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Control of LargeScale Complex Systems From Hierarchical to Autonomous and now to System of Systems

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Full (Original) Model: dx(t)/dt = Ax(t) Bu(t) y(t) = Dx(t) Reduced Model: ... Robotic Colonies, etc.,etc. WHAT ARE SYSTEM OF SYSTEMS? ... – PowerPoint PPT presentation

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Title: Control of LargeScale Complex Systems From Hierarchical to Autonomous and now to System of Systems


1
Control of Large-Scale Complex Systems From
Hierarchical to Autonomous and now to System of
Systems
  • Mo Jamshidi
  • Electrical and Computer Engineering Department
    and Autonomous Control
  • Engineering (ACE) Center
  • University of New Mexico, Albuquerque
  • moj_at_wacong.org

2
OUTLINE
  • Definition of a Large-Scale System
  • Modeling of Large-Scale Systems
  • Hierarchical Control
  • Decentralized Control
  • Applications
  • System of Systems

3
DEFINITION 1
A system is large in scale if it can be
decomposed into subsystems.

LSS
Hierarchical Control

ss1
ss2
ss3
ssN
4
DEFINITION 1, Contd.
Pictorial representation of system decomposition
and coordination, (a) An interconnected system
(b) a hierarchically structured system

5
DEFINITION 2
A system is large in scale if concept of
centrality no longer holds.

y
LSS
u
LSS
uN
CN
u2
y1
yN
Decentralized Control

C2
C1
y2
u1
6
LSS is

Associated with three concepts 1.
Decomposition 2. Centrality 3. Complexity
7
Modeling
There are 3 classes of models for Large-scale
systems Aggregation Perturbation Descriptive
variable

8
Aggregation, contd.
  • A 4th order system (left) has been approximated
    with 2nd order system (right)

Key properties, like stability, needs to be
preserved from system x to system z.
9
Aggregation, contd. 2
Full (Original) Model dx(t)/dt Ax(t)
Bu(t) y(t) Dx(t)
z(t) C x(t)
Reduced Model dz(t)/dt Fz(t) Gu(t)
y(t) Hz(t)
C is aggregation matrix
10
Balanced Aggregation
Full (A,B,D) ? Reduced (F,G,H)
  • Balanced Realization Aggregation
  • Principle Component Analysis
  • (A,B,C) gt (Ab, Bb, Cb), where
  • Ab A-1AS, Bb S-1B, C Cb S
  • S LcUS 1/2
  • U is orthogonal modal matrix
  • is the diagonal symmetric matrix of a certain
    eigenvalue / eigenvector problem
  • Lc is a lower triangular Cholesky factros of
    controllability Grammian Gc of (A,B)

11
Balanced Aggregation, Contd.
Transformed matrices (Ab, Bb, Cb) represent an
ordered diagonal set of modes with the most
controllable and most observable mode appearing
in location 1,1 of the matrices. Hence, F
Subset (Ab), G Subset (Bb), etc. Matlab m
files are available for all of the above
manipulation of model reduction.
12
PERTURBATION
An perturbed model of a system is described by
reduce model consisting of a structure
after neglecting certain interactions within the
model. Regular Perturbation weak couplings
Singular Perturbation strong Coupling
13
PERTURBATION, Contd. 2
SINGULAR Perturbation A mathematical process in
which a system's variables are designated
"slow" or "fast" in time-scale variations.
dx/dt Ax Bu dxs/dt Asxs Bsu
Asfxf ?dxf/dt Afxf Bfu
Approximation
Fast variable
14
PERTURBATION, Contd 3
SINGULAR Perturbation Boundary Layer Coorection
for fast variables. Boundary layer correction for
fast state z(t). ---, (t) , (t). ?(t).
15
Decentralized Controllers
Taken from the theory of large-scale (complex)
systems one can share the control action among a
finite number of local controllers
Input
Output
LARGE-SCALE SYSTEM
un
u1
. . .
Controller 1
Controller n
y1
yn
16
Hierarchical Controllers
Again, taken from the theory of large-scale
(complex) systems one can share the control among
a finite number of local controllers
Supreme Coordinator
a1
interaction factor
xn,un
state, control
an
x1,u1

