universal laws and architectures - arpa-e...earthquakes, turbulence, music, buildings, cities, art,...
TRANSCRIPT
John Doyle 道陽
Jean-Lou Chameau Professor
Control and Dynamical Systems, EE, & BioE
tech 1 # Ca
Universal laws
and architectures: Theory and lessons from
grids, brains, bugs, nets, planes, docs, fire, bodies, fashion,
earthquakes, turbulence, music, buildings, cities, art, running, throwing, Synesthesia, spacecraft, statistical mechanics
John Doyle 道陽
Jean-Lou Chameau Professor
Control and Dynamical Systems, EE, & BioE
tech 1 # Ca
Universal laws
and architectures: Theory and lessons from
grids, brains, bugs, nets, planes, docs, fire, bodies, fashion,
earthquakes, turbulence, music, buildings, cities, art, running, throwing, Synesthesia, spacecraft, statistical mechanics
Efficiency and robustness
in sustainable infrastructure
• Accept previous talks as givens
‒ New efficiencies and instability/fragility
‒ Needs distributed/layered/complex/active control
• What could go wrong (longterm)?
• How to fix/avoid (technical) problems.
• Persistent errors/confusion in science & engineering
Efficiency and robustness
• Efficient use of resources
– Less inertia and damping instability
• Robustness on all scales
– Fluctuations in supply and demand
– Component uncertainty and failure*
– Adaptability to large changes*
– Evolvability on long time scales*
* Aspects of “plug and play” modularity
Efficiency/instability/layers/feedback
• Sustainable infrastructure? (e.g. smartgrids) • Money/finance/lobbyists/etc • Industrialization • Society/agriculture/weapons/etc • Bipedalism • Maternal care • Warm blood • Flight • Mitochondria • Oxygen • Translation (ribosomes) • Glycolysis (2011 Science)
• All create new efficiencies but also unstable/fragile
• Needs new distributed/layered/complex/active control
• Persistent errors/confusion in science & engineering
Major transitions
in evolution
• Nets/Grids (cyberphys)
• Brains
• Bugs (microbes, ants)
• Medical physiology
(tomorrow)
• Lots of aerospace
• Wildfire ecology
• Earthquakes
• Physics: – turbulence,
– stat mech (QM?)
• “Toy”: – Lego
– clothing, fashion
• Buildings, cities • Synesthesia
Case StudyI
wasteful
fragile
efficient
robust
Actual
Ideal
The main tradeoff
Efficiency/instability/layers/feedback
• Sustainable infrastructure? (e.g. smartgrids) • Money/finance/lobbyists/etc • Industrialization • Society/agriculture/weapons/etc • Bipedalism • Maternal care • Warm blood • Flight • Mitochondria • Oxygen • Translation (ribosomes) • Glycolysis (2011 Science)
• New efficiencies but also instability/fragility
• New distributed/layered/complex/active control
Live demo?
costly
fragile
efficient
robust
Tradeoffs (swim/crawl to run/bike)
Function=
Locomotion
costly
fragile
efficient
robust
Tradeoffs
4x
>2x
wasteful
fragile
efficient
robust
Universal laws
“Universal laws”
limit achievable
robust efficiency.
wasteful
fragile
efficient
robust Ideal
Actual
Universal laws
wasteful
fragile
efficient
robust Ideal
Actual
The risk
wasteful
fragile
efficient
robust Ideal
Universal laws
and architectures
Flexibly achieves
what’s possible
control feedback
RNA
mRNA
RNAp
Transcription
Other
Control
Gene
Amino
Acids
Proteins
Ribosomes
Other
Control
Translation
Metabolism Products
Signal transduction
ATP
DNA
New
gene
Sensory Motor
Prefrontal
Striatum
Reflex
Software
Hardware
Digital
Analog
Horizontal
Gene
Transfer
Horizontal
App
Transfer
Horizontal
Meme
Transfer
Evolvable
architectures
Requires
shared “OS”
Sensory Motor
Prefrontal
Striatum
Slow
Flexible
Learning
Ashby & Crossley
Slow
Reflex (Fastest,
Least
Flexible)
Extreme heterogeneity
Sensory Motor
Prefrontal
Striatum
Fast
Fast
Inflexible
Slow
Flexible
Reflex (Fastest,
Least
Flexible)
Ashby & Crossley
Learning can
be very slow.
