Courses
Course  Course TItle  Units  Instructor  Description 

ChE152A  Process Dynamics and Control I  
ChE152B  Process Dynamics and Control II  
ChE154  Engineering Approaches to Systems Biology  
ChE211A/CS211A/ECE210A/Math206A/ME210A  Matrix Analysis and Computation  4 
Graduate levelmatrix theory with introduction to matrix computations. SVD's, pseudoinverses, variational characterization of eigenvalues, perturbation theory, direct and iterative methods for matrix computations. 

ChE230C  Nonlinear Analysis of Dynamical Systems  3 
Bifurcation and stability theory of solutions to nonlinear evolution equations 

ChE252  Monitoring Process and Control System Performance  4  
ChE255  Methods in Systems Biology  
ChE256  Model Predictive Control 
Applications of engineering tools and methods to solve problems in systems biology. Emphasis is placed on integrated approaches that address multiscale and multirate phenomena in biological regulation. Modeling, optimization, and sensitivity analysis tools are introduced. 

ChE256  Seminar in Process Control  34 
Selected research topics in process control. 

ChE295/ECE295/ME295/CS592  Control, Dynamical Systems, and Computations Seminar 
A series of weekly lectures given by university staff and outside experts in the fields of control systems, dynamical systems, and computation. 

CS211B/Math206B/ME210B/ChE211B/ECE210B  Numerical Simulation  4 
Linear multistep methods and RungeKutta methods for ordinary differential equations: stability, order and convergence. Stiffness. Differential algebraic equations. Numerical solution of boundary value problems. Recommended preparation: Students should be proficient in basic numerical methods, linear algebra, mathematically rigorous proofs, and some programming language. 

CS211C/Math206C/ME210C/ChE211C  Numerical Solution of Partial Differential Equations—Finite Difference Methods  4 
Finite difference methods for hyperbolic, parabolic and elliptic PDEs, with application to problems in science and engineering. Convergence, consistency, order and stability of finite difference methods. Dissipation and dispersion. Finite volume methods. Software design and adaptivity. Recommended preparation: Students should be proficient in basic numerical methods, linear algebra, mathematically rigorous proofs, and some programming language. 

CS211D/Math206D/ME210D/ChE211D  Numerical Solution of Partial Differential Equations—Finite Elements Methods  4 
Weighted residual and finite element methods for the solution of hyperbolic, parabolic and elliptical partial differential equations, with application to problems in science and engineering. Error estimates. Standard and discontinuous Galerkin methods. Recommended preparation: Students should be proficient in basic numerical methods, linear algebra, mathematically rigorous proofs, and some programming language. 

ECE101  How to train your dragon  
ECE130B  Signal Analysis and Processing (Linear Algebra)  
ECE130C  Signal Analysis and Processing (Linear Algebra)  
ECE141A/ME141A  Introduction to MicroElectroMechanical Systems (MEMS)  
ECE147A  Feedback Control Systems  Theory and Design  5 
Feedback systems design, specifications in time and frequency domains. Analysis and synthesis of closed loop systems. Computer aided analysis and design. 

ECE147B  Digital Control Systems  Theory and Design  7 
Analysis of sampled data feedback systems; state space description of linear systems: observability, controllability, pole assignment, state feedback, observers. Design of digital control systems. 

ECE147C  Control System Design Project  5 
Students are required to design, implement, and document a significant control systems project. The project is implemented in hardware or in highfidelity numerical simulators. Lectures and laboratories cover special topics related to the practical implementation of control systems. 

ECE179D/ME179D  Introduction to Robotics: Robot Dynamics and Control  4 
Dynamic modeling and control methods for robotic systems. Lagrangian method for deriving equations of motion, introduction to the Jacobian, and modeling and control of forces and contact dynamics at a robotic end effector. Laboratories encourage a problemsolving approach to control. Emphasis on nonlinear and underactuated dynamics systems, particularly mobile robots. 

ECE179L/ME179L  Introductions to Robotics: Design Laboratory  4 
A robotics laboratory course focused on designing, programming, and testing mobile robots. The robot design problems are formulated in terms of robot performance so that students must solve electromechanical problems in an unstructured framework similar to professional engineering environments. Students develop skills in brainstorming, concept selection, spatial reasoning, teamwork and communication. Robots are controlled with microcontrollers using the C programming language, and interfaced to sensors and motors. 

ECE179P/ME179P  Introduction to Robotics: Planning and Kinematics 
Motion planning and kinematics topics with an emphasis on geometric reasoning, programming, and matrix computations. Motion planning: configuration spaces, sensorbased planning, decomposition and sampling methods, and advanced planning algorithms. Kinematics: reference frames, rotations and displacements, kinematic motion models. 

