Optimal Distributed State Estimation and Control, in the Presence of Communication Costs Nuno C....
Transcript of Optimal Distributed State Estimation and Control, in the Presence of Communication Costs Nuno C....
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