Courses

Mechanical and Aerospace Engineering

MAE 142. Dynamics and Control of Aerospace Vehicles: The dynamics of vehicles in space or air are derived for analysis of the stability properties of spacecraft and aircraft. The theory of flight, lift, drag, Dutch roll and phugoid modes of aircraft are discussed. Optimal state space control theory for the design of analog and digital controllers (autopilots).

MAE 143A. Signals and Systems: Dynamic modeling and vector differential equations. Concepts of state, input, output. Linearization around equilibria. Laplace transform, solutions to ODEs. Transfer functions and convolution representation of dynamic systems. Discrete signals, difference equations, z-transform. Continuous and discrete Fourier transform.

MAE 143B. Linear Control: Analysis and design of feedback systems in the frequency domain. Transfer functions. Time response specifications. PID controllers and Ziegler-Nichols tuning. Stability via Routh-Hurwitz test. Root locus method. Frequence response: Bode and Nyquist diagrams. Dynamic compensators, phase-lead and phase-lag. Actuator saturation and integrator wind-up.

MAE 144. Embedded Control and Robotics: Each student builds, models, programs, and controls an unstable robotic system built around a small Linux computer. Review/synthesis of: A) modern physical and electrical CAD. B) dynamics, signals and systems, linear circuits; PWMs, H-bridges, quadrature encoders. C) embedded Linux, C, graphical programming; multithreaded applications; bus communication to supporting ICs. D) classical control theory in both continuous-time (CT) and discrete-time (DT); interconnection of CT and DT elements.

MAE 145. Introduction to Robotic Planning and Estimation: This course is an introduction to robotic planning algorithms and programming. Topics include sensor-based planning (bug algorithms), motion planning via decomposition and search (basic search algorithms on graphs, A*), the configuration-space concept, free configuration spaces via sampling, collision detection algorithms, (optimal) planning via sampling (probabilistic trees), environment roadmaps, and filtering for robot localization and environment mapping (SLAM).

MAE 146. Intro to ML algorithms: An introduction to the principles used to design and implement machine learning algorithms, as well as an understanding of their advantages and limitations. The topics covered are python review, supervised learning (linear, logistic/sigmoid regression, generalized linear models, nonlinear regression via Kernels), neural network types (convolutional, recurrent, deep NN), unsupervised learning (k-means clustering). Application of ML in different examples.

MAE 148. Introduction to Autonomous Vehicles: Fundamentals of autonomous vehicles. Working in small teams, students will develop 1/8-scale autonomous cars that must perform on a simulated city track. Topics include robotics system integration, computer vision, algorithms for navigation, on-vehicle vs. off-vehicle computation, computer learning systems such as neural networks, locomotion systems, vehicle steering, dead reckoning, odometry, sensor fusion, GPS autopilot limitations, wiring, and power distribution and management.

MAE 149. Sensor Networks: Cross-listed with ECE 156.) Characteristics of chemical, biological, seismic, and other physical sensors; signal processing techniques supporting distributed detection of salient events; wireless communication and networking protocols supporting formation of robust censor fabrics; current experience with low power, low-cost sensor deployments.

MAE 204. Robotics: This course covers topics in robotics, dynamics, kinematics, mechatronics, control, locomotion, and manipulation.

MAE 274. Model Reduction: Students will learn the mathematical tools, theory, and algorithms of model reduction so as to reproduce and predict behaviors in complex systems with low-dimensional models. Covers a wide range of methods and theory: system-theoretic (balanced truncation, transfer-function interpolation), data-driven and projection-based (proper orthogonal decomposition), and model learning approaches (dynamic mode decomposition, operator inference, Loewner-based system identification, eigensystem realization).

MAE 270. Multidisciplinary Design Optimization: Introduction to engineering design optimization involving multidisciplinary models. Topics covered include local sensitivity analysis, gradient-based optimization, gradient-free optimization, surrogate models, discrete optimization, and multidisciplinary design optimization architectures.

