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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