ECE229  Hybrid Systems  4 
Introduction to hybrid systems that combine continuous dynamics with discrete logic. Topics include a modeling framework that combines elements from automata theory and differential equations, simulation tools, analysis and design techniques for hybrid systems, and applications of hybrid control. Recommended preparation: The students should be proficient in linear algebra and basic differential equations (at the level of MATH5AC) and some scientific programming language (e.g., MATLAB). Basic knowledge of controls concepts (at the level of ECE147A) is helpful but not essential. 

ECE230A/ME243A  Linear Systems I  4 
State space description, solution of state equations, state transition matrix, variation of constants formula. Controllability, observability, Kalman decomposition. Realizations, minimal realizations, canonical realization. Stability (Lyapunov, inputoutput). Pole assignment, compensator design, state observers. 

ECE230B/ME243B  Linear Systems II  4 
Modern compensator design. Disturbance localizations and decoupling. Leastsquares control. Leastsquares estimation 

ECE232/ME256  Robust Control with Applications  4 
Robust control theory 

ECE234  Modeling, Identification, and Validation for Control  4 
Parametric and nonparametric models, open and closedloop identification, bias and variance effects, model order selection, probing signal design, subspace identification, closedloop probing, autotuning, model validation, iterative identification and design. 

ECE235  Stochastic Processes in Engineering  4 
A firstyear graduate course in stochastic processes, including: review of basic probability; Gaussian, Poisson, and Wiener processes; widesense stationary processes; covariance function and power spectral density; linear systems driven by random inputs; basic Wiener and Kalman filter theory. 

ECE236/ME236  Nonlinear Control Systems  4 
Analysis and design of nonlinear control systems. Focus on Lyapunov stability theory, with sufficient time devoted to contrasts between linear and nonlinear systems, inputoutput stability and the describing function method 

ECE237/ME237  Nonlinear Control Design  4 
Stabilizability by linearization and by geometric methods. State feedback design and input/output linearization. Observability and output feedback design. Singular perturbations and composite control. Backstepping design of robust controllers for systems with uncertain nonlinearities. Adaptive nonlinear control. 

ECE238  Advanced Control Design Laboratory  4 
A laboratory course requiring students to design and implement advanced control systems on a physical experiment. Experiments from any engineering or scientific discipline are chosen by the student. 

ECE247  System Identification  4 
Online identification of continuous and discretetime systems. Linear parameterizations. Continuous gradient and least squares algorithms. Stability, persistent excitation and parameter convergence. Robust algorithms for imperfect models. Averaging. Discretetime equationerror identifiers. Outputerror methods. 

ECE248  Kalman and Adaptive Filtering  4 
Leastsquares estimation for processes with statespace models. Wiener filters and spectral factorization. Kalman filters, smoothing and squareroot algorithms. Steadystate filters. Extended Kalman filters for nonlinear models. Fixedorder and orderrecursive adaptive filters. 

ECE249  Adaptive Control Systems  4 
Models of plants with unknown parameters. Boundedness properties of parameter update laws. Adaptive linear control. Stability and robustness to modeling errors and disturbances. Backstepping statefeedback design of direct adaptive nonlinear control. Outputfeedback design. Nonlinear swapping. Indirect adaptive nonlinear control. 

ECE270  Game Theory  4 
Formulation of problems as mathematical games and provides the basic tools to solve them. Covers both static and dynamic games. Intended for graduate students (but is not restricted to) in communications, controls, signal processing, and computer science. 

ECE271A  Principles of Optimization: Convex Optimization  4 
Linear programming: simplex and revised simplex method, duality theory, primaldual algorithms, Karmarkar's algorithm. Network flow problems: maxflow/mincut theorem, FordFulkerson algorithm, shortest path algorithms. Complexity and NPcompleteness theory: the classes of P and NP, reductions between NPcomplete problems, pseudopolynomial and approximation algorithms. 

ECE271B  Numerical Optimization Methods  4 
Unconstrained nonlinear problems: basic properties of solutions and algorithms, global convergence, convergence rate, and complexity considerations. Constrained nonlinear problems: basic properties of solutions and algorithms. Primal, penalty and barrier, cutting plane, and dual methods. Computer implementations. 

ECE271C  Dynamic Optimization: Optimal Control  4  
ECE271C/ME254  Optimal Control of Dynamic Systems  4 
Calculus of variations and Gateaux and Frechet derivatives. Optimization in dynamic systems and Pontryagin’s principle. Invariant Imbedding and deterministic and stochastic Dynamic Programming. Numerical solutions of optimal control problems. Minmax problems and differential games. Extensive treatment of Linear Quadratic Problems. 

ECE281B/CS281B  Advanced Topics in Computer Vision  4 
Advanced topics in computer vision: image sequence analysis, spatiotemporal filtering, camera calibration and handeye coordination, robot navigation, shape representation, physicallybased modeling, multisensory fusion, biological models, expert vision systems, and other topics selected from recent research papers. 