MAE 227. Convex Optimization for Engineers: This course focuses on convex optimization theory, convexification of non-convex problems, engineering applications, modeling and implementation in a programming language. This course covers convex sets and functions, convex optimization problems (LP, QP, SOCP, SDP), weak and strong duality, optimality conditions, and solution and shadow price interpretation. Some applications include design in mechanical engineering, optimal control problems, machine learning, energy, transportation, etc.

MAE 242. Robot Motion Planning: Modeling, solving, and analyzing planning problems for single robots or agents. Configuration space for motion planning, sampling-based motion planning, combinatorial motion planning, feedback motion planning, differential models, and nonholonomic constraints. Basic decision-theory and dynamic programming, sensor, and information spaces.

MAE 244. Renewable Energy Integration: The objective of this course is to introduce students to the research field of integration of renewable energy (RE) in power systems. This course covers some relevant literature and the state of the art in the following subareas related to RE integration: capacity expansion models, optimal power flow, power dynamics, electricity markets, RE variability and forecasting, machine learning and AI for power systems, microgrids and islanded grids, electrical vehicles and demand response, among others.

MAE 247. Cooperative Control of Multi-agent Systems: Tools for the design of cooperative control strategies for multi-agent systems are presented. Topics include continuous and discrete-time evolution models, proximity graphs, performance measures, invariance principles, and coordination algorithms for rendezvous, deployment, flocking, formation of autonomous vehicles and consensus

MAE 249. Soft Robotics: Roboticists have begun to explore the design of automated systems using soft materials (e.g., elastomers, gels, fluids) with the goal of achieving the versatility and robustness of biological organisms. This course provides a survey of topics important for the design, analysis, and control of soft robotics, including modeling (e.g., nonlinear elasticity), actuation (e.g., fluidic elastomer actuators), sensing (e.g., liquid metal sensors), and design optimization (e.g., using artificial evolution).

MAE 280A. Linear Systems Theory: Linear algebra, inner products, outer products, vector norms, matrix norms, least squares problems, Jordan forms, coordinate transformations, positive definite matrices, etc. Properties of linear dynamic systems described by ODEs: observability, controllability, detectability, stabilizability, trackability, optimality. Control systems design: state estimation, pole assignment, linear quadratic control.

MAE 280B. Linear Control Design: Parameterization of all stabilizing output feedback controllers, covariance controllers, H-infinity controllers, and L-2 to L-infinity controllers. Continuous and discrete-time treatment. Alternating projection algorithms for solving output feedback problems. Model reduction.

MAE 281A. Nonlinear Systems: Existence and uniqueness of solutions of EDE’s, sensitivity equations. Stability, direct and converse Lyapunov theorems, LaSalle’s theorem, linearization, invariance theorems. Center manifold theorem. Stability of perturbed systems with vanishing and nonvanishing perturbations, input-to-state ability, comparison method. Input-output stability. Perturbation theory and averaging. Singular perturbations. Circle and Popov criteria.

MAE 281B. Nonlinear Control: Small gain theorem, passivity. Describing functions. Nonlinear controllability, feedback linearization, input-state and input-output linearization, zero dynamics. Stabilization, Brockett’s necessary conditions (local), control Lyapunov functions, Sontag’s formula (global). Integrator back stepping, forwarding. Inverse optimality, stability margins. Disturbance attenuation, deterministic and stochastic, nonlinear H-infinity.

MAE 283A. Parametric Identification: Theory and Methods: Constructing dynamical models from experimental data. Deterministic and stochastic discrete time signals. Discrete time systems. Nonparametric identification: correlation and spectral analysis. Parametric identification: realization and prediction error methods, least squares estimation, approximate modeling. Experiment design. Frequency domain identification.

MAE 283B. Approximate Identification and Control: Identification for control: approximate identification, estimation of models via closed-loop experiments. Closed-loop identification techniques. Estimation of model uncertainty. Model invalidation techniques. Iterative techniques for model estimation and control design.

MAE 284. Robust and Multivariable Control: Multivariable feedback systems: transfer function matrices, Smith-McMillan form, poles, zeros, principal gains, operator norms, limits on performance. Model uncertainties, stability and performance robustness. Design of robust controllers, H_inf and mu synthesis. Controller reduction.

