Introduction to Mathematical Fundamentals for Systems and Control Theory - ECE60281
This course serves as background for ECE602, Lumped System Theory; ECE695, Epidemic Processes over Networks; and ECE695, Structure and Dynamics of Large-Scale Networks; and other similar courses. The course will make the necessary mathematical background for these courses accessible by decomposing and illustrating difficult concepts with real-world examples and problems.
Learning Objective:
After completing this course, you will be able to:
- Analyze equations involving matrices by applying algebraic concepts such as rank, nullspace, linear independence, and eigenvalues.
- Define graph properties such as diameter, degrees, and connectivity, and apply them to analyze networked systems.
- Define properties of linear systems, including controllability, observability, and stability, and apply them to design state estimators and feedback controllers.
- Define probability distributions and moments of random variables, and characterize the long-term behavior of stochastic processes
- Specify the fundamental optimality conditions for optimization problems and implement basic algorithms to find the optimizers.
Description:
This course serves as background for ECE602, Lumped System Theory; ECE695, Epidemic Processes over Networks; and ECE695, Structure and Dynamics of Large-Scale Networks; and other similar courses. The course will make the necessary mathematical background for these courses accessible by decomposing and illustrating difficult concepts with real-world examples and problems. The course consists of five modules: 1) Linear Algebra, 2) Basic Graph Theory, 3) Basic Control Theory, 4) Probability, and 5) Optimization.
Topics Covered:
Automatic Control (AC)
Prerequisites:
Linear Algebra (MA 26500 or 26266) or equivalent ECE 302, Probabilistic Methods in Electrical and Computer Engineering or equivalent
Homework:
Four homework assignments. Answers should be typed in LaTeX. One quiz.
Exams:
One comprehensive proctored final exam.
Textbooks:
No textbook; recommended reading will be provided.
Computer Requirements:
A computer with a webcam and microphone (built-in or USB) will be required for quiz and exam proctoring.
Other Requirements:
MATLAB or equivalent.