Sense
Fast
Slow
Flexible Inflexible
Motor
Prefrontal
Fast
Reflex
HMT Horizontal
Meme
Transfer
Sense
Fast
Slow
Flexible Inflexible
Motor
Prefrontal
Fast
Reflex
Horizontal
Hardware
Transfer
HHT
Sense
Fast
Slow
Flexible Inflexible
Motor
Prefrontal
Fast
Reflex
Apps
OS
HW
HMT
HHT
Fast
Slow
Flexible Inflexible
General Special
Apps
OS
HW
Fast
Slow
Flexible Inflexible
General Special
Apps
OS
HW
Horizontal
App
Transfer
Horizontal
Hardware
Transfer
Slow
Flexible
Fast
Inflexible
Architecture
(constraints that
deconstrain)
General Special
Universal laws and architectures
(Turing)
ideal
Slow
Flexible
Fast
Inflexible
General Special
NP(time)
P(time)
analytic
Npspace=Pspace
Decidable
Computation
(on and off-line)
control feedback
RNA
mRNA
RNAp
Transcription
Other
Control
Gene
Amino
Acids
Proteins
Ribosomes
Other
Control
Translation
Metabolism Products
Signal transduction
ATP
DNA
New
gene
Sensory Motor
Prefrontal
Striatum
Reflex
Software
Hardware
Digital
Analog
Horizontal
Gene
Transfer
Horizontal
App
Transfer
Horizontal
Meme
Transfer
Accelerating
evolution
Requires
shared “OS”
control feedback
RNA
mRNA
RNAp Transcription
Other
Control
Gene
Amino
Acids
Proteins
Ribosomes
Other
Control
Translation
Metabolism Products
Signal transduction
ATP
DNA
New
gene
Sensory Motor
Prefrontal
Striatum
Reflex
Software
Hardware
Digital
Analog
Horizontal
Gene
Transfer
Horizontal
App
Transfer
Horizontal
Meme
Transfer
What can
go wrong?
Before
exploring
mechanisms
Horizontal
Bad Gene
Transfer
Horizontal
Bad App
Transfer
Horizontal
Bad Meme
Transfer
Parasites
&
Hijacking
Fragility?
Exploiting
layered
architecture
Virus
Virus
Meme
Horizontal
Bad Meme
Transfer
Our
greatest
fragility?
Meme
Many human
beliefs are:
• False
• Unhealthy
Slow
Fast
Flexible Inflexible
General Special
Apps OS HW Dig. Lump. Distrib.
OS HW Dig. Lump. Distrib.
Digital Lump. Distrib.
Lumped Distrib.
Distrib.
HGT DNA repair Mutation DNA replication Transcription Translation Metabolism
Signal
Sense Motor
Prefrontal
Fast
Reflex
vision
VOR
slow
flexible
fast
inflexible
fragile
robust
Slow
Fast
Flexible Inflexible
General Special
slow
flexible
fast
inflexible
waste
efficient
fragile
robust
slow
flexible
fast
inflexible
fragile
robust
waste
efficient
fragile
robust
slow
flexible
fast
inflexible
fragile
robust
waste efficient
fragile
robust
waste efficient
fragile
robust
slow
flexible
fast
inflexible
fragile
robust
costly
fragile
efficient
robust
Function=
Movement
costly
fragile
efficient
robust
hard
harder
A convenient cartoon
easy
Function=
Movement
“costly”
fragile
“efficient”
robust easy
hard
harder
up&short
cartoon demo
down or long
fragile
robust easy
hard
up&short down or long
Gravity is
stabilizing
Gravity is
destabilizing
Law #1 : Mechanics
Law #2 : Gravity
Universal laws?
Efficiency/instability/layers/feedback
• Sustainable infrastructure? (e.g. smartgrids) • Money/finance/lobbyists/etc • Industrialization • Society/agriculture/weapons/etc • Bipedalism • Maternal care • Warm blood • Flight • Mitochondria • Oxygen • Translation (ribosomes) • Glycolysis (2011 Science)
• New efficiencies but also instabilities
• New distributed/layered/complex/active control
stabilizing
destabilizing
fragile
robust
harder
up&short down or long
More
unstable
Law #1 : Mechanics
Law #2 : Gravity
Law #3 : ??
Law #4 : ??
hard harder hardest!
Easy to prove using simple models.
What is sensed matters.
Why?
Why?!?
fragile
robust
harder
up&short down or long
hardest!
Why?
Accident or necessity?
Universal laws?