MAE 286. Hybrid Systems: Definition of hybrid system. Examples in mechanics, vision, and multi-agent systems. Trajectories of hybrid systems. Chattering, Zeno phenomena. Stability analysis. Arbitrary switching: common Lyapunov functions. Slow switching: dwell time. State-dependent switching: multiple Lyapunov functions, Invariance Principle. Hybrid control design.

MAE 287. Control of Distributed Parameter Systems: Lyapunov stability; exact solutions to PDEs; boundary control of parabolic PDEs (reaction-advection-diffusion and other equations); boundary observer design; control of complex-valued PDEs (Schrodinger and Gunzburg-Landau equations); boundary control of hyperbolic PDEs (wave equations) and beam equations; control of first-order hyperbolic PDEs and delay equations; control of Navier-Stokes equations; motion planning for PDEs; elements of adaptive control for PDEs and control of nonlinear PDEs.

MAE 288A. Optimal Control: Deterministic methods: Pontryagin’s Maximum Principle, dynamic programming, calculus of variations. Stochastic methods: Gauss-Markov processes, Linear Quadratic control, Markov chains. Linear Quadratic Gaussian Control and the Separation Principle.

MAE 288B. Optimal Estimation: Least Squares and Maximum Likelihood Estimation methods, Gauss-Markov models, State Estimation and Kalman Filtering, prediction and smoothing. The extended Kalman filter.

MAE 289A. Mathematical Analysis for Applications: Topics in mathematical analysis, with the emphasis on those of use in applications. The topics may include metric spaces, open and closed sets, compact sets, continuity, differentiation, series of functions and uniform convergence, convex sets and functions, transforms, and Stokes theorem.

MAE 289B. Real Analysis for Applications: Topics in real analysis, with the emphasis on those of use in applications. May include countable/uncountable, open and closed sets, topology, Borel sets, sigma algebras, measurable functions, integration (Lebesgue), absolute continuity, function spaces, and fixed-point theorems.

MAE 289C. Functional Analysis and Applications: Topics in functional analysis, with the emphasis on those of use in applications. May include function spaces, linear functionals, dual spaces, reflexivity, linear operators, strong and weak convergence, Hahn-Banach Theorem, nonlinear functionals, differential calculus of variations, Pontryagin Maximum Principle.

MAE 293. Flow Control: Intersection of control theory and fluid mechanics. Applications: transition delay, turbulence mitigation, noise reduction, weather forecasting, shape optimization, and UAV’s (perching). Tractable feedback (Riccati-based) formulations via parallel and parabolic flow assumptions. Regularization of variational (adjoint-based) formulations for MPC and MHE. EnKF and EnVE approaches for forecasting.

Courses

Electrical and Computer Engineering

ECE 109. Engineering Probability and Statistics: Axioms of probability, conditional probability, total probability theorem, random variables, densities, expected values, characteristic functions, transformation of random variables, central limit theorem. Random number generation, engineering reliability, estimation elements, random sampling, sampling distributions, tests for hypothesis.

ECE 121A. Power Systems Analysis and Fundamentals: This course introduces concepts of large-scale power system analysis: electric power generation, distribution, steady-state analysis and economic operation. It provides the fundamentals for advanced courses and engineering practice on electric power systems, smart grid, and electricity economics.

ECE 153. Probability and Random Processes for Engineers: Random processes. Stationary processes: correlation, power spectral density. Gaussian processes and linear transformation of Gaussian processes. Point processes. Random noise in linear systems.

ECE 171A. Linear Control System Theory I: Stability of continuous- and discrete-time single-input/single-output linear time-invariant control systems emphasizing frequency domain methods. Transient and steady-state behavior. Stability analysis by root locus, Bode, Nyquist, and Nichols plots. Compensator design.

ECE 171B. Linear Control System Theory II: Time-domain, state-variable formulation of the control problem for both discrete-time and continuous-time linear systems. State-space realizations from transfer function system description. Internal and input-output stability, controllability/observability, minimal realizations, and pole-placement by full-state feedback.

