# Mathematics of control theory

1. Dec 23, 2003

### snakeize

Hi, I'm an undergrad major in electrical engineering and physics; I am also minoring in mathematics. I am thinking of going into the field of control theory. I was wondering what branches of mathematics are particularly relevant to the field of control theory (I had a mathematics professor who was a control theorist)? And, also subjects in physics I may find particularly useful, directly or indirectly? I thank you all for your input in advance.

2. Dec 23, 2003

### enigma

Staff Emeritus
Differential Equations,

Specifically Laplace Transforms.

Almost the entire class was in "Laplace World" as my professor put it.

Also be sure to live, learn, and love logarithms and complex numbers. It may sound like I'm talking down to you, but when I took my control systems class, I was a little shaky on complex numbers since I hadn't done anything with them since high school. You use them a lot.

3. Dec 24, 2003

### snakeize

thx enigma, i'll keep that in mind. i'll definetly take that "functions of a complex variable" class in the math department. any other input from anyone else?

4. Dec 24, 2003

### NateTG

I expect that numerical methods would probably also be usefull.

In addition, you'll obviously have to deal with the usual suspects -- trigonometry, calculus, and maybe linear algebra.

5. Dec 30, 2003

### mmwave

Become an expert at linear algebra, modern systems have large numbers of inputs and that's the only way to deal with them. Noise is always present so study probability and stochastic systems. For myself I could never study enough discrete systems theory but that may be because I didn't like it. Become an expert at Matlab, Maple or Mathematica programming.

6. Dec 12, 2007

### unplebeian

You should be good at ODEs (modern control theory), lin algebra (also for modern control theory), Laplace transforms, and numerical methods for solving ODEs (Runge Kutta 4) But all this was said above anyway.

I would suggest taking a DSP course (Digital signal processing) as it will give you insight into digital control and open a new door of possibilities for you.

7. Dec 12, 2007

### rbj

specifically matrices and vectors. this is necessary for state-variable modelling of anything. much of modern control systems are based on the state-variable model.

8. Dec 13, 2007

### TheAnalogKid83

differential equations initially, linear algebra is used a lot in state space (matrices, linear independence, systems of equations, eigenvectors/values) later on in addition to diff eq. My controls professor also had to take a chaos theory math course in grad school because controls deals a lot with nonlinearities and instability which is sometimes chaotic, and these are factors in any real world control problem. Also numerical methods where you learn about euler's method and more sophisticated ways of representing continuous signals as discrete signals (z domain, w domain, bilinear transformation, etc.), and also simulation.

You will see a lot of parallels to your signals and systems and DSP courses, because in the end it is all based on the same ideas. A PID control algorithm will look almost identical to a standard IIR/FIR filter. You will see that your feedback control and even your systems are filters and can be represented by transfer functions when simplified and approximated.

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