Survival Guide

MEs Without Controls Background

Typically, the controls background of an ME (Mech. Engg.) undergrad is limited to frequency domain methods for linear SISO systems, i.e. Root Locus, Bode Plot, and Nyquist Plot. New ME grad students starting research in nonlinear/hybrid controls are in for a rude awakening regarding the chasm between what they know and what they should to even begin conducting research. Having gone through this myself, I feel responsible to share my insights with future grad students.

  • Mathematics:
    Controls draws a lot from pure math fields, indeed some view it as a field of applied math. It is important to learn how to read and write proofs which for MEs is understandably difficult. Our undergrad limits us to solving equations and using tricks; writing rigorous proofs is not something we are trained in but must learn. To this end, I recommend starting from a simple book on logic. Start with propositional logic and then move on to first order logic. Logic is a tool that is often not taught but is extremely important. Read proofs that you encounter in papers and discuss with someone who is more accomplished than you in math, preferably your advisor. Once you are confident in your ability to read basic proofs, I recommend taking courses on Analysis (Real Analysis, Measure Theory, Complex Analysis, Functional Analysis) from the Math department. If you are not too theoretically inclined in your research, at least real analysis must be taken. These courses will mature you in reading/writing proofs. Beyond analysis, taking courses relevant to your specific field of research from the math department may come handy, like differential geometry, graph theory, or proability. As a general thumb rule, the more mathematically educated you are, the easier it will be conduct research in controls.

  • Reading Papers:
    Learning how to read papers quickly and effeciently is another useful skill to have which takes some time to develop. In the beginning of my PhD it took me centuries to read a single paper because I tried to understand each and every technical detail. This is a good approach to build a background, however, as you grow older you will have to crunch more material in less time and find papers relevant to your research. I recommend going through a paper multiple times. In the first pass, try to grasp the contribution. Only read the statemets of thoerems and propositions, don't worry about the proofs yet. After understanding the high-level contribution of the paper, and gauging its significance to your research, you can make a decision whether you should go through the technical proofs in detail or not. If not, you are done, otherwise start pouring over the material with a piece of paper and pen. As a general thumb rule, if you cannot visualize the result and it is only a bunch of mathematical steps on paper, you need to re-read and re-think. While reading always keep the problems you are solving in mind, if you are lucky, you may be able to apply something you read.

  • Books on Nonlinear/Hybrid Controls:
    In my opinion, a good starting point is Ch 2 and Ch 3.1-3.4 from Applied Nonlinear Control by Slotine and Li. Then, you can switch to Nonlinear Systems by Khalil and read Chapters 2-4 for a more rigorous treatment. These are the necessary basic fundamentals of nonlinear control and are by no means sufficient. On becoming comfortable with these books, you can go for a more advanced text like Nonlinear Control Systems by Isidori. I strongly recommend reading the Appendix of Isidori before jumping into the actual book. Other books of interest for those in Hybrid Controls include Switching in Systems and Control by Liberzon, Impulsive and Hybrid Dynamical Systems by Haddad, Chellaboina, and Nersesov, and Hybrid Dynamical Systems by Goebel, Sanfelice, and Teel. This is by no means an exhaustive list but just a list of books that I have referred to in the past.

More to follow when I get time…