# Control / Feedback Theory

I am more interested in the engineering perspective of this topic, but I realize that fundamentally this is a very interesting mathematical topic as well. Also, at an introductory level they would be very similar from both perspectives. So, what are some good introductory texts on Control/Feedback theory for an advanced undergraduate/early graduate student?

Thanks!

-

Edit: In European Journal of Control (2007) appeared this 11 page article "In Control, Almost from the Beginning Until the Day After Tomorrow by Jan C. Willems" that gives you a very good perspective of the history of the field and its present situation:

"We have recently seen a strong growth in the number of applications. Especially model predictive control appears to be a leading circle of ideas here. For my own taste, it has perhaps too little system theory and too much brute force computation in it, but MPC is an area where essentially all aspects of the field, from modeling to optimal control, and from observers to identification and adaptation, are in synergy with computer control and numerical mathematics."

My opinion is somewhat outdated. Having worked in Control in electrical power plants and process industries, but not in any Academy, I could indicate you the best German Book (by Otto Follinger, Regellungstechnik) on the subject published 30 years ago, but that is perhaps not what you need.

I suggest these:

• Feedback Systems: An Introduction for Scientists and Engineers, Åström, Karl Johan and Murray, Richard M., Princeton University Press, Princeton, 2008

• Mathematical Control Theory: Deterministic Finite Dimensional Systems, Eduardo D. Sontag, Second Edition, Springer, New York, 1998

• Feedback Control Theory, John Doyle, Bruce Francis, Allen Tannenbaum, Macmillan Publishing Co., 1990

-
The first book you mention is the one they use at MIT, but this one star review that it got on amazon really scared me –  Diego Apr 21 '11 at 18:53
You can find here (caltechbook.library.caltech.edu/226/2/…) the Table of Contents and here ( caltechbook.library.caltech.edu/226 ) the chapters from CaltechBOOK developed by School of Electronics and Computer Science at the University of Southampton. –  Américo Tavares Apr 21 '11 at 20:46
Have you read that book personally? Does that review have any weight? –  Diego Apr 22 '11 at 11:32
Diego: No. I gave my suggestion based on a brief look at it, in the site I linked, and because you wrote "engineering perspective" . It is in a listed compiled by a graduate student at UCSB. –  Américo Tavares Apr 22 '11 at 11:40
@AméricoTavares, thanks a lot. I couldn't keep myself of writing and expressing my gratitude. The historical paper was supercool! :) –  Cupitor Sep 11 '13 at 15:03

Classic and sufficient for beginners.

• Feedback control of dynamic systems, GF Franklin

• Robust and optimal control, K Zhou

• Applied optimal control, AE Bryson

• Nonlinear systems, Hassan K. Khalil

-

One possible way of analyzing optimal control problems is via Markov Decision Processes. For an introductory view I recommend Sutton & Barto's "Reinforcement Learning: An Introduction" (this is free online).

For more details and theory, two books by Dimitri Bertsekas: Dynamic Programming and Stochastic Control, and Approximate Dynamic Programming.

Bertsekas webpage also has some interesting stuff: http://web.mit.edu/dimitrib/www/home.html

Bruno

-

In stead of any textbook, I strongly recommend you the following survey paper

A˚ström, Karl J., and P.R. Kumar. 2014. “Control: A Perspective.” Automatica 50 (1): 3–43. doi:10.1016/j.automatica.2013.10.012.

written by Karl J. Astrom and P.R. Kumar, where feedback is a key element through the paper, I would like to share with you the ABSTRACT

Feedback is an ancient idea, but feedback control is a young field. Nature long ago discovered feedback since it is essential for homeostasis and life. It was the key for harnessing power in the industrial revolution and is today found everywhere around us. Its development as a field involved contributions from engineers, mathematicians, economists and physicists. It is the first systems discipline; it represented a paradigm shift because it cut across the traditional engineering disciplines of aeronautical, chemical, civil, electrical and mechanical engineering, as well as economics and operations research. The scope of control makes it the quintessential multidisciplinary field. Its complex story of evolution is fascinating, and a perspective on its growth is presented in this paper. The interplay of industry, applications, technology, theory and research is discussed.

-