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@wacong.org

OUTLINE

1. Definition of a Large-Scale System

2. Modeling of Large-Scale Systems

3. Hierarchical Control

4. Decentralized Control

5. Applications

6. System of Systems

DEFINITION 1

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

LSS

…ss1 ss2 ss3 ssNHierarchicalControl

DEFINITION 1, Cont’d.

Pictorial representation of system decomposition and coordination, (a) An interconnected system; (b) a hierarchically structured system

DEFINITION 2

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

LSS

LSS

y

y1yN

y2

uN

u2

u1

u

CN

C2 C1…DecentralizedControl

LSS is …

Associated with three concepts:

1. Decomposition

2. Centrality

3. Complexity

Modeling

There are 3 classes of models for

Large-scale systems:

Aggregation

Perturbation

Descriptive variable

Aggregation, cont’d.

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.

Aggregation, cont’d. 2

Full (Original) Model:

dx(t)/dt = Ax(t) + Bu(t)

y(t) = Dx(t) Reduced Model:

dz(t)/dt = Fz(t) + Gu(t)

y(t) = Hz(t)

z(t) = C x(t)

C is aggregation matrix

Balanced Aggregation

Full: (A,B,D) Reduced: (F,G,H)

Balanced Realization Aggregation : Principle Component Analysis (A,B,C) == > (Ab, Bb, Cb), whereAb = A-1AS, Bb = S-1B, C = Cb S S = LcU –1/2

U is orthogonal modal matrix is the diagonal symmetric matrix of a certain eigenvalue / eigenvector problemLc is a lower triangular Cholesky factros of controllability Grammian Gc of (A,B)

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.

PERTURBATION

An perturbed model of a system is described by reduce model consisting of a structure afterneglecting certain interactionswithin the model. Regular Perturbation – weak couplings Singular Perturbation – strong Coupling

PERTURBATION, Cont’d. 2

SINGULAR Perturbation A mathematical process in which a system's variables are designated "slow" or "fast" in time-scale variations.

Fast variable

Approximation

dx/dt = Ax + Bu

dxs/dt = Asxs + Bsu + Asfxf

dxf/dt = Afxf + Bfu

PERTURBATION, Cont’d 3

SINGULAR Perturbation Boundary Layer Coorection for fast variables.Boundary layer correction for fast state z(t). ---, Ž(t); ——, Ž(t). + (t).

Decentralized Controllers

Taken from the theory of large-scale (complex) systemsone can share the control action among a finite number of localcontrollers

LARGE-SCALE SYSTEM

Controller 1 Controller n

u1 un

y1 yn

. . .

Input Output

Hierarchical ControllersAgain, taken from the theory of large-scale (complex) systemsone can share the control among a finite number of localcontrollers

Supreme Coordinator

Subsystem 1 (Coordinator)

Subsystem n (Coordinator)

Subsytem 1 Subsystem m Subsystem 1 Subsystem k

…

… …

a1

an{x1,u1}{xn,un}

interaction factorstate, control

LISA - Advanced Avionics Systems for Dependable Computing in Future Space

Exploration - Astrophysics

Laser Interferometry Space Antenna (LISA)

0

f

D

R

p=0o

DeployInterval

ObservationInterval

RecoveryInterval

Scenario A: Hyperbolic (e>1) Flyby

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

Scenario B: Elliptical Orbit of Planet with Hyperbolic Flyby of Moon

Interval 3:Observation

Interval 4:Recover

Interval 1:Plan / Service

Interval 2: Deploy

θ0

θf

θD

θR

θpE= 0o

θpH= 0o

Fuzzy TransitionFrom Elliptical to HyperbolicModel

Fuzzy TransitionFrom Hyperbolic to EllipticalModel

Scenario C: Continuous Elliptical (0<e<1) or Circular (e=0) Observation

θp= 0o

θp= 0o

θp= 0oDeployProbes

MaintainFormation

- Adjust whenformation boundsreached

RecoverProbes

.

