Nuts and Bolts

How to start research? Lay out a decent curriculum to train students. The curriculum, in my opinion, should lay a solid foundation with nuts and bolts taste.

Here is an example in control engineering. Before doing optimal control or nonlinear control, let's get very clear on the basics: the classical control. Not only know the principle, techniques, Matlab command but also a few applications to make use of the principles. Another example in optimization. Get down to the algorithms. Get into the details of interior point method, for example.

I list a few books to lay out foundation. Power Systems: Bergen's book. Power Electronics:  Mohan's book. Drive: Bose's book. Optimization: Boyd's book. and of course, as we move forward, many many more excellent textbooks: Wood/Wollenberg's book, Crow's computation book, many control books. Stephen Boyd's many books. In a summary, research starts from textbooks.

Fundamental courses

Fundamentals are important. You may want to watch a few online courses on math & control. Here is a list of recommended courses:

1. Caltech feedback control course: http://www.cds.caltech.edu/~murray/courses/cds101/
CDS 101 Design and Analysis of Feedback Systems
Read through the lecture slides

You may have already taken a feedback control (classical control) course. However, Caltech's course offers in-depth details. Pay attention to Week 9 lecture on "Limits of Performance". http://www.cds.caltech.edu/~murray/courses/cds101/fa04/lectures/L9.1_limits.pdf. Eg. Bode's integral formula and the "waterbed" effect is something not usually seen in application papers.

2. Linear algebra
http://www.stanford.edu/class/ee263/index.html
Stephen Boyd, Standford University, provides online lectures.
This course: Intro to Linear Dynamical Systems is essentially linear algebra. MIT open course has a course "Linear Algebra". I think Boyd's delivery is better. Fundamental materials --- however Boyd's delivery offers many new insights, such as orthogonality, QR decomposition of a matrix.

The outcome: you will be very comfortable dealing with matrices.

3. Following EE 263, there is another course EE 363 Linear Dynamic Systems on optimal control. Most important equation: Hamilton-Jacobi-Bellman equation, central to optimal control theory. I did see HJB appearing elsewhere such as Markov model.

4. MIT open course has DSP delivered by Oppenheim in 1970s. Good one. Makes one very clear about frequency domain/time domain. Experiments are offered along with theoretical explanation.

5. Stephen Boyd: Convex Optimization. A computing tool CVX is used throughout the course homework.

Online Courses

Here is my thank you note to online courses delivered by MIT and Stanford instructors.

The following are the courses I have watched from youtube or other online venues.
1) MIT multivariable calculus course 30 lectures delivered by French mathematician Prof. Denis Auroux. Auroux is a great mathematician and also a great instructor. The lectures are simply put: excellent. Here you find an axiom or theorem with applications in well-known areas. One example is the Kapler's law. Auroux used Kapler's law as an application to explain a theorem. Another example, The geometry meaning of Lagrangian multiplier. The strength of this course is to relate concepts with geometric meaning and applications. Yes, I have taken calculus in my undergraduate years. Re-watching the videos, my admiration to the clarity of math and the genius of the instructor increases by lectures.

2) MIT circuits and electronics course delivered by Anant Agarwal. This course has been covered by IEEE Spectrum recently. Agarwal is talented in multiple areas including music. And he is energetic and wrote very fast. Agarwal also gave many examples in computer application whenever he was trying to explain concepts.

3) Steven Boyd of Standford. Linear Dynamic Systems, Convex Optimization I and Convex Optimization II. At first look, Steven Boyd is much laid back compared to the MIT instructors. The recording method is very different. MIT lectures seem to have recording staff following the instructors and record their handwriting nicely. This is not the case of Standford. The cameras were set still. Hence majority of the time, Boyd talked with a standstill power point or latex slides. It requires high skill to deliver a vivid lecture. Well, Boyd is a great instructor. Very hippy. Made fun of Physics and Santa Fe institute nonlinear chaos guys.

Nonetheless to say these courses are necessary to have a solid math background. Yes, I've taken linear systems before. Yet revisiting Linear Dynamic Systems made me wonder so many simple concepts such as rank can have so much meaning.

Great lectures. Must see.