Four Universal laws =
vision
Act
delay
+ Neuroscience
Balancing
an inverted
pendulum
Mechanics+
Gravity +
Light +
expz p
T pz p
Some
minimal
math
details
easy
hard
Law #1 : Mechanics
Law #2 : Gravity
0
O
M m x ml u
x l g
y x l
&&&&
&&&&
linearize
1d motion
2cos sin
cos sin 0
sinO
M m x ml u
x l g
y x l
&& &&&
&&&&
hard harder
Easy to prove using simple models.
vision
Act
delay
Law #3 : Light
0
O
M m x ml u
x l g
y x l n
&&&&
&&&&
eye
l
N noise E error
E
T jN
Frequency
domain
?T
eye vision
slow
Act
delay
Control
l
N noise E error
E
T jN
expT p
Universal laws, art, music, Lego
vision
Act
delay
Balancing
an inverted
pendulum
Mechanics+
Gravity +
Light +
1p
l
.3s
2 2
0
1exp ln exp ln
sup
pT T j d
p
T T j
@
exp lnexp
Tp
T
Amplification (noise to error)
Entropy rate
Energy (L2)
exp lnexp
Tp
T
Entropy rate
Energy (L2)
exp pt
delay
Before
you can
react
time
state
intuition
10
100
Length, m
.1 1 .5 .2 2
exp p
1p
l
.3s
Shorter
expT p
10
Length, m .1 1 .5 .2
2
loglog
0.2 0.4 0.6 0.8 1 2
4
6
8
10
linear
exp p
Also
exponential
in delay!
eye vision
Act
delay
Control
l noise
error
P
+
noise
error
C
E
T jN
Cerebellum
P
+
noise
error
C
E
T jN
sup sup Re( ) 0|T T j T s s
Max modulus
Proof?
Easy
1
exp
( ) ( ) exp
exp
Ms P s s
T M M p p p
T p
P
1
1
( ) ( )
P p T p
M p p
( ) ( ) ( ) ( ) 1
exp
T s M s s j
s s
hard harder hardest!
Easy to prove using simple models.
What is sensed matters.
Why?
hard harder hardest!
What is sensed matters.
Unstable poles Unstable zeros
0l l0l l
exp lnexp
T z pp
z pT
Fragility two ways (Bode* and Zames):
Unstable zeros
P
+
noise
error
C
sup sup Re( ) 0|T T j T s s
Proof?
( ) ( ) ( ) ( ) 1
exp
T s M s s j
s zs s
s z
1
exp
( ) ( ) exp
exp
M
s zs P s s
s z
z pT M M p p p
z p
z pT p
z p
P
exp
expex
lp
n z pp
z p
Tp
T
hardest!
0l l
0l l
exp p
expz p
pz p
10
100
Length, m
.1 1 .5 .2 2
1p
l
.3s
hardest! hard
exp
expex
lp
n z pp
z p
Tp
T
10
100
Speed 1/
.1 1 .5 .2 2
.3s
exp p
vision
Act
delay
Vary delay?
easy harder
“costly”
fragile
“efficient”
robust
Hard tradeoff
“costly”
fragile
“efficient”
robust
Bad
design
Gratuitous
fragility
10
100
Speed 1/
.1 1 .5 .2 2
.3s
exp p
vision
Act
delay
Delay kills.
“costly”
fragile
“efficient”
robust
exp lnexp
z pT
Tp
z p
Same constraints:
Mechanics+
Gravity+
Different
consequences Constrained
sensing
unconstrained
The nature of “laws”
“costly”
fragile
“efficient”
robust easy
hard
harder hardest!
up&short down or long
Different
consequences
wasteful
fragile
efficient
robust
Universal laws
and architectures
Flexibly achieves
what’s possible
Cortex
eye vision
Act slow
delay
VOR
fast
Object
motion
Head
motion
Cerebellum
+
Error Tune gain
gain
AOS
AOS = Accessory Optical system
noise
Act
Highly
evolved
(hidden)
architecture
Cortex
eye vision
Act slow
delay
VOR
fast
Object
motion
Head
motion
Cerebellum
+
Error Tune gain
gain
AOS
AOS = Accessory Optical system
noise
Act
slowest
Cortex
eye vision
Act slow
delay
VOR
fast
Object
motion
Head
motion
Cerebellum
+
Error Tune gain
gain
AOS
AOS = Accessory Optical system
noise
Act
Delays
everywhere
Distributed
control
slowest
Cortex
eye vision
Act slow
delay
VOR
fast
Object
motion
Head
motion
Cerebellum
+
Error Tune gain
gain
AOS
noise
Act
slowest Heterogeneous
delays
everywhere
Efficiency/instability/layers/feedback
• Sustainable infrastructure? (e.g. smartgrids)
• Money/finance/lobbyists/etc
• Industrialization
• Society/agriculture/weapons/etc
• Bipedalism
• Maternal care
• Warm blood
• Flight
• Mitochondria
• Oxygen
• Translation (ribosomes)
• Glycolysis (2011 Science)
Major transitions
How universal? Very.
