Optimal Distributed State Estimation and Control, in the Presence of Communication Costs Nuno C. Martins [email protected] AFOSR, MURI Kickoff Meeting,

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