optimal distributed state estimation and control, in the presence of communication costs nuno c....
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Optimal Distributed State Estimation and Control, in the Presence of Communication Costs
Nuno C. [email protected]
AFOSR, MURI Kickoff Meeting, Washington D.C., September 29, 2009
Department of Electrical and Computer EngineeringInstitute for Systems Research
University of Maryland, College Park
• Setup is a network whose nodes might comprise of: Linear dynamic systems
Sensors with transmission capabilities
Receivers including state estimator
A Simple Configuration:
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.
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 ControlPI: Martins, Co PIs: Abshire, Smella, Bergbreiter
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.
Introduction
• Setup is a network whose nodes might comprise of: Linear dynamic systems
Sensors with transmission capabilities
Receivers including state estimator
A Simple Configuration:
Ultimately, we want to tackle generalinstances of the multi-agent case.
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 EstimationScheme via Majorization Theory”, submitted to TAC, 2009
Optimal solution:
timeErasure
Transmit
Transmit
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 EstimationScheme via Majorization Theory”, submitted to TAC, 2009
Optimal solution:
timeErasure
Transmit
Transmit
Numerical method to computeOptimal thresholds
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 EstimationScheme via Majorization Theory”, submitted to TAC, 2009
Optimal solution (a modified Kalman F.):
Erasure?yes
no
Execute K.F.
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 EstimationScheme via Majorization Theory”, submitted to TAC, 2009
Past work:
A New Method for Certifying Optimality
Frigyes Riesz
Issai Schur
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 EstimationScheme via Majorization Theory”, submitted to TAC, 2009
Past work:
Key to our proof is the useof majorization theory.
A New Method for Certifying Optimality
…
Tandem Topology
Recent Extensions
…
Tandem Topology
OptimalModified K.F.Threshold policy Memoryless forward
Recent Extensions
…
Tandem Topology
OptimalModified K.F.Threshold policy Memoryless forward
Control with communication costs (Lipsa, Martins, Allerton’09)
Recent Extensions
Multiple-stage Gaussian test channel
Problems with Non-Classical Information Structure
Multiple-stage Gaussian test channel
Lipsa and Martins, CDC’08
Problems with Non-Classical Information Structure
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 EstimationScheme via Majorization Theory”, submitted to TAC, 2009
Extensions:
…
Future directions:
-More General Topologies, Including Loops
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 EstimationScheme 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
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 EstimationScheme 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
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 EstimationScheme 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
-Include Adversarial Action (Game Theoretic Approach)
Summary and Future Work
Thank youThank you