# EECI08: Distributed Estimation and Control

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In this lecture, we will take a look at the fundamentals of distributed estimation and control. We begin by considering a random variable being observed by mutiple sensors. Under the assumptions of Gaussian noises and linear measurements, we will derive the weighted covariance combination of estimators. We will then touch upon the issues of distributed static sensor fusion and dynamic sensor fusion, i.e., distributing a Kalman filter so that multiple sensors can estimate a dynamic random variable. We then move onto the problem of distributed control and demonstrate, via a variant of the Witsenhausen counterexample, why distributed optimal control is nonconvex and nonlinear.

## Lecture Materials

- Lecture notes: Distributed Estimation and Control (RMM handwritten notes)
- Lecture notes: Distributed Estimation and Control (typeset notes by Vijay Gupta)

## Reading

S. K. Mitter and A. Sahai, "Information and control: Witsenhausen revisited," in Learning, Control and Hybrid Systems: Lecture Notes in Control and Information Sciences 241, Y. Yamamoto and S. Hara, Eds. New York, NY: Springer, 1999, pp. 281-293.

"Separation of Estimation and Control for Discrete Time Systems", H. S. Witsenhausen, Proceedings of the IEEE, vol. 59, no. 11, pp. 1557-1566, Nov. 1971.