Chandra, Buzi, and Doyle
UG biochem, math,
control theory
Insight
Accessible
Verifiable
Glycolytic oscillations
• Exhaustively studied
– Extensive experiments and data
– Detailed models and simulations
– Great! But all just deepen the mystery
• Perfectly illustrates “conservation law”
• Without which? Bewilderment.
exp ln T z p
z pT
Law #1 : Chemistry (vs mechanics)
Law #2 : Autocatalysis (vs gravity)
( RHP p and z)
exp ln T z p
z pT
Law #3:
k
z p
z p
10 -1
10 0
10 1 10
0
10 1
too
fragile
complex
No tradeoff
expensive
fragile
Law #1 : Chemistry
Law #2 : Autocatalysis
( RHP p and z)
Law #3:
exp ln T z p
z pT
0 100 200 300 400 0 100 200 300 400
40
60
80
100
120
140
160
180
HR
High mean, low variability
Low mean, high variability
sec
controls
external
disturbances
heart rate
ventilation
errors
O2
BP
energy
Homeostasis
and HRV
Universal
laws?
10
100
Length, m
.1 1 .5 .2 2
k10 -1
10 0
10 1 10
0
10 1
expensive
fragile
exp lnexp
T z pp
z pT
wasteful
fragile
efficient
robust Ideal
Info Thry
Control, OR
Compute
Physics Orthophysics
(Eng/Bio/Math)
Optimization Statistics
Comms for
Comp/Cntrl/Bio
Theory
Localized (distributed) control
• Localizable control: Wang, Matni, You and Doyle ACC ’14
• Localized LQR control: Wang, Matni, and Doyle CDC’14
Another extremely toy model
• Concretely illustrate important new ideas
• Minimal complexity otherwise
• Familiar, intuitive circuit dynamics
• Emphasize role of delays
• Instability mechanism is artificial
• Comparable to biological instabilities
• … but (so far) rare in tech infrastructure
• LC circuit
• Each node = grounded capacitance
• Each link = inductance
System Model
• Assuming each L and each C has unit value, the dynamics of the system are
where x(t) is states of node voltage and link current, M is the incidence matrix of the circuit graph.
(Will reorder for plotting later.)
Discrete Time System Model
• A first order (Euler) approximation is
• With step = 0.2, the maximum eigenvalue of Ad is 1.0768
• Artificially create a very unstable system
• Only biology is systematically this unstable, so far.
Simplified diagram (2 states per node)
Actuated and sensed
Only sensed
Actuated and sensed
Only sensed
Only sensed
Simplified diagram (2 states per node)
Actuated and sensed
Only sensed
Actuated and sensed
Only sensed
Only sensed
Actuated and sensed
Only sensed
Simplified diagram (2 states per node)
Actuated and sensed
Only sensed
Actuated and sensed
Only sensed
Nominally each has delay 1.
Expensive? 0. Physical 1. Actuation
Simplified diagram (2 states per node)
Controller
Physical plant
Actuated and sensed
Only sensed
Sense, comm/comp, act.
Expensive? 0. Physical 1. Actuation 2. Comms speed 3. Comp speed 4. Sensing …
Controller
Physical plant
Data “plane”
Controller “plane”
SDN/ODP
Physical
Data “plane”
Cyber
Controller “plane”
Actuated and sensed
Only sensed
Sense, comm/comp, act. Nominally each has delay 1.
Actuated and sensed
Only sensed
Expensive: • physical plant • passive stability • actuation • low delay (comms
and comp)
Cheap: • comms bandwidth • compute memory • sensing
True for cells, nets, grids, brains, but not in general
System Model
• The discrete time system equation is
• Example: 30 C, 29 L
Open loop dynamics
Simplified diagram
( )x t
( )x t
t
0 50 -1
0
1
Open loop
( )x t
t
0 50 100 150 200 250 -1
0
1
Open loop
( )x t
t
0 50 100 150 200 250 -1
0
1
15( )v t
Threshold to |x(t)|< 1
( )x t
Open loop
t
0 50 100 150 200 250 -1
0
1
0 50 100 150 200 250 -1
0
1
0 50 100 150 200 250
-1
0
1
2 ( )v t
9 ( )v t
15( )v t
Disturbance propagation
Threshold to |x(t)|< 1
( )x t
Open loop
t
0 50 100 150 200 250 -1
0
1
0 50 100 150 200 250 -1
0
1
0 50 100 150 200 250 -1
0
1
2 ( )v t
9 ( )v t
15( )v t
22( )v t
29( )v t
log ( )x t
( )x t
t
log ( )x t
Open
loop
Space-time cone
log ( )x t
plot log ( )x t
( )x t
t
log ( )x t
Open
loop
log ( )x t
plot log ( )x t
0 50 100 150 200 250 -1
0
1
15( )v t
Threshold to |x(t)| < 1
( )x t
t
log ( )x t
Space-time cone
log ( )x t
log ( )x tOpen
loop
( )x t
tSpace-time state cone
State
Controller Design
Critical Issues
1. Transient LQ (H2) cost: (x’x+u’u)
2. Actuator Density
3. Communication (vs plant) Speed
4. Locality/Scalability (Computation)
5. Time/space horizon
Actuator Density
• Standard (centralized) optimal H2 control
• No delay (initially)
• Defer other issues ( comm, comp, sense)
• Objective: min sum (x’x+u’u)
• Actuator density = # actuators / # states
• Trade-off: actuator density vs norm
• Example: 30 C, 29 L
1
1
10 2
10 4
Actuation
.5 .2
1
3
Norm - Actuator Density (normalized)
Opt H2
norm
Artificially unstable system
sparse dense
Actuated and sensed
Only sensed
1
1
10 2
10 4
Actuator Density
norm 1
3
Comm speed = 0 delay
Standard control
(circa 1970)
Opt undelay central state
Opt undelay central ctrl
Sparse actuation
Optimal Controller
+ Norm H2 optimal
‒ Communication undelayed
‒ Design/model global/huge P
‒ Implementation local/huge P
Color
code?
