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

Nuno C. Martins

[email protected]

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


Introduction

  • 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 Control

PI: 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.


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.


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


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


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


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:


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


Recent Extensions

Tandem Topology


Recent Extensions

Tandem Topology

Threshold policy

Memoryless forward

Modified K.F.

Optimal


Recent Extensions

Tandem Topology

Threshold policy

Memoryless forward

Modified K.F.

Optimal

Control with communication costs (Lipsa, Martins, Allerton’09)


Problems with Non-Classical Information Structure

Multiple-stage Gaussian test channel


Problems with Non-Classical Information Structure

Multiple-stage Gaussian test channel

Lipsa and Martins, CDC’08


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


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


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


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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