Thursday, 16 May 2013

Common math in control theory

If you have selected control as your graduate studies, it would be best that you know what kind of math that you need later on. In this post, I want to share with you some of those more important math in control theory. Make sure you make the necessary preparation before you start your courses and research.

One of the major foundation for control is probably discrete mathematics. If you have never took this course and you are still in school, then trying auditing it. It is not too hard but it helps to give you a solid foundation in math. You want to focus on: (i) logical statements, (ii) methods of proof, (iii) set theory,  and (iv) functions. These topics are often used in control theory. If you are going to work discrete event system, then you need to learn Automata too.Unfortunately, there is no good online courses that covers topics that we, control engineers need. However, I can recommend a book - Discrete Mathematics with Applications by Susanna S. Epp. All you need is to read the chapters on the above topics I mentioned. This book also have a good number of citation on Google Scholar.

In control theory, linear algebra is hidden everywhere. I believe discrete event system is one of the area that doesn't use it much. Unfortunately, many undergraduate courses doesn't use linear algebra often. This means most engineer don't have solid foundation in linear algebra and have to catch up on it. You want to focus on these topics: (i) rank of matrices, (ii) eigenvalues and eigenvectors, (iii) properties of matrix/vector operations and (iv) special matrices - positive definite matrix, orthogonal matrix and more. One good online course that you can take is MIT OCW's Linear Algebra course. Make sure by the end, you can work out the final exam they provided. For reference purposes, I suggest you to an online resource that I used often - the Matrix Cookbook. Another slightly more advance book that is good research in control theory is Richard Bellman's Introduction to Matrix Analysis.

These are the two major area I would suggest students that are coming into control to improve on. Of course, you will need to have a good foundation in Calculus. Other mathematics which you will need to improve on depends on the courses you take and the research you are doing. I hope you find this post useful.

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