log ( )x t
log ( )u t
( )x t
( )u t
t
Actuated and sensed
Only sensed
Expensive? 0. Physical 1. Actuation 2. Comms speed 3. Comp speed 4. Sensing …
Communication speed
Versus plant speed
Nominally delay 1. Expensive? 0. Physical 1. Actuation 2. Comms speed 3. Comp speed 4. Sensing …
undelay central ctrl undelay central state
Communication speed =
undelay central state
Communication speed =
undelay central ctrl
0 2 4 6 8 10 1
1.05
1.1
1.15
1.2
Communication
Speed
Distributed
Localized
Norm
1.5
Undelayed central
slow fast
undelay central ctrl undelay central state
delay distr state delay distr
ctrl
undelay central ctrl
central state
delay distr state
delay distr
ctrl
delay distr state delay distr
ctrl
Distributed (QI) Controller
+ Norm (H2) “small”
+ Optimal for constraints
+ Communication delayed
‒ Design/model global/huge P
‒ Implementation local/huge P
delay distr
ctrl
delay local ctrl delay local state
delay distr state
delay distr state
delay distr
ctrl
delay local
delay local
ctrl
delay local state
Localized Controller
+ Norm (H2) “small”
+ Optimal for constraints
+ Communication delayed
+ Design/model local/small
+ Implementation local/small
+ State local
Everything is scalable.
1
1
10 2
10 4
Actuator Density
norm 1
3
Centralized
0 2 4 6 8 10 1
1.05
1.1
1.15
1.2
Communication Speed
Distributed
Localized
Norm
1.5
Tradeoffs
Conjecture:
Norm bad
before method
breaks
Extras
For “handout” and further study
0 2 4 6 8 10 1
1.05
1.1
1.15
1.2
Communication Speed
Distributed
Localized
Norm
1.5
Undelayed central
Normalized by undelayed centralized
delay local
ctrl
delay local state
[ ] 0x T
x
u
X
U
Linear equations
( )x t
tSpace-time state cone
State
( )x t
t
finite
impulse
response
(FIR)
Communication
and Control Cone
Space-time state cone
State
( )x t
tfinite
impulse
response
(FIR)
Control
[ ] 0x T
x
u
X
U
Space-time state cone
Local space-time controllability
( )x tPast
t
Past delayed
state needed
to compute
control
Communications
( )x t
tfinite
impulse
response
(FIR)
Control
[ ] 0x T
x
u
X
U
Space-time state cone
Local space-time controllability
Past
This can linearly
constrain any
optimization
Optimal delayed localized (very new, scalable)
Optimal delayed distributed (newish)
(but not scalable)
Optimal undelayed centralized state (old)
State
State
undelay central ctrl undelay central state
delay local ctrl delay local state
AWGN in C2, L26, C29
( )x t
tfinite
impulse
response
(FIR)
Control
[ ] 0x T
x
u
X
U
Space-time state cone
Local space-time controllability
Past
This can linearly
constrain any
optimization
Localized Controller
+ Norm (H2) small
+ Optimal for constraints
+ Communication is delayed
+ Design/model local/small
+ Implementation local/small
+ State local
Localized Controller
+ Norm (H2) small
+ Optimal for constraints
+ Design/model is local
+ Implementation is local
+ State stays local
- Bandwidth is
? Output feedback?
? Approximately local?
? Layering?
? Nonlinear, MPC, etc?