Subsystem 1 (Coordinator)
Subsystem n (Coordinator)


Subsytem 1
Subsystem k
Subsystem m
Subsystem 1
17
LISA - Advanced Avionics Systems for Dependable
Computing in Future Space Exploration -
Astrophysics
Laser Interferometry Space Antenna (LISA)
18
Scenario A Hyperbolic (egt1) Flyby
19
Scenario B Elliptical Orbit of Planet with
Hyperbolic Flyby of Moon
Interval Array Activity Configuration
1 Plan / Service Probes docked
2 Deploy Probes depart Mothership
3 Data Collection Probes free-fall / payload
on 4 Recover Probes return to Mothership
Interval 4 Recover
?pE 0o
Fuzzy Transition From Hyperbolic to
Elliptical Model
?R
?f
Interval 1 Plan / Service
?pH 0o
?0
?D
Interval 3 Observation
Fuzzy Transition From Elliptical to
Hyperbolic Model
Interval 2 Deploy
20
Scenario C Continuous Elliptical (0ltelt1) or
Circular (e0) Observation
.
?p 0o
Deploy Probes
?p 0o
Maintain Formation - Adjust when formation
bounds reached
?p 0o
Recover Probes
21
. . .Hierarchical System Structure . . .
Level II
Mothership Structure
Mother Ship Agent
Message Center
  • Self Preservation
  • Determine Phase of Operation

Level IIa
Earth-link Comm
Message Center
  • Optimize ref. trajectory
  • Compute Thrust vector

Message Center
Trajectory Control
Cross-link Comm
Message Center
Message Center
Attitude Control
  • Maintain as specified
  • Manage momentum

Traj Attitude Determination
Message Center
Message Center
Sensor Control
Probe Docking Control
Message Center
Message Center
Thruster Control
FDIR
Message Center
Message Center
Electrical Power System
22
. . .Hierarchical System Structure . . .
Probe Spacecraft Structure
Level II
  • Self Preservation

Level IIa
Cross-link Comm
Message Center
  • Optimize ref. trajectory
  • Compute Thrust vector

Message Center
Trajectory Control
Traj Attitude Determination
Message Center
Message Center
Attitude Control
  • Maintain as specified
  • Manage momentum

Probe Docking Control
Message Center
Message Center
Sensor Control
Message Center
Thruster Control
FDIR
Message Center
Message Center
Electrical Power System
23
SYSTEM OF SYSTEMS ENGINEERING
  • A Future for
  • Large-Scale Systems
  • And
  • Systems Engineering

24
OUTLINE
  • Introduction
  • What are Systems of Systems
  • System of System Characteristics
  • Distinction Between System Engineering and SoSE
  • Research Areas
  • SoS Examples
  • Concluding Remarks

25
INTRODUCTION
  • Changing Aerospace and Defense Industry
  • Emphasis on large-scale systems integration
  • Customers seeking solutions to problems, not
    asking for specific vehicles
  • Emerging System of System Context
  • Mix of multiple systems capable of independent
    operation but interact with each other

26
EMERGING CONTEXT SYSTEM OF SYSTEMS
  • Meeting a need or set of needs with a mix of
    independently operating systems
  • New and existing aircraft, spacecraft, ground
    equipment, other independent systems
  • System of Systems Examples
  • Coast Guard Deepwater Program
  • FAA Air Traffic Management
  • Army Future Combat Systems
  • _ Robotic Colonies, etc.,etc.

27
WHAT ARE SYSTEM OF SYSTEMS?
  • Metasystems that are themselves comprised of
    multiple autonomous embedded complex systems that
    can be diverse in technology, context, operation,
    geography and conceptual frame.
  • An airplane is not SoS, an airport is a SoS.
  • Significant challenges
  • Determining the appropriate mix of independent
    systems
  • The operation of a SoS occurs in an uncertain
    environment
  • Interoperability

28
SYSTEM OF SYSTEM CHARACTERISTICS
  • What distinguishes Systems of Systems from other
    large systems?
  • Operational Independence of the Elements
  • Managerial Independence of the Elements
  • Evolutionary Development
  • Emergent behaviors
  • Geographic Distribution

