Feedback Systems in Engineering and Nature · uncertainty in complex systems ... •Many molecular...

Feedback Systems in Engineering and Nature

Richard M. MurrayControl and Dynamical Systems

California Institute of Technology

Richard M. Murray, Caltech CDSNCWIT, 14 May 08

Outline

I. Feedback and Control TheoryII. Applications in Science & EngineeringIII. Linkages to Computer Science

(Grand Challenges)IV. Summary

Jean Carlson (UCSB) John Doyle (Caltech) Naomi Leonard (Princeton) Simon Levin (Princeton)

Jerry Marsden (Caltech) Linda Petzold (UCSB)

Richard M. Murray, Caltech CDSNCWIT, 14 May 08 3

What is Feedback & Why is it Important?Feedback = mutual interconnection of two (or more) systems• System 1 affects system 2• System 2 affects system 1• Cause and effect is tricky; systems

are mutually dependent

Feedback is ubiquitous in natural and engineered systems• Major mechanism for managing

uncertainty in complex systems• Often leads to “robust yet fragile”

behavior• Claim: Understanding complex

systems requires an understanding of feedback

Terminology

System 2

System 1

System 2System 1

System 2System 1

ClosedLoop

OpenLoop


Example #1: Flyball Governor“Flyball” Governor (1788)• Regulate speed of steam engine

• Reduce effects of variations in load (disturbance rejection)

• Major advance of industrial revolution

Balls fly out as speed increases,

Valve closes,slowing engine

http://www.heeg.de/~roland/SteamEngine.htmlBoulton-Watt steam engine

Flyballgovernor

Steamengine


Two Main Principles of FeedbackRobustness to Uncertainty through Feedback• Feedback allows high performance in the

presence of uncertainty• Example: repeatable performance of

amplifiers with 5X component variation• Key idea: accurate sensing to compare

actual to desired, correction through computation and actuation

Design of Dynamics through Feedback• Feedback allows the dynamics (behavior)

of a system to be modified• Example: stability augmentation for highly

agile, unstable aircraft• Key idea: interconnection gives closed

loop that modifies natural behavior

Control involves (computable) tradeoffs between robustness and performance X-29 experimental aircraft


Flight behavior in Drosophila(a) Cartoon of the adult fruit fly showing the

three major sensor strictures used in flight: eyes, antennae, and halteres (detect angular rotations)

(b) Example flight trajectories over a 1 meter circular arena, w/ & w/out internal targets.

(c) Schematic control model of flight system

6

Example #2: Insect Flight

More information:• M. D. Dickinson, Solving the mystery of insect

flight, Scientific American, June 2001

Different architecture than engineering• Large collection of diverse sensors

(many more than required)• Very slow computation with lots of

parallel pathways

Card and Dickinson (Caltech)


Feedback in Nature and Society

Biological Systems• Physiological regulation (homeostasis)• Bio-molecular regulatory networks

Environmental Systems• Microbial ecosystems• Global carbon cycle

Financial Systems• Markets and exchanges• Supply and service chains ESE


Control Theory: 1940-2000Modeling• Input/output representations for

subsystems + interconnection rules• System identification theory and

algorithms • Theory and algorithms for reduced

order modeling + model reduction

Analysis• Stability of feedback systems,

including robustness “margins”• Performance of input/output systems

(disturbance rejection, robustness)

Synthesis• Constructive tools for design of

feedback systems• Constructive tools for signal

processing and estimation

Basic feedback loop

• Plant, P = process being regulated• Reference, r = external input (often

encodes the desired setpoint)• Disturbances, d = external environment• Error, e = reference - actual• Input, u = actuation command• Feedback, C = closed loop correction• Uncertainty: plant dynamics, sensor

noise, environmental disturbances

r C(s) ++

d

ye

P(s)u

-1


Canonical Feedback Example: PID Control

Three term controller • Present: feedback proportional to current

error

• Past: feedback proportional to integral of past error

- Insures that error eventual goes to 0- Automatically adjusts setpoint of input

• Future: derivative of the error- Anticipate where we are going

PID design• Choose gains k, ki, kd to obtain the

desired behavior• Stability: solutions of the closed loop

dynamics should converge to eq pt• Performance: output of system, y,

should track reference• Robustness: stability & performance

properties should hold in face of disturbances and plant uncertainty

r C(s) ++

d

ye

P(s)u

-1


Example #3: Chemotaxis

Chemotactic response has “perfect adaptation”• When exposed to a high attractant level,

receptors are methylated to provider higher ligand binding

• Result: activity level returns to nominal level in presence of a constant input

• Form of integral feedback (Yi et al, 2004)

10

http://www.genomics.princeton.edu/ryulab

Rao, Kirby and ArkinPLoS Biology, 2004

Sensing

Actuation

Computation


Robust Yet Fragile BehaviorFeedback shifts uncertainty from process to sensors• Provide robust behavior using accurate

sensors combined with feedback• Example: 10x uncertainty in transistors, 2%

uncertainty in resistors

Feedback provides robustness to some types of uncertainty, fragility to others• Fundamental tradeoffs between robustness,

performance, and stability• Higher performance in certain pathways

leads to increased sensitivity in other pathways

• Can be made rigorous through conservation laws in control theory

• Example: biological systems resistant to known environmental effects, but susceptible to new diseases

Control

Δ

Sensor

Process


Future Directions: Control in an Information Rich World1. Executive Summary2. Overview of the Field

• What is Control?• Control System Examples• Increasing Role of Information-

Based Systems• Opportunities and Challenges

3. Applications, Opportunities & Challenges• Aerospace and Transportation• Information and Networks• Robotics and Intelligent Machines• Biology and Medicine• Materials and Processing• Other Applications

4. Education and Outreach5. Recommendations

SIAM, 2003


Information and NetworksPervasive, ubiquitous, convergent networking• Heterogeneous networks merging communica-

tions, computing, transportation, finance, utili-ties, manufacturing, health, entertainment, ...

