Issues in Optimal Control of Dynamic DESs

Lenko Grigorov and Karen Rudie

Queen’s UniversityKingston, Canada

July, 2005 Lenko Grigorov and Karen Rudie, Queen's University

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DynamicDiscrete-Event Systems

July, 2005 Lenko Grigorov and Karen Rudie, Queen's University

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DynamicDiscrete-Event Systems

July, 2005 Lenko Grigorov and Karen Rudie, Queen's University

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DynamicDiscrete-Event Systems

July, 2005 Lenko Grigorov and Karen Rudie, Queen's University

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DynamicDiscrete-Event Systems

July, 2005 Lenko Grigorov and Karen Rudie, Queen's University

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Online Control

Online Controller

Discrete-Event System

Controloptions Events

July, 2005 Lenko Grigorov and Karen Rudie, Queen's University

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Look-ahead tree

1

25

6

3

4

7

8

controllable

uncontrollable

July, 2005 Lenko Grigorov and Karen Rudie, Queen's University

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Simple Optimal Algorithm

1

25

6

3

4

7

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Value: v(x)

v(5)= v+v

v(2)=max(v(5),v(6))v(3)=max(v(7),v(8))v(1)=min(v(3),v(4))

July, 2005 Lenko Grigorov and Karen Rudie, Queen's University

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Issues with Optimal Control

Insufficient information vs. Overspecialization

Long-term planning vs. Greediness

July, 2005 Lenko Grigorov and Karen Rudie, Queen's University

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Example system

Photo by Patrick HigginsPhoto courtesy of Daniel Janzen

Small truck, 10 logs Big truck, 10 or 20 logs

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Values of events

v(goS) = -100 v(goB) = -150v(fetch10) = 500v(fetch20) = 1000

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Specifications Different number and types of

trucks available.

We can rent only one truck at a time.

We need 40 logs.

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Insufficient information

Depth = 1

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OverspecializationTime 0

Future

Depth = 4

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Overspecialization Real situation:

T0: T2: T4: Algorithmic solution (v=1600):

T0: T2: T4: Best solution (v=1650):

T0: T2: T4:

July, 2005 Lenko Grigorov and Karen Rudie, Queen's University

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Long-term planning vs. GreedinessDepth = 3

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Discussion Optimal control for static systems

is not suitable for dynamic systems Less emphasis on strings far in the future

Greedy approach

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Current research Online control with normalizationLoss of optimality Speedup

Tree depth Tree depth

July, 2005 Lenko Grigorov and Karen Rudie, Queen's University

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Queen’s University