? Comms codesign? See also Javad’s new relaxations
Mostly good news, but
incomplete
Extensions
• Scalable optimal control
– Localizable control: Y.-S. Wang, N. Matni, S. You and J. C. Doyle ACC ’14
– Localized LQR control: Y.-S. Wang, N. Matni, and J. C. Doyle CDC’14
– Output feedback progress
• Dealing with varying-delays (jitter)
– Two player LQR with varying delays: N. Matni and J. C. Doyle CDC’ 13, N. Matni, A. Lamperski and J C. Doyle IFAC ‘14
More Nikolai Matni
• Distributed/scalable system identification – Low-rank + Low-order decompositions: N. Matni and
A. Rantzer, CDC’ 14
• Structured Robustness – Distributed Controllers Satisfying an H∞ norm bound:
N. Matni CDC ‘14
• Regularization for Design
– Topology/interconnection design: N. Matni, CDC ‘13 (best student paper), TCNS ’14
– More broadly (including actuator/sensor placement): N. Matni and V. Chandrasekaran, CDC ’14
More Extensions/Apps • Apps: neuro, smartgrid, CPS, cells
• IMC/RHC, etc (all of centralized control theory)
• Cyber theory: Delay jitter (uncertainty)
• Cyber: Comms co-design (CDC student prize paper)
• Physical: Robustness (unmodeled dynamics, noise)
• Cyber-phys: System ID, ML, adaptive
• SDN (Software defined nets, OpenDaylight)
• Revisit “layering as optimization”?
• Poset causality (streamlining)?
• Quantization and network coding?
Controller
Physical plant
Revisit layering as optimization decomposition Chiang, Low, Calderbank, Doyle, 2007
Data “plane”
Controller “plane”
SDN/ODP
Physical
Data “plane”
Cyber
Controller “plane” Layered
Architectures
1
1
10 2
10 4
Actuator Density
norm 1
3
Centralized
0 2 4 6 8 10 1
1.05
1.1
1.15
1.2
Communication Speed
Distributed
Localized
Norm
1.5
Undelayed central Tradeoffs
Conjecture:
Norm bad
before method
breaks
0 2 4 6 8 10 1
1.05
1.1
1.15
Communication Speed
Delayed Centralized
Decentralized
Localized
norm
Speed
(=1/delay)
Local control theory
Error
0
0 2 4 6 8 10 1
1.05
1.1
1.15
Communication Speed
Delayed Centralized
Decentralized
Localized
norm
Speed
(=1/delay)
Local control theory
Error
0
Speed
(=1/delay)
Rate (BW)
Local control theory
Info theory
Error
Communications
0
Error
0
Due to quantization,
loss, noise
Speed
(=1/delay)
Rate (BW)
Local control theory
Error Error
Communications
0 0
Info theory
Error
Speed
(=1/delay)
Rate (BW)
Local control theory
Error Error
Communications
0 0
Info theory
Speed
Rate
Local control theory Info
theory
Error Error
0 0
Communications
Speed
Rate
Local control theory Info
theory
Error Error
Communications
0
Error
Speed
Rate
Local control theory Info
theory
Error Error
Communications
0
Error
ideal
Speed
Rate
Error Error
Local control
0
Error
ideal
Resource 2
Resource 1
Error Error
Tradeoffs
0
Error
ideal
d e=d-u -
decode/ control/
encode
Plant
(P) CA
source/ disturbance
CS
sense/ encode
delay
decode/ actuate
Channels
min 0,log AS d p C
log SS d p C
E jS j
D j
@
0P p p
a)
b)
c)
d)
e)
2 2
1ln ln if
2
z z p pS j d p z
z z p z
f) 0P z
0
1f d f d
@
Control over limited channels (Martins et al)
Slow Fast
Architecture
(constraints that
deconstrain)
General
Special
Universal laws and architectures
(Turing)
ideal
Speed
Slow Fast
General
Special
Speed
Memory
Memory is cheap, reusable, powerful.
Time is not.
Resource 2
Resource 1
Error Error
Tradeoffs
0
Error
ideal
Error Error
0
ideal
Speed
(comms, comp)
Actuation
Critical Tradeoffs
• Cheap: memory, bandwidth, sensors
• Not : time (1/speed), actuators • Brains/bodies, cells, CyberPhySys, …
0
ideal
Speed
(comms, comp)
Actuation
Critical Tradeoffs
All costs are ultimately “physical.”
Cost
eye vision
Act
delay
Control
l noise
error E
T jN
P
+
noise
error
C
Understand this more deeply?
+ Neuroscience
Mechanics+
Gravity +
Light +
Control theory
exp lnexp
T z pp
z pT
eye vision
Act
delay
Control
l noise
error
Understand this more deeply?
