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Optimal Decisions with Limited Information : Overview. Geir E. Dullerud University of Illinois PhD Defense: Ather Gattami Lund Institute of Technology June 8, 2007. Optimal Decisions with Limited Information. Global objective to attain.

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Optimal Decisions with Limited Information : Overview


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    1. Optimal Decisions with Limited Information: Overview Geir E. Dullerud University of Illinois PhD Defense: Ather Gattami Lund Institute of Technology June 8, 2007

    2. Optimal Decisions with Limited Information • Global objective to attain. • How can a team of decision makers, each with different information about the world, achieve the objective?

    3. System Team Problems y u Formulation.

    4. destination source network source destination Data networks: Internet Attempt to achieve globally optimal utility: • sources and destinations on edge of network • transmision rates based partial observations inside

    5. Example: UAVs Teams Boeing picture of UAVs removed Cooperative vehicle teams: • Military • Civilian

    6. Example: Power Networks • Mission critical on large geographic scale • local control and observation • global stability

    7. System Team and Centralized Problems y u Formulation.

    8. Team Example

    9. Team Example

    10. Theme to Thesis • First solve the static case • Then consider dynamic case • Restrict to non-signaling case • Show the dynamic case can be solved using static approach

    11. Static and Dynamic Estimation

    12. Single-Player Static Estimation: Minimax

    13. Single-Player Static Estimation: Other costs Stochastic Estimation Error-Operator Minimization

    14. Team Static Estimation: Minimax

    15. Optimal Distributed Filtering • static problem can be used to solve a type of distributed filtering problem, in conjunction with Kalman filtering (infinite horizon) • works for both 2-norm and infinity norm on transfer functions

    16. Stochastic Team Decisions

    17. Static Stochastic Team Decision Problem

    18. Static Stochastic Team Decision Problem

    19. Signaling in Team Problems

    20. Signaling Incentive

    21. Distributed LQG Control

    22. Distributed LQG Control

    23. Minimax Team Decision

    24. Static Minimax Team Decision Problem

    25. Static Minimax Team Decision Problem

    26. Distributed H Control

    27. Distributed H Control

    28. Additional Contributions

    29. Additional Contributions • Considered distributed control over infinite horizons (H-2 and H-infty); achieved via new approach for centralized state feedback case. • Quadratic control with non-convex power constraints; solve finite horizon non-stationary problem and extend to infinite horizon.

    30. Questions Scalability of synthesis solutions? Significant examples worked? General architectures for distributed control? Minimax and Witsenhausen counter example? Exponential-of-Gaussian and minimax team problem? Some technical clarifications?

    31. Optimal Decisions with Limited Information: Overview Geir E. Dullerud University of Illinois PhD Defense: Ather Gattami Lund Institute of Technology June 8, 2007