• Robustness/reliability are dominant challenges• Need “unified field theory” of communications,

computing, and control

Many applications• Congestion control on the Internet• Power and transportation systems• Financial and economic systems• Quantum networks and computation• Biological regulatory networks and evolution• Ecosystems and global change

Control of the network

Control over the network


Biology and Medicine“Systems Biology”• Many molecular mechanisms for biological organisms are

characterized• Missing piece: understanding of how network

interconnection creates robust behavior from uncertain components in an uncertain environment

• Transition from organisms as genes, to organisms as networks of integrated chemical, electrical, fluid, and structural elements

Key features of biological systems• Integrated control, communications, computing• Reconfigurable, distributed control, at molecular level

Design and analysis of biological systems• Apply engineering principles to biological systems• Systems level analysis is required• Processing and flow of information is key


Ecological SystemsWhat makes ecosystems robust?

Understand well enough to help manage ecosystems?• System evolution emerges from the interplay of processes at

diverse scales

• Explain robustness in terms of evolutionary forces acting at levels well below that of the patterns we observe

Case Study: Marine Ecosystems and Fisheries Management• Fisheries have not been robust to harvesting

• Fish feed on zooplankton and phytoplankton

• Plankton are patchy on almost every scale

• Understand spatial patterns, dynamics, robustness

Case Study: Wildfire management• Derive physical fire spread constitutive laws

• E.g: Fire/atmosphere coupling, dynamics, and feedback

• Wild land management, policy, training, and hazard mitigation

Some Themes: Role of Multi-Scale Dynamics and Feedback


CDS Panel Recommendations1. Substantially increase research aimed at the integration of

control, computer science, communications, and networking.

2. Substantially increase research in control at higher levels of decision making, moving toward enterprise level systems.

3. Explore high-risk, long-range applications of control to areas such as nanotechnology, quantum mechanics, electromagnetics, biology, and environmental science.

4. Maintain support for theory and interaction with mathematics, broadly interpreted.

5. Invest in new approaches to education and outreach for the dissemination of control concepts and tools to non-traditional audiences.

http://www.cds.caltech.edu/~murray/cdspanel


Grand Challenge #1: Autonomy and RoboticsAutonomous Desert Race• 175 miles; trails, dirt roads, open terrain• Vehicle must be completely autonomous• Corridor specified 2 hours in advance;

defines boundaries of race• First vehicle to complete the course in less

than 10 hours wins $2M

2007: Urban driving• Lanes, intersections, parking lots, other cars

Major challenges• Perception – what are we looking at• Decision making – where should we go• Technical driving – rough roads, slipping• System integration – getting everything to

work together

Future directions: service robotics, human/robot interaction

Barstow

Primm


Grand Challenge #2: Control Using Slow ComputingTask: find food• Take off, avoid obstacles, find plume,

track plume to source

Approach #1: traditional control• Trajectory generation + feedback

• Requires substantial sensing and computing (ala Alice)

Approach #2: sensory-motor cascade• 300-500k neurons with

millisecond response times

• Large number of redundant sensors

• Excellent robustness, very good performance (over time)

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approach &landing

take-off

visualnavigation

odortracking target

recognition

collisionavoidance

local search&

exploration


Grand Challenge #3: Synthetic Biology

MIT Bio-Bricks program

Crawling Neutrophil “Chasing” a Bacterium • Human polymorphonuclear leukocyte (neutrophil) on blood film• Red blood cells are dark in color, principally spherical shape. • Neutrophil is "chasing" Staphylococcus aureus micro-organisms, added to

film. Tom Stossel, June 22, 1999 http://expmed.bwh.harvard.edu/projects/motility/neutrophil.html

Synchronization of a repressilator, IAP ‘03

7 Jan

14 Jan

Elowitz and Lieber, 2000

21 Jan

28 Jan

Elowitz and Lieber, 2000


Mathematical Modelswith Uncertainty

Emerging Challenge: ModularityObservation: biological circuits do not compose well

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Del Vecchio et al,Mol Sys Bio, 2008


Feedback Systems in Engineering and NatureEmerging challenges in analysis and design of complex systems (natural and engineered)

• Develop the mathematical framework for unraveling the organization of highly constrained, uncertain, large scale, nonlinear networked systems

• New design tools for managing complexity, uncertainty, scalability, performance

Past successes of computer science are needed in new areas• Techniques for verification of large-scale, complex systems• Modular design methods that allow abstraction, composition

Further Reading: • Åström and Murray, Feedback Systems: An Introduction for

Scientists and Engineers. Princeton University Press, 2008. - Electronic: http://www.cds.caltech.edu/~murray/amwiki

• U. Alon, An Introduction to Systems Biology. Chapman & Hall/CRC, 2007

• M. D. Dickinson, Solving the mystery of insect flight, Scientific American, June 2001

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