+ Neuroscience
Vision
Motion
Robust vision w/motion
• Object motion
• Self motion
Vision
Motion
eye vision
Act
delay
Control
noise error
Cortex
eye vision
Act slow
delay
VOR
fast
Object
motion
Head
motion
Cerebellum
+
Error Tune gain
gain
AOS
AOS = Accessory Optical system
noise
Act
Highly
evolved
(hidden)
architecture
Cortex
eye vision
Act slow
delay
VOR
fast
Object
motion
Head
motion
Cerebellum
+
Error Tune gain
gain
AOS
AOS = Accessory Optical system
noise
Act
Fast
Slow
Flexible Inflexible
Vision
Explain this
amazing
system.
Layering
Feedback
Experiment • Motion/vision control without blurring
• Which is easier and faster?
Robust vision with
• Hand motion
• Head motion
Fast
Slow
VOR
vision
Why?
• Mechanism
• Tradeoff
Cerebellum
Fast
Slow
Flexible Inflexible
VOR
vision
Vestibular
Ocular
Reflex
(VOR)
Mechanism
Tradeoff
Slow
Flexible
vision
eye vision
Act slow
delay
Fast
Inflexible
Slow
Flexible
vision
eye vision
Act slow
delay
Fast
Inflexible
VOR
fast
Slow
Flexible
eye
Act
Fast
Inflexible
VOR
fast
Vestibular
Ocular
Reflex
(VOR)
Slow
Flexible
eye
Act
Fast
Inflexible
VOR
fast
It works in the
dark or with your
eyes closed, but
you can’t tell.
Slow
Flexible
vision
eye vision
Act slow
delay
Fast
Inflexible
VOR
fast
vision
eye vision
Act slow
delay
VOR
Slow
Flexible
Fast
Inflexible
Illusion
Highly
evolved
(hidden)
architecture
Layering
Feedback
eye vision
Act
VOR
Layering
Automatic
Unconscious
Partially
Conscious
Cerebellum
eye vision
Act slow
delay
VOR
fast
Layering
Feedback
vision
eye vision
Act slow
delay
VOR
Slow
Flexible
Fast
Inflexible
Illusion
fast
Architecture
layered/
distributed
vision
eye vision
Act slow
delay
VOR
Slow
Flexible
Fast
Inflexible
Illusion
fast
Architecture
layered/
distributed
Robust or fine-tuned? Both
Modular or plastic? Both
Slow
Flexible
vision
eye vision
Act slow
delay
Fast
Inflexible
VOR
fast
3D + motion
See Marge
Livingstone
Color?
Slow
Flexible
vision
eye vision
Act slow
delay
Fast
Inflexible
VOR
fast
See Marge
Livingstone
3D + motion
color
vision
Slowest
Stare at the intersection
Stare at the intersection.
Stare at the intersection.
Slow
Flexible
vision
eye vision
Act slow
delay
Fast
Inflexible
VOR
fast
3D + motion
color
vision
Slowest
Slow
Flexible
vision
Fast
Inflexible
VOR
color
vision
Seeing is dreaming
• is simulation • requiring “internal model”
gradient
Biased random walk
Ligand
Signal
Transduction
Motion Motor
CheY
+CH 3 R
ATP ADP P
~
flagellar motor
Z
Y
P
Y
P i B
B
P
P i
CW
-CH 3
ATP
W A
MCPs
W A
+ATT
-ATT
MCPs SLOW
FAST
ligand
binding
motor
Bacterial chemotaxis
• Internal model necessary for robust chemotaxis
• Reality is 3d, but…
• Internal model virtual and 1d
Slow
Flexible
Fast
Inflexible
Architecture
(constraints that
deconstrain)
General Special
Universal laws and architectures
(Turing)
ideal
Slow
Flexible
Fast
Inflexible
General Special
NP(time)
P(time)
analytic
Npspace=Pspace
Decidable
Computation
(on and off-line)
Slow
Flexible
vision
Fast
Inflexible
VOR
color
vision
Layering
Distributed
Feedback
Cortex
eye vision
Act slow
delay
VOR
fast
Object
motion
Head
motion
Error
+
Very rough cartoon
Cortex
eye vision
Act slow
delay
VOR
fast
Object
motion
Head
motion
Cerebellum
Error
+
Error Tune
gain
Slightly better
gain AOS
AOS = Accessory Optical system
Cortex
eye vision
Act slow
delay
VOR
This fast
“forward”
path
Object
motion
Head
motion
Cerebellum
Error
+
Error Tune
gain
Slightly better
gain AOS
AOS = Accessory Optical system
Needs
“feedback”
tuning
Via AOS and
cerebellum
(not cortex)
Cortex
eye vision
Act slow
delay
VOR
fast
Object
motion
Head
motion
Cerebellum
+
Error Tune gain
gain
AOS
AOS = Accessory Optical system
noise
Act
Highly
evolved
(hidden)
architecture
Cortex
eye vision
Act slow
delay
VOR
fast
Object
motion
Head
motion
Cerebellum
+
Error Tune gain
gain
AOS
AOS = Accessory Optical system
noise
Act
Cortex
eye vision
Act slow
delay
VOR
fast
Object
motion
Head
motion
Cerebellum
+
Error Tune gain
gain
AOS
AOS = Accessory Optical system
noise
Act
Highly
evolved
(hidden)
architecture
vision
eye vision
Act slow
delay
VOR
Slow
Flexible
Fast
Inflexible
Illusion
Highly
evolved
(hidden)
architecture
Layering
Distributed
Feedback
10
100
Length, m
.1 1 .5 .2 2
k10 -1
10 0
10 1 10
0
10 1
too
fragile
complex
No tradeoff
expensive
fragile
exp ln
expT z p
pz pT
Slow
Flexible
vision
eye vision
Act slow
delay
Fast
Inflexible
VOR
fast Universal
laws?