ECE283  Machine Learning: A signal Processing Perspective  4 
Machine learning algorithms from a signal processing viewpoint; unsupervised learning (Kmeans, deterministic annealing, EM algorithm); supervised learning (Support Vector Machines, neural networks); regression; Bayesian inference and tracking using Markov chain Monte Carlo and sequential Monte Carlo (particle filter) techniques. 

ECE594D  Fourier Analysis for Engineers  4  
ECE594D  Discrete Time and Hybrid Stochastic Processes  4  
ECE594D  Robot Locomotion  
Engr3  Introduction to Programming for Engineers  3 
General philosophy of programming for engineering majors. Students will be introduced to a modern programming language or software package. Specific areas of study will include algorithms, basic decision structures, arrays, matrices, and graphing. Engineering applications will be emphasized. 

Math118ABC  Introduction to Real Analysis  4 (each) 
The real number system, elements of set theory, continuity, differentiability, Riemann integral, implicit function theorems, convergence processes, and special topics. 

Math201ABC  Real Analysis  4 (each) 
Measure theory and integration. Point set topology. Principles of functional analysis. Lpspaces. The Riesz representation theorem. Topics in real and functional analysis. 

Math233ABC  Applied Functional Analysis  4 (each) 
Topics in applied functional analysis such as convex analysis, optimization, minimax theorems, variational analysis, distribution theory and harmonic analysis, global analysis (psedodifferential operators and index theorems). 

ME104  Mechatronics  3 
Interfacing of mechanical and electrical systems and mechatronics. Basic introduction to sensors, actuators, and computer interfacing and control. Transducers and measurement devices, actuators, A/D and D/A conversion, signal conditioning and filtering. Practical skills developed in weekly lab exercises. 

ME104  Sensors, Actuators and Computer Interfacing  
ME106A  Advanced Mechanical Engineering Laboratory  3 
An advanced lab course with experiments in dynamical systems and feedback control design. Students design, troubleshoot, and perform detailed, multisession experiments. 

ME125  Nonlinear Geometric Control  
ME155A  Control System Design I  3 
The discipline of control and its application. Dynamics and feedback. The mathematical models: transfer functions and state space descriptions. Simple control design (PID). Assessment of a control problem, specification, fundamental limitations, codesign of system and control. 

ME155B  Control System Design II  3 
Dynamic system modeling using statespace methods, controllability and observability, statespace methods for control design including pole placement, and linear quadratic regulator methods. Observers and observerbased feedback controllers. Sampleddata and digital control. Laboratory exercises using MATLAB for simulation and control design. 

ME16  Engineering Mechanics: Dynamics  4 
Vectorial kinematics of particles in space, orthogonal coordinate systems. Relative and constrained motions of particles. Dynamics of particles and systems of particles, equations of motion, energy and momentum methods. Collisions. Planar kinematics and kinematics of rigid bodies. Energy and momentum methods for analyzing rigid body systems. Moving frames and relative motion. 

ME163  Engineering Mechanics: Vibrations  3 
Topics relating to vibration in mechanical systems; exact and approximate methods of analysis, matrix methods, generalized coordinates and Lagrange's equations, applications of systems. Basic feedback systems and controlled dynamic behavior. 

ME169/ECE183  Nonlinear Phenomena  
ME17  Mathematics of Engineering  
ME201  Advanced Dynamics I  3 
Vectorial dynamics, conservation theorems, particle and rigid body motion; analytical dynamics, Lagrange equations, rigid body dynamics, normal modes of oscillations 

ME202  Advanced Dynamics II  3 
Variational methods, Hamiltonian mechanics, HamiltonJacobi equation, Liouville's theorem, Lyapunov stability, qualitative theory of dynamical systems. 

ME203  Nonlinear Mechanics  3 
Phase plane analysis, criteria of stability, study of Van der Pol, Duffing, Mathieu equations, PoincareBendixson theorem, method of KrylovBogoliuboff, equivalent linearization, perturbation methods. 

ME215A  Applied Dynamical Systems I  3 
Phaseplane methods, nonlinear oscillators, stability of fixed pints and periodic orbits, invariant manifolds, structural stability, normal form theory, local bifurcations for vector fields and maps, applications from engineering, physics, chemistry, and biology. 

ME215B  Applied Dynamical Systems II  3 
Local codimension two bifurcations, global bifurcations, chaos for vector fields and maps, Smale horseshoe, symbolic dynamics, strange attractors, universality, bifyrcation with symmetry, perturbation theory and averaging, Melnikov's methods, canards, applications from engineering, physics, chemistry, and biology. 