ECE 172A. Introduction to Intelligent Systems: Robotics and Machine Intelligence: This course will introduce basic concepts in machine perception. Topics covered will include edge detection, segmentation, texture analysis, image registration, and compression.

ECE 174. Introduction to Linear and Nonlinear Optimization with Applications: The linear least squares problem, including constrained and unconstrained quadratic optimization and the relationship to the geometry of linear transformations. Introduction to nonlinear optimization. Applications to signal processing, system identification, robotics, and circuit design.

ECE 175A. Elements of Machine Intelligence: Pattern Recognition and Machine Learning: Introduction to pattern recognition and machine learning. Decision functions. Statistical pattern classifiers. Generative vs. discriminant methods for pattern classification. Feature selection. Regression. Unsupervised learning. Clustering. Applications of machine learning.

ECE 250. Random Processes: Random variables, probability distributions and densities, characteristic functions. Convergence in probability and in quadratic mean, Stochastic processes, stationarity. Processes with orthogonal and independent increments. Power spectrum and power spectral density. Stochastic integrals and derivatives. Spectral representation of wide sense stationary processes, harmonizable processes, moving average representations.

ECE 228 Machine Learning for Physical Applications: This course provides an introduction to deep learning and its applications in physical systems and control. The course includes both the practical and theoretical aspects of the following topics: multi-layer perceptron, convolutional neural networks, recurrent neural networks, Transformers, graph neural networks, physics-informed neural networks, neural operators, and basics of deep reinforcement learning.

ECE 255A. Information Theory: Introduction to basic concepts, source coding theorems, capacity, and noisy-channel coding theorem.

ECE 271A. Statistical Learning I: Bayesian decision theory; parameter estimation; maximum likelihood; the bias-variance trade-off; Bayesian estimation; the predictive distribution; conjugate and noninformative priors; dimensionality and dimensionality reduction; principal component analysis; Fisher’s linear discriminant analysis; density estimation; parametric vs. kernel-based methods; expectation-maximization; applications.

ECE 271B. Statistical Learning II: Linear discriminants; the Perceptron; the margin and large margin classifiers; learning theory; empirical vs. structural risk minimization; the VC dimension; kernel functions; reproducing kernel Hilbert spaces; regularization theory; Lagrangian optimization; duality theory; the support vector machine; boosting; Gaussian processes; applications.

ECE 272A. Stochastic Processes in Dynamic Systems I: Diffusion equations, linear and nonlinear estimation and detection, random fields, optimization of stochastic dynamic systems, applications of stochastic optimization to problems.

ECE 272B. Stochastic Processes in Dynamic Systems II: Continuous and discrete random processes, Markov models and hidden Markov models, Martingales, linear and nonlinear estimation. Applications in mathematical finance and real options.

ECE 273. Convex Optimization and Applications: This course covers some convex optimization theory and algorithms. It will mainly focus on recognizing and formulating convex problems, duality, and applications in a variety of fields (system design, pattern recognition, combinatorial optimization, financial engineering, etc.).

ECE 275A. Parameter Estimation I: Linear least Squares (batch, recursive, total, sparse, pseudoinverse, QR, SVD); Statistical figures of merit (bias, consistency, Cramer-Rao lower-bound, efficiency); Maximum likelihood estimation (MLE); Sufficient statistics; Algorithms for computing the MLE including the Expectation Maximation (EM) algorithm. The problem of missing information; the problem of outliers.

ECE 275B. Parameter Estimation II: The Bayesian statistical framework; Parameter and state estimation of Hidden Markov Models, including Kalman Filtering and the Viterbi and Baum-Welsh algorithms. A solid foundation is provided for follow-up courses in Bayesian machine learning theory.

ECE 285. Semidefinite and Sum-of-Squares Optimization: Convex optimization has profound impacts on many problems in control theory, discrete and nonlinear optimization, theoretical computer science, and machine learning. It is a fundamental tool to ensure efficient, resilient, and safe operations of many engineering systems, such as smart power grid, transportation, robotics, and many others. Optimization in these areas often takes the form of conic optimization, especially semidefinite programs. This course will cover semidefinite optimization which is a far-reaching generalization of linear programs.