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Optimal Distributed State Estimation and Control, in the Presence of Communication Costs

Optimal Distributed State Estimation and Control, in the Presence of Communication Costs. Nuno C. Martins. nmartins@umd.edu. Department of Electrical and Computer Engineering Institute for Systems Research University of Maryland, College Park.

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Optimal Distributed State Estimation and Control, in the Presence of Communication Costs

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  1. Optimal Distributed State Estimation and Control, in the Presence of Communication Costs Nuno C. Martins nmartins@umd.edu Department of Electrical and Computer Engineering Institute for Systems Research University of Maryland, College Park AFOSR, MURI Kickoff Meeting, Washington D.C., September 29, 2009

  2. Introduction • Setup is a network whose nodes • might comprise of: • Linear dynamic systems • Sensors with transmission • capabilities • Receivers including state • estimator A Simple Configuration:

  3. Introduction • Setup is a network whose nodes • might comprise of: • Linear dynamic systems • Sensors with transmission • capabilities • Receivers including state • estimator A Simple Configuration: • Applications: • Tracking of stealthy aerial vehicles via (costly) • highly encrypted channels.

  4. Introduction • Setup is a network whose nodes • might comprise of: • Linear dynamic systems • Sensors with transmission • capabilities • Receivers including state • estimator A Simple Configuration: • Applications: • Tracking of stealthy aerial vehicles via (costly) • highly encrypted channels. • Distributed learning and control over power • limited networks. NSF CPS: Medium 1.5M Ant-Like Microrobots - Fast, Small, and Under Control PI: Martins, Co PIs: Abshire, Smella, Bergbreiter

  5. Introduction • Setup is a network whose nodes • might comprise of: • Linear dynamic systems • Sensors with transmission • capabilities • Receivers including state • estimator A Simple Configuration: • Applications: • Tracking of stealthy aerial vehicles via (costly) • highly encrypted channels. • Distributed learning and control over power • limited networks. • Optimal information sharing in organizations.

  6. A Simple Configuration: • Setup is a network whose nodes • might comprise of: • Linear dynamic systems • Sensors with transmission • capabilities • Receivers including state • estimator Ultimately, we want to tackle general instances of the multi-agent case.

  7. A New Method for Certifying Optimality Major results: Nonlinear, non-convex. Optimality was a long standing open problem. Solution is provided in: G. M. Lipsa, N. C. Martins, “Certifying the Optimality of a Distributed State Estimation Scheme via Majorization Theory”, submitted to TAC, 2009 Optimal solution: Transmit Erasure time Transmit

  8. A New Method for Certifying Optimality Major results: Nonlinear, non-convex. Optimality was a long standing open problem. Solution is provided in: G. M. Lipsa, N. C. Martins, “Certifying the Optimality of a Distributed State Estimation Scheme via Majorization Theory”, submitted to TAC, 2009 Optimal solution: Transmit Numerical method to compute Optimal thresholds Erasure time Transmit

  9. A New Method for Certifying Optimality Major results: Nonlinear, non-convex. Optimality was a long standing open problem. Solution is provided in: G. M. Lipsa, N. C. Martins, “Certifying the Optimality of a Distributed State Estimation Scheme via Majorization Theory”, submitted to TAC, 2009 Optimal solution (a modified Kalman F.): yes Erasure? Execute K.F. no

  10. A New Method for Certifying Optimality Major results: Nonlinear, non-convex. Optimality was a long standing open problem. Solution is provided in: G. M. Lipsa, N. C. Martins, “Certifying the Optimality of a Distributed State Estimation Scheme via Majorization Theory”, submitted to TAC, 2009 Past work:

  11. A New Method for Certifying Optimality Major results: Nonlinear, non-convex. Optimality was a long standing open problem. Solution is provided in: G. M. Lipsa, N. C. Martins, “Certifying the Optimality of a Distributed State Estimation Scheme via Majorization Theory”, submitted to TAC, 2009 Past work: Issai Schur Key to our proof is the use of majorization theory. Frigyes Riesz

  12. Recent Extensions Tandem Topology …

  13. Recent Extensions Tandem Topology … Threshold policy Memoryless forward Modified K.F. Optimal

  14. Recent Extensions Tandem Topology … Threshold policy Memoryless forward Modified K.F. Optimal Control with communication costs (Lipsa, Martins, Allerton’09)

  15. Problems with Non-Classical Information Structure Multiple-stage Gaussian test channel

  16. Problems with Non-Classical Information Structure Multiple-stage Gaussian test channel Lipsa and Martins, CDC’08

  17. Summary and Future Work Major results: Nonlinear, non-convex. Optimality was a long standing open problem. Solution is provided in: G. M. Lipsa, N. C. Martins, “Certifying the Optimality of a Distributed State Estimation Scheme via Majorization Theory”, submitted to TAC, 2009 Extensions: … • Future directions: • -More General Topologies, Including Loops

  18. Summary and Future Work Major results: Nonlinear, non-convex. Optimality was a long standing open problem. Solution is provided in: G. M. Lipsa, N. C. Martins, “Certifying the Optimality of a Distributed State Estimation Scheme via Majorization Theory”, submitted to TAC, 2009 Extensions: … Future directions: -More General Topologies, Including Loops -Optimal Distributed Function Agreement with Communication Costs and Partial Information

  19. Summary and Future Work Major results: Nonlinear, non-convex. Optimality was a long standing open problem. Solution is provided in: G. M. Lipsa, N. C. Martins, “Certifying the Optimality of a Distributed State Estimation Scheme via Majorization Theory”, submitted to TAC, 2009 Extensions: … • Future directions: • -More General Topologies, Including Loops • -Optimal Distributed Function Agreement with Communication Costs and Partial Information • Game convergence and performance analysis

  20. Summary and Future Work Major results: Nonlinear, non-convex. Optimality was a long standing open problem. Solution is provided in: G. M. Lipsa, N. C. Martins, “Certifying the Optimality of a Distributed State Estimation Scheme via Majorization Theory”, submitted to TAC, 2009 Thank you Extensions: … • Future directions: • -More General Topologies, Including Loops • -Optimal Distributed Function Agreement with Communication Costs and Partial Information • Include Adversarial Action (Game Theoretic Approach)

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