29
Nature of SoSE Engineering
Keating, et al., 2003
30
System of Systems
Keating, et al., 2003
31
System of Systems Engineering
  • The design, deployment, operation, and
    transformation of metasystems that must function
    as an integrated complex system to produce
    desirable results.
  • Keating, et. al 2003
  • Jamshidi, 2005

32
System of Systems
  • SoS A metasystem consisting of multiple
    autonomous embedded complex systems that can be
    diverse in
  • Technology
  • Context
  • Operation
  • Geography
  • Conceptual frame
  • An airplane is not SoS, an airport is a SoS.
  • A robot is not a SoS, but a robotic colony is a
    SoS
  • Significant challenges
  • Determining the appropriate mix of independent
    systems
  • The operation of a SoS occurs in an uncertain
    environment
  • Interoperability

Keating, et al., 2003
33
System of Systems Definitions
  • SoS No universally accepted definition
  • 1. Operational Mang. independenceGeographical
    Dist. Emerging BehvrEvol. Dev. (ML, Space)
  • 2. IntegrationInter-Operability.Optmiz. to
    enhance battlefield scenarios (ML)
  • 3. Large scale distributed Systems Leading to
    more complex systems (Private Enterprize)
  • 4. Within the context of warfighting systems
    Inter Op.Comd. SynergyCont. Comp. Comm.
    Info. (C4I) Intel. (ML)

Keating, et al., 2003
34
DISTINCTION BETWEEN SYSTEM ENGINEERING AND SoSE
  • SoSE represents a necessary extension and
  • evolution of traditional system engineering.
  • Greatly expanded SoS requirements for tiered
    levels of discipline and rigor.
  • Centralized control structure vs. de-centralized
    control structure
  • A typical individual system (well defined end
    state, fixed budget, well defined schedule,
    technical baselines, homogeneous)
  • A typical System of Systems (not well defined end
    state, periodic budget variations, heterogeneous
    )

35
RESEARCH AREAS
  • Optimization, combinatorial problem solving and
    control
  • Important for design, architecting, and control
    of a System of Systems to ensure optimal
    performance to complete the assigned task or
    missions.
  • Non-deterministic assessment, and decision-making
    and design under uncertainty
  • Non-deterministic operating environments
  • Reliability prediction
  • Decision-making support for SoS
  • Which constituent systems provide which
    contributions?
  • Domain-specific modeling and simulation
  • Identify areas of potential risk, areas which
    require additional analysis
  • Concept of operation development,mission
    rehearsal,training of assets
  • Assist in optimizing the design and operation to
    better meet requirements

36
EXAMPLES
  • Air Traffic Control
  • Personal Air Vehicles
  • Future Combat Cystem
  • Internet
  • Intelligent Transport Systems
  • US Coast Guard Integrated Deepwater System

37
US COAST GUARD INTEGRATED DEEPWATER SYSTEM
  • The United States Coast Guard
  • Protect the public, the environment, and U.S.
    economic and security interests in any maritime
    region
  • International waters and America's coasts,
    ports, and inland waterways.
  • Missions
  • Maritime Security
  • Maritime Safety
  • Maritime Mobility
  • National Defense
  • Protection of Natural Resources

38
US COAST GUARD INTEGRATED DEEPWATER SYSTEM
  • An integrated approach to upgrading existing
    assets while transitioning to newer, more capable
    platforms with improved systems for command,
    control,communications, computers, intelligence,
    surveillance, and reconnaissance and innovative
    logistics support.
  • Ensure compatibility and interoperability of
    deepwater asstes, while providing high levels of
    operational effectiveness.

39

LSS vs SoS Models
Modeling of Systems of Systems?
TOP

LSS
TOP
BOT.

BOT.
LSS
Traditional LSS Modeling
SoSE Modeling Difficulty
40
System of SystemsPROBLEM THEMES
  • 1. Fragmented Perspectives
  • 2. Lack of Rigorous Development
  • 3. Lack of Theoretical Grounding
  • 4. IT Dominance
  • 5. Limitations of trad. SE single system focus
  • 6. Whole Systems Analysis

Keating, et al., 2003
41

Thank you.
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