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![Page 1: Issues in Optimal Control of Dynamic DESs Lenko Grigorov and Karen Rudie Queen’s University Kingston, Canada.](https://reader034.fdocuments.us/reader034/viewer/2022052607/5a4d1b467f8b9ab0599a34f6/html5/thumbnails/1.jpg)
Issues in Optimal Control of Dynamic DESs
Lenko Grigorov and Karen Rudie
Queen’s UniversityKingston, Canada
![Page 2: Issues in Optimal Control of Dynamic DESs Lenko Grigorov and Karen Rudie Queen’s University Kingston, Canada.](https://reader034.fdocuments.us/reader034/viewer/2022052607/5a4d1b467f8b9ab0599a34f6/html5/thumbnails/2.jpg)
July, 2005 Lenko Grigorov and Karen Rudie, Queen's University
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DynamicDiscrete-Event Systems
![Page 3: Issues in Optimal Control of Dynamic DESs Lenko Grigorov and Karen Rudie Queen’s University Kingston, Canada.](https://reader034.fdocuments.us/reader034/viewer/2022052607/5a4d1b467f8b9ab0599a34f6/html5/thumbnails/3.jpg)
July, 2005 Lenko Grigorov and Karen Rudie, Queen's University
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DynamicDiscrete-Event Systems
![Page 4: Issues in Optimal Control of Dynamic DESs Lenko Grigorov and Karen Rudie Queen’s University Kingston, Canada.](https://reader034.fdocuments.us/reader034/viewer/2022052607/5a4d1b467f8b9ab0599a34f6/html5/thumbnails/4.jpg)
July, 2005 Lenko Grigorov and Karen Rudie, Queen's University
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DynamicDiscrete-Event Systems
![Page 5: Issues in Optimal Control of Dynamic DESs Lenko Grigorov and Karen Rudie Queen’s University Kingston, Canada.](https://reader034.fdocuments.us/reader034/viewer/2022052607/5a4d1b467f8b9ab0599a34f6/html5/thumbnails/5.jpg)
July, 2005 Lenko Grigorov and Karen Rudie, Queen's University
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DynamicDiscrete-Event Systems
![Page 6: Issues in Optimal Control of Dynamic DESs Lenko Grigorov and Karen Rudie Queen’s University Kingston, Canada.](https://reader034.fdocuments.us/reader034/viewer/2022052607/5a4d1b467f8b9ab0599a34f6/html5/thumbnails/6.jpg)
July, 2005 Lenko Grigorov and Karen Rudie, Queen's University
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Online Control
Online Controller
Discrete-Event System
Controloptions Events
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July, 2005 Lenko Grigorov and Karen Rudie, Queen's University
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Look-ahead tree
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25
6
3
4
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8
controllable
uncontrollable
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July, 2005 Lenko Grigorov and Karen Rudie, Queen's University
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Simple Optimal Algorithm
1
25
6
3
4
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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))
![Page 9: Issues in Optimal Control of Dynamic DESs Lenko Grigorov and Karen Rudie Queen’s University Kingston, Canada.](https://reader034.fdocuments.us/reader034/viewer/2022052607/5a4d1b467f8b9ab0599a34f6/html5/thumbnails/9.jpg)
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
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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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July, 2005 Lenko Grigorov and Karen Rudie, Queen's University
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Values of events
v(goS) = -100 v(goB) = -150v(fetch10) = 500v(fetch20) = 1000
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July, 2005 Lenko Grigorov and Karen Rudie, Queen's University
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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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July, 2005 Lenko Grigorov and Karen Rudie, Queen's University
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Insufficient information
Depth = 1
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July, 2005 Lenko Grigorov and Karen Rudie, Queen's University
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OverspecializationTime 0
Future
Depth = 4
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July, 2005 Lenko Grigorov and Karen Rudie, Queen's University
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Overspecialization Real situation:
T0: T2: T4: Algorithmic solution (v=1600):
T0: T2: T4: Best solution (v=1650):
T0: T2: T4:
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July, 2005 Lenko Grigorov and Karen Rudie, Queen's University
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Long-term planning vs. GreedinessDepth = 3
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July, 2005 Lenko Grigorov and Karen Rudie, Queen's University
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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
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July, 2005 Lenko Grigorov and Karen Rudie, Queen's University
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Queen’s University