## TEACHING

### ECE272A: Stochastic Processes and Dynamical Systems I: (Spring 2023)

This graduate-level course provides an introduction to the theory behind linear dynamical systems characterized by differential equations and recursions. Topics include: definition of solutions, variations of constants formula, equilibrium points, stability notions, controllability, observability, stabilizability, detectability, Lyapunov analysis, Kalman decompositions, canonical forms, state-based feedback control, output-based feedback control, the linear quadratic regulator, the linear quadratic regulator control, and the linear quadratic gaussian control.

Topics: Introduction to the analysis of nonlinear, finite-dimensional, dynamical systems. Topics covered in the class include: existence of solutions of nonlinear ODEs, uniqueness of solutions, Lyapunov stability theory, invariance principles, passivity and dissipativity, small-gain theorems, averaging and singular perturbation theory, and nonlinear control design. Different examples and applications in the areas of optimization, feedback control, machine learning, and cyber-physical systems are used to illustrate the main concepts of the class.

### Hybrid Dynamical Systems: Theory and Applications: (Spring 2019, Spring 2020)

Topics: mathematical tools for the modeling, analysis, and design of well-posed hybrid dynamical systems (systems that combine continuous-time dynamics and discrete-time dynamics). Topics covered in the class include basic properties of differential and difference equations and inclusions: Existence of solutions, non-uniqueness, and sequential compactness. Introduction to basic hybrid systems that combine continuous-time and discrete-time dynamics: automata, switched systems, systems with timers, and spatial regularization. Lyapunov theory for hybrid systems: Sufficient conditions for uniform asymptotic/exponential/finite-time/fixed-time stability, ultimate boundedness, etc. Invariance principle for hybrid systems, and robustness corollaries.

### Extremum Seeking Methods: (Spring 2021)

This graduate-level course provides an introduction to extremum-seeking methods: feedback-based algorithms for the solution of model-free optimization problems with dynamic plants in the loop via averaging and singular perturbation theory. Different architectures and tools are studied using tools from control theory and algorithmic optimization. Particular attention is given to non-smooth and hybrid algorithms that combine continuous-time and discrete-time dynamics to overcome the fundamental limitations of smooth approaches traditionally studied in the literature.  Different examples and applications in engineering systems are also discussed.