the role of adaptive control in & dynamics quantum ... · mark j. balas distinguished professor...
Post on 24-Jul-2020
2 Views
Preview:
TRANSCRIPT
The Role of Adaptive Control in
Quantum Information Systems
Mark J. Balas
Distinguished Professor
Aerospace Engineering Department
Embry-Riddle Aeronautical University
Daytona Beach, FL
1
Mark’s Autonomous
Control Laboratory
Control
EstimationModeling
& DynamicsGuidance
Control
EstimationModeling
& DynamicsGuidance
Control
EstimationModeling
& DynamicsGuidance
Control
EstimationModeling
& DynamicsGuidance
Control
EstimationModeling
& DynamicsGuidance
Control
EstimationModeling
& DynamicsGuidance
Application
Theory
iain-HamiltonControl
ResolventCompact
AdjointSelf
0 )(
uHHt
i C
It’s not theories about stars;
it’s the actual stars that count.”
……… Freeman Dyson
Plant
Parameter
Estimation
+
Gain
Re-calculator
State Estimator
State
Feedback
Gain
ur
Indirect Adaptive Control
Note: Called “Self-Organizing” System (Kalman)
& “Self-Tuning” Regulator ( Astrom)
u y
3
4
Direct Adaptive Model Following Control
(Wen-Balas 1989)
0tye
Plant
Reference
Model
Gm
Gu
Ge
um ym
xm
y u
+
Adaptive
Gain Laws
SignalsKnown ),,( ymm exu
Infinite
Dimensional
5
Direct Adaptive Persistent Disturbance Rejection
(Fuentes-Balas 2000)
0tye
Plant
Reference
model
Ge
um ym
xm
y u
+
Adaptive
Gain Laws
SignalsKnown ),,,(
Basis eDisturbanc
Dymm exu
Disturbance
Generator
Persistent Disturbance Example
6
D
BA
utu
1
0)(
1
0
00
10
D
D
t
taaatataau
t
tlltAu
L
D
D
D
L
DDDD
2
210
2
210
21
1
cos
sin )sin(
esDisturbanc
Known
Basis
Known
Basis
Unknown
7
)(
)()(Plant Nonlinear
xCy
uxBxAt
x
Adaptive Regulation
u
Gy
Nonlinear Adaptive Gain Law
0; TyyG
y
G
Controller
0t
x
Adaptive Control Is Not Complicated !
Use ONLY
Outputs &
Know Almost
NOTHING
about the Plant
“Simplicity” via Infinite
Dimensional Spaces
8
0;)(),(
)(
SpaceHilbert or Banach )0(
)()(
000
txtUwtx
xCy
Xxx
uxBxAt
x
XinEvolution
NonlinearorLinear
“Boil Away” all the special properties of N
Infinite-Dimensional Space
Viewpoint: Linear Semigroups
9
0;)()()(),(
operatorlinear defineddensely closed, )(:
