# Control of Large-Scale Complex Systems – From Hierarchical to Autonomous and now to System of Systems Mo Jamshidi Electrical and Computer Engineering Department.

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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 … ss 1 ss 2 ss 3 ss N Hierarchical Control

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 y y1yN y2 uN u2 u1 u CN C2 C1 … Decentralized Control

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 4 th order system (left) has been approximated with 2 nd 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) == > (A b, B b, C b ), where A b = A -1 AS, B b = S -1 B, C = C b S S = L c U  –1/2 U is orthogonal modal matrix  is the diagonal symmetric matrix of a certain eigenvalue / eigenvector problem L c is a lower triangular Cholesky factros of controllability Grammian G c of (A,B)

Balanced Aggregation, Contd. Transformed matrices (A b, B b, C b ) 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 (A b ), G = Subset (B b ), 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 after neglecting certain interactions within 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 dx s /dt = A s x s + B s u + A s f x f  dx f /dt = A f x f + B f u

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) systems one can share the control action among a finite number of local controllers LARGE-SCALE SYSTEM Controller 1 Controller n u1u1 unun y1y1 ynyn... InputOutput

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 Subsystem 1 (Coordinator) Subsystem n (Coordinator) Subsytem 1 Subsystem mSubsystem 1 Subsystem k … … … a1a1 anan {x 1,u 1 } {x n,u n } interaction factor state, control

LISA - Advanced Avionics Systems for Dependable Computing in Future Space Exploration - Astrophysics Laser Interferometry Space Antenna (LISA)

00 ff DD RR  p =0 o Deploy Interval Observation Interval Recovery Interval Scenario A: Hyperbolic (e>1) Flyby

IntervalArray ActivityConfiguration 1Plan / Service Probes docked 2DeployProbes depart Mothership 3Data CollectionProbes free-fall / payload on 4Recover 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 θ0θ0 θfθf θDθD θRθR θ pE = 0 o θ pH = 0 o Fuzzy Transition From Elliptical to Hyperbolic Model Fuzzy Transition From Hyperbolic to Elliptical Model

Scenario C: Continuous Elliptical (0<e<1) or Circular (e=0) Observation θ p = 0 o Deploy Probes Maintain Formation - Adjust when formation bounds reached Recover Probes.

Mothership Structure Cross-link Comm Message Center Earth-link Comm Message Center Level II Level IIa Traj & Attitude Determination Message Center Probe Docking Control Message Center Optimize ref. trajectory Compute Thrust vector Mother Ship Agent Message Center Message Center Message Center Message Center Message Center Trajectory Control Attitude Control Sensor Control Thruster Control FDIR Message Center Message Center Electrical Power System Maintain as specified Manage momentum Self Preservation Determine Phase of Operation...Hierarchical System Structure...

Probe Spacecraft Structure Cross-link Comm Message Center Level II Level IIa Traj & Attitude Determination Message Center Probe Docking Control Message Center Optimize ref. trajectory Compute Thrust vector Message Center Message Center Message Center Message Center Trajectory Control Attitude Control Sensor Control Thruster Control FDIR Message Center Message Center Electrical Power System Maintain as specified Manage momentum Probe Agent 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 Engineering Existing Complex Systems Exclusive, Autonomous, Local Transformation Keating, et al., 2003

System of Systems Integrated, Aligned, and Transforming System of Systems Interconnected, Integrated Mission, Global, Emergent Structure Keating, et al., 2003

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

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 frame 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

System of Systems Definitions SoS: No universally accepted definition 1. Operational & Mang. independence+Geographical Dist. + Emerging Behvr+Evol. Dev. (ML, Space) 2. Integration+Inter-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.+Com ’ d. Synergy+Cont.+ Comp.+ Comm. +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 Models Modeling of Systems of Systems? LSS … Traditional LSS Modeling LSS TOP BOT. TOP SoSE Modeling Difficulty

System of Systems PROBLEM 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

Thank you.

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