1 / 20

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.

rosalyn-rowland
Download Presentation

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

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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)

More Related