)0(
000
0
tXdFtUxtUwtx
XXADA
xx
FAxt
x
t
0)at t continuous ( )(
) generates ( )()()(
property) (semigroup )()()(
:)( Operators Bounded of Semigroup
000
0
xxtU
U(t)AAtUtAUtUdt
d
sUtUstU
tUC
t
Hilbert Space
with inner
product ),( yx
J. Wen & M.Balas, “Robust Adaptive Control in Hilbert
Space ”,
J. Mathematical. Analysis and Applications, Vol 143, pp 1-26,1989.
J. Wen & M.Balas ,"Direct Model Reference Adaptive
Control in Infinite-Dimensional Hilbert Space," Chapter in
Applications of Adaptive Control Theory, Vol.11,
K. S. Narendra, Ed., Academic Press, 1987
Example: Heat Diffusion
10
2
2
2
0
;
( ) ( ) / smooth and BC: 0 0
( )
with , ( ) ( )
(0) ( )
( , ); ( ) ( )
Ax
x xbu
t z
b z D A x x(t, ) x(t,l)
X L
x y x t y t dt
x x D A
y c x c z D A
)(),0(0 zfzxx
0)0,( tx 0),( ltx
z
)(ty)(tu
Euler-Bernoulli Beam
11
4
4
00
( )( )0t t
A
Iw w
u tEIw w b zt
z
Symmetric Hyperbolic Systems
12
0;0),()(:
);()(; 2
constant
0
1
symmetricconstant
tztzzConditions
Boundary
LXADxAz
At
l
A
lxl
n
i ilxl
i
resolvent.compact has and 0),(),(
)( Coercive are ConditionsBoundary )4
)(dim)3
02)
0rnonsingula is)(:Symbol )1
1967) Phillips-Lax from help w1974, Balas(:
1
NormSobolev
*
0
1
AAA
A
AN
AA
AA
Theorem
o
nn
i
ii
Examples
13
t
z
z
AAA
t
x
x
x
x
x
xxz
x
z
xx
xz
x
z
x
t
x
2
1
021
where
000
1011
0001
0010
0010
0101
1000
0100
0001
0110
0100
1000
)(equation wavedim-2
21
2
2
2
1
2
2
2
2
Wave Equation
23
4
1
Dirac Equation: ( ) ( )i
i iPauliSpinMatrices
mcc A i I
t x
Relativistic Fields ( Mandl & Shaw 2010)
14
Stability via Lyapunov-Barbalat
0
0
allfor as 0)(0)(*
0)0(
0 when 0)(
)( :Function like-Energy Find
)0(
)(DynamicsNonlinear
xttxxfgradVV
V
xxV
xV
xx
xfx
N
bounded are )( ies trajectorAll 0 txV
ttVtV as 0)(continuousuniformly and 0)(
:lemma sBarbalat' From
Often does
Not happen
15
Infinite-Dimensional Lyapunov-Barbalat Theory: PDE & Delay Systems
0;)()(with
)(2
1),(),,(
Let
0
1
tXxtUtx
GGtrxtVGxtV T
SpaceBanach or Hilbert X
var
( ( , ) ) ( , , ) ( ( , ) )Theorem: If
( , , ) ( ) 0
( ( )) ( )and ( ) is bounded, then ( ( )) 0 and bounded.
If is coercive in the partial state
t
FrechetDeri ive
x G V t x G x G
V t x G W x
dW x t W x tW x t G
dt x t
W(x)
x ,or ( ) ( ), then ( ) 0.t
W x x x t
Linear or Nonlinear
Evolution
16
Cxy
uBuAxx D
Adaptive Model Tracking
in the Presence
of Persistent Disturbances
y
u
DD Lu
Adaptive Gain Law
),,,( DmmyDmue yuehGGGGG
Controller
),0(or 0 *RNety
mmm
mmmmm
xCy
uBxAx
Reference Model
my
),0(or 0 ** RNxxxt
Adaptive Control Law
where
ionStabilizatRejection eDisturbancTracking Model
T
yye
T
DyD
T
mym
T
myu
yeDDmmmu
eeG
eG
xeG
ueG
eGGwGuGu
Gain Adaptation
Laws
17
Using Ideal Trajectories
Solar Power System Satellite
Long Ago
and Far Away
18
NASA-Johnson
Hubble, Bubble, Toil and Trouble
19
NASA MSFC
Deployable
Optical Telescope
DOT
Primary Mirror
Supports
AFRL-Kirtland
Deployable Optical Telescope Experiment R. Fuentes, M. Balas, K. Schrader, and R.S. Erwin "Direct Adaptive Disturbance Rejection and Control for a Deployable
Space Telescope, Theory and Application”, Proceedings of ACC, Arlington, VA, June 2001.
Steering
Mirrors
22
Evolving Systems=
Autonomously
Assembled
Active Structures
Or Self-Assembling
Structures,
which Aspire to a
Higher Purpose;
Cannot be attained
by Components Alone
Control
EstimationModeling
& DynamicsGuidance
Control
EstimationModeling
& DynamicsGuidance
Control
EstimationModeling
& DynamicsGuidance
Control
EstimationModeling
& DynamicsGuidance
Control
EstimationModeling
& DynamicsGuidance
Control
EstimationModeling
& DynamicsGuidanceEvolving Systems
NASA-JPL & MSFC
23
Genetics of Evolving
Systems: Inheritance
of
Component Traits
Controllability/Observability
Stability
Optimality
Robustness
Disturbance Rejection/Signal Tracking
Source: CNN.com
Stability is Necessary During the
Entire Evolution Process
Irony: Synthetic Biology ???
