Transcript Issues in Optimal Control of Dynamic DESs

Issues in Optimal Control of
Dynamic DESs
Lenko Grigorov and Karen Rudie
Queen’s University
Kingston, Canada
Dynamic
Discrete-Event Systems
July, 2005
Lenko Grigorov and Karen Rudie,
Queen's University
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Dynamic
Discrete-Event Systems
July, 2005
Lenko Grigorov and Karen Rudie,
Queen's University
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Dynamic
Discrete-Event Systems
July, 2005
Lenko Grigorov and Karen Rudie,
Queen's University
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Dynamic
Discrete-Event Systems
July, 2005
Lenko Grigorov and Karen Rudie,
Queen's University
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Online Control
Online Controller
Control
options
Events
Discrete-Event System
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Lenko Grigorov and Karen Rudie,
Queen's University
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Look-ahead tree
5
2
1
6
3
4
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controllable
uncontrollable
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Lenko Grigorov and Karen Rudie,
Queen's University
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Simple Optimal Algorithm


1
2
6
3
4
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5
7
8
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))
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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Lenko Grigorov and Karen Rudie,
Queen's University
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Example system
Small truck, 10 logs
Big truck, 10 or 20 logs
Photo courtesy of Daniel Janzen
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Lenko Grigorov and Karen Rudie,
Queen's University
Photo by Patrick Higgins
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Values of events
v(goS)
v(goB)
v(fetch10)
v(fetch20)
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= -100
= -150
= 500
= 1000
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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Lenko Grigorov and Karen Rudie,
Queen's University
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Insufficient information
Depth = 1
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Lenko Grigorov and Karen Rudie,
Queen's University
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Overspecialization
Time 0
Depth = 4
Future
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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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Lenko Grigorov and Karen Rudie,
Queen's University
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Long-term planning vs.
Greediness
Depth = 3
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Lenko Grigorov and Karen Rudie,
Queen's University
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Discussion

Optimal control for static systems is
not suitable for dynamic systems

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Less emphasis on strings far in
the future
Greedy approach
Lenko Grigorov and Karen Rudie,
Queen's University
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Current research

Online control with normalization
Loss of optimality
Tree depth
July, 2005
Speedup
Tree depth
Lenko Grigorov and Karen Rudie,
Queen's University
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Queen’s University
July, 2005
Lenko Grigorov and Karen Rudie,
Queen's University
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