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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?

6

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

RxA

RxB

RxA C

ACB

C

C

Reactor Feed Rates

9

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

10

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

11

Feed

Product

Cooling water

Stirring (Work)

1

2

3 4

BDH Tellegen:1900-1990

Brayton/MoserDesoer/Oster/PerelsonBrockett/WillemsJan van der Schaft

Prigogine/Maxwell/Nyquist theorems

12

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)

13

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”

1

optF

2

optF

1

optw

2

optw

“Balance the potentials so the

gradients are minimized.” “Distribute flows so the total flows

is maximized.”

14

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.

15

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

16

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

(Alf Isakson, ABB)

(Alf Isakson, ABB)

4756 lines

of assembly

code

15 lines

of MATLAB

codeCMU

Pitt

Industrial Application of Adaptive MPC 1983