# Estimation and Control in Networked Systems

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In this lecture, we will touch upon some of the open issues when estimation and control have to be carried out in a communication constrained network control environment. We will concentrate on three constraints: topology, quantization issues and stochastic packet drops by communication channels. We will discuss the major research directions in these areas.

## Lecture Materials

## Reading

Most of the cited papers are available using IEEE Xplore[1]. If you are unable to obtain any, please send me [2] a mail.

Section 1 of the lecture (topology synthesis) is from the following reference.

"Minimal Interconnection Topology in Distributed Control Design", Cedric Langbort and Vijay Gupta, American Control Conference, 2006 (ACC '06). Accepted.

The quantization aspects have been considered in many papers, some of which have been cited in the references. The following papers should give you a feel of how such results are proven.

- R. W. Brockett and D. Liberzon, ``Quantized Feedback Stabilization of Linear Systems
*, IEEE Transactions on Automatic Control, 45(7), 2000, pp. 1279-89.* - G. N. Nair and R. J. Evans, ``Stabilizability of Stochastic Linear Systems with Finite Feedback Data Rates
*, SIAM Journal on Control and Optimization, 43(2), July 2004, pp. 413-436.*

- R. W. Brockett and D. Liberzon, ``Quantized Feedback Stabilization of Linear Systems

For section 3, the material is covered in the following papers.

- "On a Stochastic Sensor Selection Algorithm with Applications in Sensor Scheduling and Sensor Coverage", V. Gupta, T. Chung, B. Hassibi and R. M. Murray, Automatica, Vol. 42, No. 2, February 2006, Pages: 251-260.
- "Optimal LQG Control Across Packet-Dropping Links", V. Gupta, D. Spanos, B. Hassibi and R. M. Murray, System and Control Letters, Submitted July 2005.
- "Data Transmission over Networks for Estimation", V. Gupta, A. F. Dana, J. P. Hespanha and R. M. Murray, 17th International Symposium on Mathematical Theory of Networks and Systems, (MTNS 06). Accepted.