Graduate Courses by Focus Area

**Attention**: Some courses are not offered every year. Students are encouraged to contact the instructors to find out when a particular course will be offered next.

**Linear Systems and Robust Control **

**ECE230A/ME243A**: Linear Systems I (Fall, 4 units, faculty: Bamieh, Kokotovic, Hespanha)

Prerequisites: Graduate standing

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, input-output); pole assignment; compensator design; state observers

Past syllabus: Fall'02, Fall'04

**ECE230B/ME243B**: Linear Systems II (Winter, 4 units, faculty: Bamieh, Kokotovic, Hespanha)

Prerequisites: ECE230A/ME243A

Modern compensator design; disturbance localizations and decoupling; least-squares control; least-squares estimation; Kalman filters; smoothing; the separation theorem; LQG compensator design; computational considerations; and selected additional topics

**ECE232/ME256**: Robust Control (4 units, faculty: Bamieh, Smith, Khammash)

Prerequisites: ECE230A/ME243A and ECE230B/ME243B (may be taken concurrently).

Robust control theory; uncertainty modeling; stability of systems in the presence of norm-bounded perturbations; induced norm performance problems; structured singular value analysis; H-infinity control theory; model reduction; computer simulation based design project involving practical problems

**ECE234:** Modeling, Identification, and Validation for Control (4 units, faculty: Smith)

Prerequisites: ECE230A.

Parametric and non-parametric models; open and closed-loop identification; bias and variance effects; model order selection; probing signal design; subspace identification; closed-loop probing; autotuning; model validation; iterative identification and design.

**ME225AQ:** Introduction to Robust Control (3 units, faculty: Khammash)

Prerequisites: ECE230A/ME243A (may be taken concurrently).

TBA

**Nonlinear and Adaptive Control **

**ECE236/ME236:** Nonlinear Control Systems (Winter, 4 units, faculty: Kokotovic, Teel)

Prerequisites: ECE230A.

Analysis and design of nonlinear control systems; focus on Lyapunov stability theory with sufficient time devoted to contrasts between linear and nonlinear systems; input-output stability; the describing function method

Past syllabus: Winter'04

**ECE237/ME237**: Nonlinear Control Design (odd-year Spring, 4 units, faculty: Kokotovic, Teel)

Prerequisites: ECE236/ME236.

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.

**ECE247:** System Identification (even-year Winter, 4 units, faculty: Kokotovic)

Prerequisites: ECE236/ME236

On-line identification of continuous- and discrete-time systems; linear parameterizations; continuous gradient and least squares algorithms; stability; persistent excitation and parameter convergence; robust algorithms for imperfect models; averaging; discrete-time equation-error identifiers; output-error methods

**ECE249**: Adaptive Control Systems (even-year Spring, 4 units, faculty: Kokotovic)

Prerequisites: ECE247.

Models of plants with unknown parameters; boundedness properties of parameter update laws; adaptive linear control; stability and robustness to modeling errors and disturbances; backstepping state-feedback design of direct adaptive nonlinear control; output-feedback design; nonlinear swapping; indirect adaptive nonlinear control

**ECE235**: Stochastic Processes in Engineering (Winter, 4 units, faculty: Iltis)

Prerequisites: graduate standing.

A first-year graduate course in stochastic processes, including: review of basic probability; Gaussian, Poisson, and Wiener processes; wide-sense stationary processes; covariance function and power spectral density; linear systems driven by random inputs; basic Wiener and Kalman filter theory

**ECE248**: Kalman and Adaptive Filtering (Fall, 4 units, faculty: Rhodes)

Prerequisites: ECE210A, 230A and 235 (may be taken concurrently).

Least-squares estimation for processes with state-space models; Wiener filters and spectral factorization; Kalman filters; smoothing and square-root algorithms; steady-state filters; extended Kalman filters for non-linear models; fixed-order and order-recursive adaptive filters

**ME225AV:** Stochastic Modeling Control (faculty: Astrom)

Prerequisites: consent from instructor

Stochastic Processes; state models - stochastic differential equations; analysis of linear stochastic systems; stochastic optimal control; input-output models; prediction and minimum variance control; Kalman filtering and LQG; models from data – identification; adaptive control

Past syllabus: Winter’05

**Optimization and Optimal Control **

**ECE271A**: Principles of Optimization (Fall, 4 units, faculty: Chandrasekaran)

Prerequisite: ECE210A (may be taken concurrently).

