1. Issues in Optimal Control of Dynamic DESs Lenko Grigorov and Karen Rudie Queen’s University Kingston, Canada

2. July, 2005 Lenko Grigorov and Karen Rudie, Queen's University2 Dynamic Discrete-Event Systems

3. July, 2005 Lenko Grigorov and Karen Rudie, Queen's University3 Dynamic Discrete-Event Systems

4. July, 2005 Lenko Grigorov and Karen Rudie, Queen's University4 Dynamic Discrete-Event Systems

5. July, 2005 Lenko Grigorov and Karen Rudie, Queen's University5 Dynamic Discrete-Event Systems

6. July, 2005 Lenko Grigorov and Karen Rudie, Queen's University6 Online Control Online Controller Discrete-Event System Control options Events

7. July, 2005 Lenko Grigorov and Karen Rudie, Queen's University7 Look-ahead tree 1 2 5 6 3 4 7 8 controllable uncontrollable

8. July, 2005 Lenko Grigorov and Karen Rudie, Queen's University8 Simple Optimal Algorithm 1 2 5 6 3 4 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))  

9. July, 2005 Lenko Grigorov and Karen Rudie, Queen's University9 Issues with Optimal Control Insufficient information vs. Overspecialization Long-term planning vs. Greediness

10. July, 2005 Lenko Grigorov and Karen Rudie, Queen's University10 Example system Photo by Patrick HigginsPhoto courtesy of Daniel Janzen Small truck, 10 logsBig truck, 10 or 20 logs

11. July, 2005 Lenko Grigorov and Karen Rudie, Queen's University11 Values of events v(goS) = -100 v(goB) = -150 v(fetch10) = 500 v(fetch20) = 1000

12. July, 2005 Lenko Grigorov and Karen Rudie, Queen's University12 Specifications Different number and types of trucks available. We can rent only one truck at a time. We need 40 logs.

13. July, 2005 Lenko Grigorov and Karen Rudie, Queen's University13 Insufficient information Depth = 1

14. July, 2005 Lenko Grigorov and Karen Rudie, Queen's University14 Overspecialization Time 0 Future Depth = 4

15. July, 2005 Lenko Grigorov and Karen Rudie, Queen's University15 Overspecialization Real situation: T0:T2:T4: Algorithmic solution (v=1600): T0:T2:T4: Best solution (v=1650): T0:T2:T4:

16. July, 2005 Lenko Grigorov and Karen Rudie, Queen's University16 Long-term planning vs. Greediness Depth = 3

17. July, 2005 Lenko Grigorov and Karen Rudie, Queen's University17 Discussion Optimal control for static systems is not suitable for dynamic systems Less emphasis on strings far in the future Greedy approach

18. July, 2005 Lenko Grigorov and Karen Rudie, Queen's University18 Current research Online control with normalization Loss of optimalitySpeedup Tree depth

19. July, 2005 Lenko Grigorov and Karen Rudie, Queen's University19 Queen’s University