## TEACHING

### TAUGHT IN THE PAST

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

Level: Graduate.

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.

Theory of Nonlinear Systems: (Spring 2022)

Level: Graduate.

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.

### Level: Graduate

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.

Level: Graduate

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.

Level: Graduate

This graduate-level course provides an introduction to adaptive control and RL from the control's point of view. Topics include algorithms for dynamic programming, policy evaluation, policy improvement, policy iteration, etc. The Maximum Principle for optimal control, the Hamilton-Jacobi-Bellman equation, the standard linear quadratic regulator (LQR), neural networks as approximators of functions, system identification, persistence of excitation conditions in continuous-time and discrete-time, and learning dynamics; approximate dynamic programming, excitation-based online approximate optimal control, Lyapunov-based stability theory of neural control, and model-reference adaptive control over networks. Examples and applications in engineering and sciences are also discussed.

Level: Undergraduate

This undergraduate-level course covers the following topics: Propositional logic: motivation, syntax, and semantics. Predicate logic: motivation, syntax, and semantics. Modeling with predicate logic. Satisfiability modulo theories: Z3. Quantifiers. Proof systems and inference rules. Sets and Functions: Naive set theory: basic notions, definitions, and properties. Russell's Paradox. Set algebra. Functions: basic notions. Injective, surjective, and bijective functions. Infinite sets: cardinality and bijection. Countable and uncountable sets. Diagonalization, the Halting Problem, and reductions. From Computability to Complexity: Growth of functions: asymptotics and practical considerations. The computational complexity of algorithms and decision problems. Complexity classes, tractability. Reducibility among problems, completeness. Induction: Weak and strong induction on the natural numbers. Induction and axiomatic theories of arithmetic. Well-orders. Inductive definitions. Recursive algorithms. Program correctness: introduction to Hoare Logic. Inductive invariants. Models of Computation: Formal languages and grammars. Regular expressions. Finite-State Automata. Limitations of finite-state models of computation. Beyond finite-state: machines with stacks and tapes. The Church-Turing thesis. Intro to Number Theory and Cryptography. Prime numbers and the Euclidean algorithm. Linear congruences and Fermat's little theorem. Private and public-key cryptography. The RSA cryptosystem. Intro to Combinatorics.