ECE6970/SYSEN5420: Network Systems and Games
Network systems pervade our society in both social and technological contexts. On the one hand, social networks play a central role in the transmission of information or viruses with fundamental consequences for product marketing, technology adoption, voting decisions, spread of false news and epidemiology. On the other hand, network topology fundamentally affects the performance and resilience properties of large-scale multi-agent systems, such as the power grid, the internet of things, traffic and robotic networks.
In this class you will learn the necessary mathematical and modeling tools needed to describe and understand these network systems. Questions of interest will be how the network structure impacts the dynamics of network systems, how network properties can be exploited to maximize system performance or resilience and how one can address these questions while also accounting for strategic human behavior.
ECE5210: Theory of Linear Systems
This course has two objectives. First, you will learn how to analyze and control dynamical systems described by a linear system. Linear systems arise in many applications involving mechanical and electrical systems and are also useful to study the dynamics of non-linear systems linearized around a desired trajectory. In this course, we will study properties of linear systems such as existence and uniqueness of the solution, stability of the system asymptotically in time, reachability and observability; we will also introduce concepts of realization theory and feedback/observer design. Time permitting, we will investigate more advanced control tools such as linear quadratic regulator and H-Infinity control.
The second and less obvious objective of the course is for students to experience something about doing research in automatic control, in particular developing mathematical proofs and formal logical arguments. Linear systems theory is ideally suited for this task and almost all the derivations given in the class will be carried out in complete detail, down to the level of basic algebra.