Distributed Decision Making: The Adaptive...
Transcript of Distributed Decision Making: The Adaptive...
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Distributed Decision Making: The Adaptive Enterprise
2040 Visions of Process Systems Engineering
Symposium on the Occasion of George Stephanopoulos's 70th Birthday and Retirement from MIT
B. Erik YdstieCAPD, Carnegie Mellon University
Some Slides Adapted from “Network Session” and positon paper from FIPSE II, Crete• Alf Isakson (ABB)• Ricardo Scattolini (Politecnico di Milano)
Paln
PlanningScheduling
Realtimeoptimization
ModelPredictiveControl
RegulatoryControl
PLC
CPC Announces the Development of Hierarchical ControlShell Process Control Workshop, Houston TX, Dec, 1986
The Pyramid!
Dynamic Information flows up
AIM: Stability and Robustness
$
FOCAPO Develops Hierarchical Optimization
The Inverted Pyramid!
PalnPlanningScheduling
Realtimeoptimization
ModelPredictiveControl
RegulatoryControl
PLC
Decisions flow down under the authority of the optimizer
AIM: Maximize Profit (NPV) $
AIM: Optimal Decisions
PSE Application Challenges
• Control and optimization in CPS apply to networked (flat) systems
• Design and verify automation and safety systems with discrete decisions in real time (>10^200 states)
• Lots of (big) data (time-series, audio, video), but - how much information is there really?
• How to integrate models, algorithms, sensors and physical devices to adapt in real time?
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DATA FITTING
signals thematching
0
)sin(orbit tiai
i
"By the study of the orbit of Mars,
we must either arrive at the
secrets of astronomy or forever
remain in ignorance of them." -
Johannes Kepler
Regression
Analysis
Process models and Big Data
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PHYSICS
maF
Regression
AnalysisPhysical
Models
Isaac Newton’s laws using
the physics
(Hamilton principle of
minimum action)
Process models and Big Data
Nature calculates optimal trajectories
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Minimum entropy production
Minimizing Dissipation by minimizing “Gradients”
geese
• Linear -> QP
• Constraints - > LP
• On-off -> IP
J. C. Maxwell:Thm. of
Minimum Heat
H. Nyquist:Fluctuation
Dissipation Thm.
I. Prigogine:Thm. of
minimum entropy
production
Tellegen (Weyl) Theorem
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Feed
Product
Cooling water
Stirring (Work)
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2
3 4
BDH Tellegen:1900-1990
Brayton/MoserDesoer/Oster/PerelsonBrockett/WillemsJan van der Schaft
Prigogine/Maxwell/Nyquist theorems
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Theorem 1: Given a process network with flows derived from a convex
potential. Then the solution to the following problems (A) and (B) are
equivalent.
constantand/or constant :B.C.
equations veConstituti
,, ,
,, ,0AF
:(A) Problem
TT
Tfp
T
WF
wWwWwAW
fpdt
dZF
constantand/or constant :B.C.
equations veConstituti
min
:(B) Problem0
*
w
TT
T
W
WF
wAW
FdWG
Dynamic simulation:
Stable if constitutive
equations are positive
Dynamic optimization:
Solution is unique if constitutive
equations are positive
(=objective function is convex)
What is the Objective Function? (Michael Wartmann, CMU PhD, 2010)
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Interpretation of the content and co-content minimization problems
* TG d
W
F WT
G d F
W Fminw
and
Fmin
The “flow distribution problem”The “potential balancing problem”
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optF
2
optF
1
optw
2
optw
“Balance the potentials so the
gradients are minimized.” “Distribute flows so the total flows
is maximized.”
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Interpretation of the content and co-content minimization problems
* TG d
W
F WT
G d F
W F
The network solves 2 optimization problems by minimizing the total dissipation!
minw
and
Fmin
The “flow distribution problem”The “potential balancing problem”
1
optF
2
optF
1
optw
2
optw
T
S R R F Wmin Prigogine, min entropy prod.
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The transient problem: Minimizing entropy dissipation along a dynamic trajectory
“Minimum entropy principle holds along a dynamic trajectory.”
( ) ( ) ( )T
S R Rt t t F Wmin
s.t.
( )
( )
T
T W
T
T F
f t
f t
W
FBC
Network equations of certain state at any point in time
and further
0T TS R RR R
d d d
dt dt dt
W FF W
0 0
} }
Entropy dissipation decreases from initial state along trajectory
until final state (steady state) where it is minimized.
S
t
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A
B
Resource Product
Everything else being equal –
“Free” Market chooses the cheaper supplier.
A B
Resource Product
Companies A and B compete for a limited and fixed profit --- cooperation can lead to increased market share by reducing cost.
Distributed Decision Making
During the last decades PSE R&D has focused almost exclusively on incremental process improvements using (much improved) computational architectures, techniques and
solutions methodologies. (Hierarchical/centralized computing and communication)
SchedulingPredictive ControlProcess monitoring, Statistical analysis of process dataModeling complex systemsProcess OptimizationDesign and retrofit++++
PSE Challenge for the next 20 years
EmbeddedDevices
communication
ProductsEnergy
Achieve conflux of physical and man-made optimization (variational) principles(economics vs climate and ecology -> sustainable development)
Integrating Distributed Models and Data (SAOB- Sea Spray)(Peter Adams, CE and Dana McGuffin, ChemE)
GEOS Chem THOMAS
Aqua/Terra