10
100
Length, m
.1 1 .5 .2 2
Slow
Flexible
vision
eye vision
Act slow
delay
Fast
Inflexible
VOR
fast
exp lnexp
T z pp
z pT
How do
these fit
together?
slow
flexible
fast
inflexible
How do these fit together?
“waste” “efficient”
fragile
robust
vision
VOR
delay sec/m
.01
1
.1
area
.1 1 10 diam(m)
.01 1 100
Retinal ganglion axons?
Other myelinated
Why such extreme diversity in axon size and delay?
.01
1
delay sec/m
Aα
C
.1
Aβ
Aγ Aδ
area
.1 1 10 diam(m)
.01 1 100
Axon
size and
speed
Fast
Small
Slow
Large
delay sec/m
.01
1
.1
area
.1 1 10 diam(m)
.01 1 100
Retinal ganglion axons?
Other myelinated
Why such extreme diversity in axon size and delay?
VOR No
diversity
in VOR?
Resolution and bandwidth are cheap
speed costs
axon
Same area
= same “cost”
axon axon
2 x resolution
(less noise)
axon
2 x speed
(less delay)
Double
the
area
(and
cost)?
speed costs
Resolution and bandwidth are cheap
1delay
speed
vision
Act
delay
10
100
Speed 1/
.1 1 .5 .2 2
.3s
exp p
axon axon
axon
2 x resolution
(less noise)
axon
2 x
speed doubly
expensive
but necessary
Cortex
eye vision
Act slow
delay
VOR
fast
Object
motion
Head
motion
Cerebellum
+
Error Tune gain
gain
AOS
AOS = Accessory Optical system
noise
Act
Delays
everywhere
Distributed
control
slowest
Cortex
eye vision
Act slow
delay
VOR
fast
Object
motion
Head
motion
Cerebellum
+
Error Tune gain
gain
AOS
noise
Act
slowest Heterogeneous
delays
everywhere
expE p N
Fast
Slow
Flexible Inflexible
Reflex
Sense Motor
Prefrontal
Fast
Apps
OS
HW
vision
Act
delay
axon axon
axon
2 x resolution
(less noise)
axon
2 x
speed doubly
expensive
but necessary
slow
flexible
fast
inflexible
How do these fit together?
“waste” “efficient”
fragile
robust
vision
VOR
speed
costs
slow
flexible
fast
inflexible
In general?
wasteful efficient
fragile
robust
slow
flexible
fast
inflexible
fragile
robust
waste efficient
fragile
robust
slow
flexible
fast
inflexible
fragile
robust
waste
efficient
fragile
robust
slow
flexible
fast
inflexible
waste
efficient
fragile
robust
accessible accountable accurate adaptable administrable affordable auditable autonomy available compatible composable configurable correctness customizable debugable degradable determinable demonstrable
dependable deployable discoverable distributable durable effective
evolvable extensible fail
transparent fast fault-tolerant fidelity flexible inspectable installable Integrity interchangeabl
e interoperable learnable maintainable
manageable mobile modifiable modular nomadic operable orthogonalit
y portable precision predictable producible provable recoverable relevant reliable repeatable reproducible resilient responsive reusable
safety scalable seamless self-sustainable serviceable supportable securable simple stable standards survivable
tailorable testable timely traceable ubiquitous understandable upgradable usable
efficient
robust
sustainable
PCA Principal Concept Analysis
flexible
fast
efficient
robust
slow
flexible
fast
inflexible
waste
efficient
slow
flexible
fast
inflexible
waste
efficient
Slow
slow
inflexible
fragile
waste Same
picture