Linear programming: simplex and revised simplex method; duality theory; primal-dual algorithms; Karmarkar's algorithm. Network flow problems: max-flow/min-cut theorem; Ford-Fulkerson algorithm; shortest path algorithms. Complexity and NP-completeness theory: the classes of P and NP; reductions between NP-complete problems; pseudopolynomial and approximation algorithms.

**ECE271B**: Numerical Optimization Methods (Winter, 4 units, faculty: Hespanha)

Prerequisite: ECE210A

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.

Past syllabus: Winter'03

**ECE271C**: Dynamic Optimization (4 units, faculty: Rhodes)

Prerequisite: ECE210A

Linear functionals; adjoint operators and duality; Gateaux and Frechet derivatives of nonlinear functionals and optimality conditions; calculus of variations and Pontryagin's principle; solution of optimal control problems by iterative methods in function spaces; min-max problems and differential games

**Convex Optimization** (faculty: Khammash)

Prerequisite: ECE210A

TBA

**Optimal Control** (faculty: Kokotovic, Bhamier)

Prerequisite: ECE210A

TBA

**ECE594D:** Noncooperative games (4 units, faculty: Hespanha)

Prerequisites: ECE210A

The purpose of this course is to teach students to formulate problems as mathematical games and provide the basic tools to solve them. The course covers: Static games, starting with two-player zero-sum games and eventually building up to n-player non-zero sum games; saddle-points; Nash equilibria, and Stackelberg solutions; dynamic optimization (dynamic programming) for discrete and continuous time; dynamic games, both open and closed-loop policies.

Past syllabus: Spring'03

**CS211A/Math206A/ME210A/ChE211A/ECE210A**: Matrix Analysis and Computation (Fall, 4 units, faculty: Chandrasekaran)

Prerequisite: consent of instructor.

Recommended preparation: Students should be proficient in basic numerical methods, linear algebra, mathematically rigorous proofs, and some programming language.

Graduate level-matrix theory with introduction to matrix computations; SVD's; pseudoinverses; variational characterization of eigenvalues; perturbation theory; direct and iterative methods for matrix computations

**CS211B/ Math206B/ME210B/ChE211B/ECE210B**: Numerical Simulation (4 units, faculty: Petzold)

Prerequisite: consent of instructor.

Recommended preparation: Students should be proficient in basic numerical methods, linear algebra, mathematically rigorous proofs, and some programming language.

Linear multi-step methods and Runge-Kutta methods for ordinary differential equations; stability, order and convergence; stiffness; differential algebraic equations; numerical solution of boundary value problems

**CS211C/Math206C/ME210C/ChE211C**: Numerical Solution of Partial Differential Equations—Finite Difference Methods (4 units, faculty: Petzold)

Prerequisite: consent of instructor

Recommended preparation: Students should be proficient in basic numerical methods, linear algebra, mathematically rigorous proofs, and some programming language.

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

**CS211D/Math206D/ME210D/ChE211D**: Numerical Solution of Partial Differential Equations—Finite Elements Methods (4 units, faculty: Petzold)

Prerequisite: consent of instructor

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

Mechanical Systems and Robotics

**ME201:** Advanced Dynamics I (3 units, faculty: Mezic)

Prerequisites: ME163A-B-L or equivalent.

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 units)

Prerequisites: ME201.

Variational methods; Hamiltonian mechanics; Hamilton-Jacobi equation; Liouville's theorem; Lyapunov stability; qualitative theory of dynamical systems

**ME203:** Nonlinear Mechanics (3 units, faculty: Mezic)

Prerequisites: TBA

Phase plane analysis; criteria of stability; study of Van der Pol, Duffing, Mathieu equations; Poincare-Bendixson theorem; method of Krylov-Bogoliuboff; equivalent linearization; perturbation methods

**ME215A**: Applied Dynamical Systems I (3 units, faculty: Moehlis)

Prerequisite: graduate standing.

Phase-plane methods; non-linear 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 units, faculty: Moehlis)

Prerequisites: ME 215A; graduate standing.