Mothership Structure

Cross-linkComm

Message Center

Earth-linkComm

Message Center

Level II

Level IIa

Traj & AttitudeDetermination

Message Center

ProbeDockingControl

Message Center

• Optimize ref. trajectory• Compute Thrust vector

Mother ShipAgent

Message Center

Message Center

Message Center

Message Center

Message Center

Trajectory Control

Attitude Control

SensorControl

ThrusterControl

FDIRMessage

CenterMessage

Center

ElectricalPower

System

• Maintain as specified• Manage momentum

• Self Preservation• Determine Phase of Operation

. . .Hierarchical System Structure . . .

Probe Spacecraft Structure

Cross-linkComm

Message Center

Level II

Level IIa

Traj & AttitudeDetermination

Message Center

ProbeDockingControl

Message Center

• Optimize ref. trajectory• Compute Thrust vector

Message Center

Message Center

Message Center

Message Center

Trajectory Control

Attitude Control

SensorControl

ThrusterControl

FDIRMessage

Center

Message Center

ElectricalPower

System

• Maintain as specified• Manage momentum

ProbeAgent

Message Center

• Self Preservation

. . .Hierarchical System Structure . . .

SYSTEM OF SYSTEMS ENGINEERING

A Future for …

Large-Scale Systems

And

Systems Engineering

OUTLINE

• Introduction• What are Systems of Systems• System of System Characteristics• Distinction Between System Engineering and

SoSE• Research Areas• SoS Examples• Concluding Remarks

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

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.

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

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

Nature of SoSE EngineeringNature of SoSE Engineering

Existing Complex SystemsExisting Complex SystemsExclusive, Autonomous, Local Exclusive, Autonomous, Local TransformationTransformation

Keating, et al., 2003

System of Systems

Integrated, Aligned, and Transforming

System of SystemsSystem of SystemsInterconnected, Integrated Mission, Interconnected, Integrated Mission, Global, Emergent StructureGlobal, Emergent Structure

Keating, et al., 2003

System of Systems EngineeringThe 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

System of Systems• SoS: A metasystem consisting of multiple autonomous embedded complex systems that can be diverse in:

Technology Technology Context Context Operation Operation Geography Geography Conceptual frameConceptual 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

System of Systems Definitions SoS: No universally accepted definition

1. Operational & Mang. independence+Geographical 1. Operational & Mang. independence+Geographical Dist. + Emerging Behvr+Evol. Dev. (ML, Space)Dist. + Emerging Behvr+Evol. Dev. (ML, Space)

2. Integration+Inter-Operability.+Optmiz. to enhance 2. Integration+Inter-Operability.+Optmiz. to enhance battlefield scenarios (ML)battlefield scenarios (ML)

3. 3. Large scale + distributed Systems Leading to more Large scale + distributed Systems Leading to more complex systemscomplex systems (Private Enterprize) (Private Enterprize)

4. Within the context of warfighting systems – Inter 4. Within the context of warfighting systems – Inter Op.+Com’d. Synergy+Cont.+ Comp.+ Comm. Op.+Com’d. Synergy+Cont.+ Comp.+ Comm. +Info. (C4I) & Intel. (ML)+Info. (C4I) & Intel. (ML)

Keating, et al., 2003

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 )

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

EXAMPLES

• Air Traffic Control

• Personal Air Vehicles

• Future Combat Cystem

• Internet

• Intelligent Transport Systems

• US Coast Guard Integrated Deepwater System

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

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.

LSS vs SoS ModelsModeling of Systems of Systems?

LSS

…

Traditional LSS Modeling

LSS

TOP

BOT.

BOT.

TOP

SoSE Modeling Difficulty

System of SystemsPROBLEM THEMES

1. Fragmented Perspectives1. Fragmented Perspectives

2. Lack of Rigorous Development2. Lack of Rigorous Development

3. Lack of Theoretical Grounding 3. Lack of Theoretical Grounding 4. IT Dominance4. IT Dominance

5. Limitations of trad. SE single system focus 5. Limitations of trad. SE single system focus

6. Whole Systems Analysis6. Whole Systems Analysis

Keating, et al., 2003

Thank you.