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My opinion is somewhat outdated.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
Classic and sufficient for beginners.
Some classic advanced books:
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
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.
I understand this is an old question, but I feel that students with similar questions, who will no doubt be directed here through either google or the Math SE community, might benefit from a more traditional list.
Many people like Ogata's "Modern Control Engineering", others like Nise's "Control Systems Engineering", still others prefer Kuo's "Automatic Control Systems", and there are about a million more after that. The IEEE actually surveyed people on "what is the best classical [read: introductory] control text?" and reported it here.
Control, like anything else, is not simply one course or book but rather an entire field with a long and torrid history, combining contributions from mathematicians, scientists, and engineers alike. The first type of control you study is the classical theory. It's by far also the most widely applied theory in practice and you need to have a good grounding in it to advance. Then you have state space, and the rarely applied but prolifically published on field of optimal control. Robust control has become popular in recent years, since it is more of an outgrowth of classical control to deal with model uncertainty than a completely different way to look at control. Stochastic control has been a long promising but rarely applied field, with the Kalman filter and its variants being the sole exception, as they are rather universally applied in engineering--indeed, often whether they are necessary to the design or not!
It would be impossible to recommend a complete library which covers all types of control. Instead, after learning the classical theory, you simply need to read all you can and decide for yourself what is going to be useful for the work you do.
I teach an engineering undergraduate course on process dynamics and control and a graduate level course on dynamic estimation and control and have used a variety of resources to introduce Control/Feedback theory. Below are resources for introductory material for chemical engineers at an undergraduate and graduate level, respectively.
D.E. Seborg, T.F. Edgar, E.A. Mellichamp, F. J. Doyle, Process Dynamics and Control, 3rd edition, John Wiley & Sons, NY, 2011.
J.B. Rawlings and D.Q. Mayne, Model Predictive Control: Theory and Design, Nob Hill Publishing, 2009. (Full text PDF download).