (D, s) =
V
si
D,
l (D, s) = j' (D / V), where V = å
ÎNi
is , is straightforward, minimizes
total costs and allows any decentralization.
Procedures of decision-making (examples):
manipulable non-manipulable
IS TRUTH-TELLING PROFITABLE?

HIERARCHICAL AUTOMATIZATION
INFORMATIONAL
SYSTEMS
OLAP, BSC, DSS
ERP
MES
SCM, CRM, PMS
MRP2
MRP, CRP
SCADA, DCS
PLC, MicroPC
Finances,
material
resources,
personnel
MRP2
MRP, CRP
SCADA,DCS
PLC, MicroPC
INFORMATIONAL
SYSTEMS
Control of
TS
«Optimization » Control of OS
OLAP, BSC, DSS
ERP
MES
SCM, CRM, PMS
? ?…

PAST, PRESENT AND FUTURE OF CONTROL THEORY
(objects of control)
1860-е 1900 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020 …
Mechanical
systems
Technical systems Organizational and
informational systems
Decentralized intellectual
systems
t
- Technical systems
- Economical systems
- Ecological systems
- Live systems
- Social systems
???
Степеньдостиженияпоставленныхцелей

«Relevancy»
“Application field”
«UNCERTAINTY» PRINCIPLE
(«Application field») x («Relevancy») £ Const
Mathematics
Psyghology,
Sociology,
Pedagogy
Economics
Biology
Chemesrty
Physics
“Weak” sciences
“Strong” sciences
CONTROL
THEORY
LIMITS OF SCIENCE

HN-Models in Control

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