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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. Dynamic Discrete-Event Systems. Dynamic Discrete-Event Systems. Dynamic Discrete-Event Systems. Online Control. Online Controller. Control

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Issues in Optimal Control of Dynamic DESs

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

  2. DynamicDiscrete-Event Systems Lenko Grigorov and Karen Rudie, Queen's University

  3. DynamicDiscrete-Event Systems Lenko Grigorov and Karen Rudie, Queen's University

  4. DynamicDiscrete-Event Systems Lenko Grigorov and Karen Rudie, Queen's University

  5. DynamicDiscrete-Event Systems Lenko Grigorov and Karen Rudie, Queen's University

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

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

  8. Simple Optimal Algorithm 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))  5 2  6 1 3 7 8 4 Lenko Grigorov and Karen Rudie, Queen's University

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

  10. Example system Small truck, 10 logs Big truck, 10 or 20 logs Photo courtesy of Daniel Janzen Photo by Patrick Higgins Lenko Grigorov and Karen Rudie, Queen's University

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

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

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

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

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

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

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

  18. Current research • Online control with normalization Loss of optimality Speedup Tree depth Tree depth Lenko Grigorov and Karen Rudie, Queen's University

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

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