EECI09: Review of information theory and communications

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In this lecture, we will briefly review some concepts from information theory. While classical control design is a one-block design problem (design controller / estimator), networked control design is a two-block design problem (design encoder and decoder for every channel). Information theory provides sophisticated tools for considering two block design problems for communication. By adapting these tools for feedback control, we will derive some extensions of the classical Bode integral formula for arbitrary causal feedback, that may possibly include finite capacity communication channels.

Lecture Materials

• Lecture slides: Lecture Summary

Further Reading

• T. M. Cover and J. A. Thomas, Elements of Information Theory, Wiley Interscience. This is a classic text for information theory.

• N. C. Martins and M. Dahleh, Feedback Control in the Presence of Noisy Channels: “Bode-Like” Fundamental Limitations of Performance, IEEE Transactions on Automatic Control, 53(7):1604-1615, August 2008. This paper presents some of the extensions of the Bode integral covered in the lecture.

• N. C. Martins, M. Dahleh and J. C. Doyle, Fundamental Limitations of Disturbance Attenuation in the Presence of Side Information, IEEE Transactions on Automatic Control, 52(1):56-66, January 2007. This paper considers similar problems when a preview of the disturbance is available.