Looking for a control theory textbook for a friend

Question

I am looking for a textbook in control theory (for a friend) that covers topics such as Pontryagin's maximum principle. My friend is not a mathematician by trade, but holds a degree in applied mathematics (and is thus not math-shy, but prefers to skip detailed discussions on regularity and prefers intuition). Recent aspects of control theory (e.g., viscosity solutions) need not be present.

(I apologize for all the parameters)

Answer 1

• Lawrence C. Evans, An Introduction to Mathematical Optimal Control Theory, Department of Mathematics, University of California, Berkeley.

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

Answer 2

Although this isn't what your friend wants to hear, I suggest learning about classical control first.

Why?

1. Classical control preceded optimal control by a bit, and optimal control (at least implicitly) takes note of this. It's true that the most mathematically-oriented references may try to ignore classical control, but most engineering references (in an engineering subject) wont. Someone unfamiliar with the basics wont be able to understand a lot of that content in context.

2. Optimal control is rarely, if ever, used. There're good reasons for this. Most optimal controls are not feedback networks, but feedback is a must for a good controller. In cases like LQG, when the optimal control is a feedback network, it often finds gains which are very aggressive and hard to implement. Also, in LQG, the problem assumes full-state feedback, which is rarely available in practice.

I will give you my go-to general reference, which is Astrom and Murray. This has a great exposition of the basics and does touch on modern concepts like optimal control and robust control. There are many other classical controls books out there which you can also look at. This IEEE article names quite a few.