Composability in Synthetic Biology
“It is difficult to define signal exchanges between
biological units unambiguously”
25
F-16 Flexible Structure Model:
Fluid-Structure Interaction
USAF-Edwards AFB
Flight Test Center
Flutter
One Possible Solution
Aerodynamically
Shaped Graduate
Student
Smart Grids:
Virtual Interconnecting Forces
27
“It is surprising how quickly we replace a human operator
with an algorithm and call it SMART”
Wind Energy
1979: 40 cents/kWh
210 MW Lake Benton Wind Farm 4 cents/kWh
2006: 3 - 5 cents/kWh
2000: 4 - 6 cents/kWh
• R & D Advances
• Increased Turbine Size
• Manufacturing
Improvements
• Large Wind Farms
Who Needs Control Anyway?
NREL-NWTC
Flow Control of Wind Turbine Aerodynamics
Power System
Perturbed with a Wind Farm
• When a wind farm is placed at
a distance of α, the perturbed
power system becomes :
with
• Power flow at a distance u is :
Adaptive Control in
Quantum Information Systems
31
Merde
Quantum Computing
32
A Quantum computer will operate differently from a Classical one.
It will be involved w physical systems on an atomic scale,
eg atoms, photons, trapped ions, or nuclear magnetic moments
Quantum Gate
Unitary Reversible
Could be improved with Adaptive Control
So Quantum Error Correctiion can work!!!
Q
Quantum Information Systems
Quantum Basics
(Dirac & Von Neumann)
34
states" pure ofn combinatioconvex a is stateA "
c1&c1or 1),(
:SpaceHilbert complex State
2
1k
k
2
1k
k
k
X
A
xAx
XXA
k
xP
kk
k
k
adjoselfbounded
k
of ionseigenfunct :States Pure
),(Resolvent Compact
: Observable
1
int
Orthonormal
Eigen –Basis for X
Schrodinger Wave Equation
35
10 )( Spectrum Real Discrete
kkH
kllkkk
k
ti ketU
XXtU
, with ,)( and
e)(reversibl GroupUnitary :)(
1
0
0
)(
SpaceHilbert complex
ian-Hamilton
Control
ResolventCompact
AdjointSelf
0
uHHt
i
X
C
Marginally
Stable
OLD
NEW
itt
:Time Imaginary
with Diffusion
Quantum Measurement
36
S M
Back
Action
wh
XXX
lk
M
l
S
kkl
MS
,
)(
ntEntangleme
Ontology ( what is) vs Epistemology ( What is measured)
YOW!!
!
Uncertainty Principle
37
yx(x,y) 0
Inequality Schwarz-Cauchy
todueProperty SpaceHilbert A
BAABBABATrBA
BA
TrAATrΔA
ATrA
XXA
],[ commutator ;]),[(2
)()(
& oft Measuremen usSimultaneo :Principlety UncertainHeisenberg
)1)(&0( operatordensity or state a is where))(( Dispersion
)(Mean
Hilbert : Observable
22
2
adjoint-selfbounded
2
2
22 )2
()],[()()( Recall
i
pzTrpz
In fact ALL of Quantum Mechanics is based on a Hilbert space
of states and a (C*) algebra of bounded linear self adjoint observables
Small Quantum Systems
We can begin to experiment with just one
electron, atom or small molecule
Need:
Precise control
Isolation from the environment
Simple small systems : single particles or
small groups of particles
…… David Wineland NIST
38
Control of Individual Quantum
Systems: Quantum Feedback Loop
39
Purpose:
Use information from weak QND measurements to prepare photon number
(Fock) states of a cavity field and
protect them against decoherence.
Method:
Quantum feedback realized by atoms as QND probes and
small coherent field injections into the cavity mode as an
actuator.
Physics Nobel Prize 2012
S. Haroche & D. Wineland
40
Adaptive Quantum
Model Tracking to Reduce
Decoherence
y
u
DD Lu
Adaptive Gain Law
),,,( DmmyDmue yuehGGGGG
Adaptive Quantum Controller
),0(or 0 *RNety
Desired
Hamiltonian
*H
Reference Model:
Closed System
my
),(
)(
Re
int
0
cy
HuHHt
i
esDisturbanc
Linblad
Control
C
solventCompact
AdjoSelf
Open Physical System
QND Measurement
&Quantum Error Correction
“Physics is like sex: sure, it may give
some practical results, but that's not why
we do it.”
― Richard P. Feynman
In a tile motif on the back of the Ross Dress For Less building
on Lake Ave, Pasadena, CA
41
Infinite-Dimensional Adaptive
Control Theory
top related