ME225  Dynamical Systems with Symmetries 
Modeling and control of spatially distributed systems described by partial differential equations. The emphasis will be on linear PDE systems, and how they can be viewed as infinite dimensional generalizations of standard ODE systems. The material in the course will be strongly motivated by physical examples. The emphasis will be on spatially distributed arrays of dynamical systems, and problems from hydrodynamic stability and transition to turbulence. 

ME225  Convex Optimization 
Modeling and control of spatially distributed systems described by partial differential equations. The emphasis will be on linear PDE systems, and how they can be viewed as infinite dimensional generalizations of standard ODE systems. The material in the course will be strongly motivated by physical examples. The emphasis will be on spatially distributed arrays of dynamical systems, and problems from hydrodynamic stability and transition to turbulence. 

ME225AF  Cooperative Control of Robotic Networks  
ME225AF  Modeling and Control of Spatially Distributed Dynamical Systems  4 
Modeling and control of spatially distributed systems described by partial differential equations. The emphasis will be on linear PDE systems, and how they can be viewed as infinite dimensional generalizations of standard ODE systems. The material in the course will be strongly motivated by physical examples. The emphasis will be on spatially distributed arrays of dynamical systems, and problems from hydrodynamic stability and transition to turbulence. 

ME225AQ  Stochastic Modeling and Control  
ME225AV  Stochastic Modeling Control 
Stochastic Processes, State Models  Stochastic Differential Equations, Analysis of Linear Stochastic Systems, Stochastic Optimal Control, Inputoutput Models, Prediction and Minimum Variance Control, Kalman Filtering and LQG, Models from Data – Identification, Adaptive Control 

ME225FB  Geometric Control of Mechanical Systems  
ME225FB  Distributed Systems and Control 
The course is intended primarily for graduate students interested in cooperative control, distributed algorithms, and distributed systems. Topics will include: (1) the theory of graphs (with an emphasis on algebraic graph theory), (2) basic models of dynamical systems, (3) application area: averaging algorithms, (4) application area: robotic networks, (5) application area: coupled oscillators. 

ME225SB  Systems Biology  
ME225SO  Pattern formation and SelfOrganization  4 
In this course, we will introduce key cases of pattern formation and selforganization in physical and biological systems, as well as engineering. From crystal formation to robot swarms and embryonic development, we will discuss how these systems develop organized spatial structures and present new major challenges in these topics. 

ME245  Modeling and Control of Spatially Distributed Systems  4 
Examples and motivation, connections and equivalences between finite and infinite dimensional systems, Carleman and LieKoopman linearizations. Abstract evolution equations, regularity, well posedness and semigroups. Stability and spectral conditions. Controllability/Observability, optimal control, norms, and sensitivities of infinite dimensional systems. Approximation and numerical methods. Symmetries, arrays and spatial invariance, transform methods. Swarming, Flocking and large Multivehicle systems. Hydrodynamic stability and transition to turbulence. 

ME270A  Robot Motion  3 
Advanced course on kinematics, dynamics, and control of robots. Position and force control. Efficient computation of kinematics and dynamics. Control of kinematically redundant robots. Control of closedchain robots. Coordinated control of multiple robots. Control of multifingered robot hands. 

ME291A  Physics of Transducers  3 
The use of concepts in electromagnetic theory and solid state physics to describe capacitive, pierzoresistive, piezoelectric and tunneling transduction mechanisms and analyze their applications in microsystems technology. 

ME292  Design of Transducers  3 
Design issues associated with microscale transduction. Electrodynamics, linear and nonlinear mechanical behavior, sensing methods, MEMSspecific fabrication design rules, and layout are all covered. Modeling techniques for electromechanical systems are also discussed. 

NA  none  
PSTAT213A  Introduction to Probability Theory And Stochastic Processes  4 
Generating functions, discrete and continuous time Markov chains; random walks; branching processes; birthdeath processes; Poisson processes, point processes. 

PSTAT213B  Introduction to Probability Theory And Stochastic Processes  4 
Convergence of random variables: different types of convergence; characteristic functions, continuity theorem, laws of large numbers, central limit theorem, large deviations, infinitely divisible and stable distributions, uniform integrability. Conditional expectation. 

PSTAT213C  Introduction to Probability Theory And Stochastic Processes  4 
Martingales, martingale convergence, stopping times, optional sampling, optional stopping theorems and applications, maximal inequalities. Brownian motion, introduction to diffusions. 

SOC134N  Social Movements and Social Networks  4 
social movement relevant network constructs, opinion dynamics and behavioral cascades 

SOC147  Current Issues in Social Psychology  4 
social networks in social psychology 

SOC148/294  Social Networks Seminar  4 
seminar on recent publications in the field of social networks 

SOC148MA/248MA  Introduction to Social Network Methods  4 
Introduction to fundamental structural constructs of social network analysis and UCINET 