Intro to Math for Systems & Control Theory
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.
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
Applied / Theory:
Homework:Four homework assignments. Answers should be typed in LaTeX.