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

**ME270A**: Robot Motion (3 units, faculty: Paden, Bullo) – Seems that it is no longer offered

Prerequisites: ME170A-B-C/ECE181A-B-C, or consent of instructor.

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 closed-chain robots; coordinated control of multiple robots; control of multifingered robot hands

**ChE252**: Monitoring Process and Control System Performance (4 units, faculty: Seborg)

Prerequisite: Introductory course in either process control or automatic control.

This course provides an introduction to general strategies that can be used to monitor the performance of complex processes and their automatic control systems. Process monitoring is concerned with two broad issues (i) Is the current process operation normal or abnormal (fault detection)? (ii) If the performance is considered to be abnormal, what is the root cause (fault diagnosis)? Control system monitoring is concerned with similar issues but different monitoring strategies and methods of analysis are employed. Both model-based and data-driven monitoring strategies are considered. Emphasis is placed on statistically-based techniques that can be used to analyze multivariate time-series data.

Past syllabus: Spring’04

**ChE256**: Seminar in Process Control (3-4 Units, faculty: Seborg, Doyle)

Selected research topics in process control.

**ChE230C**: Nonlinear Analysis of Dynamical Systems (3 units, faculty: Doherty)

Prerequisite: ChE230A and consent of instructor

Bifurcation and stability theory of solutions to nonlinear evolution equations; introduction to chaotic dynamics. Emphasis on asymptotic and numerical methods for the analysis of steady-state and time-dependent nonlinear boundary-value problems.

Micro-Electro-Mechanical Systems (MEMS)

**
ME291A**: Physics of Transducers (3 units, faculty: Soh)

Prerequisite: graduate standing.

Recommended preparation: ECE 220A (may be taken concurrently).

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 units, faculty: Turner)

Prerequisites: ME291A and ECE220A

Design issues associated with microscale transduction. Electrodynamics, linear and nonlinear mechanical behavior, sensing methods, MEMS-specific fabrication design rules, and layout are all covered. Modeling techniques for electromechanical systems are also discussed.

**ME293**: Transducer Technology (3 units, faculty: Soh )

Prerequisites: ME 291A, ME292, and ECE 220A

Theoretical and laboratory instruction in micromachining processes and technology. Topics include advanced lithographic, deposition and etching processes to create non-planar devices. Process integration and materials issues that affect MEMS device reliability are discussed.

**Math118A-B-C:** Introduction to Real Analysis (4 units each)

Prerequisites: Math5A-B and Math108A-B and Math117

The real number system; elements of set theory; continuity; differentiability; Riemann integral; implicit function theorems; convergence processes, and special topics

**Math201A-B-C:** Real Analysis (4 units each)

Prerequisites: Math118A-B-C.

Measure theory and integration; point set topology; principles of functional analysis; Lp-spaces; the Riesz representation theorem; topics in real and functional analysis

**Math233A-B-C**: Applied Functional Analysis (4 units each)

Prerequisites: Math201A-B-C.

Topics in applied functional analysis such as convex analysis; optimization; minimax theorems; variational analysis; distribution theory and harmonic analysis; global analysis (pseudo-differential operators and index theorems)

**Linear Algebra for Engineering** (faculty: Putinar)

TBA

**ECE229**: Hybrid Systems (4 units, faculty: Hespanha)

Prerequisites: Graduate standing in ME, ChemE, ECE or CS. ECE 147a or similar is recommended but not essential.

Recommended preparation: The students should be proficient in linear algebra and basic differential equations (at the level of MATH5A-C) and some scientific programming language (e.g., MATLAB). Basic knowledge of controls concepts (at the level of ECE147A) is helpful but not essential.

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.

Past syllabus: Winter'04

**ECE238**: Advanced Control Design Laboratory (4 units, faculty: Smith)

Prerequisites: ECE230A; and, ECE232 or ECE237 or ME237 or ECE249 or ME270A or Chemical Engineering 252.

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.

**ECE281B/CS281B**: Advanced Topics in Computer Vision (Fall offered alternate years, 4 units, faculty: Manjunath)

Prerequisite: ECE181B.

Advanced topics in computer vision: image sequence analysis, spatiotemporal filtering, camera calibration and hand-eye coordination, robot navigation, shape representation, physically-based modeling, multi-sensory fusion, biological models, expert vision systems, and other topics selected from recent research papers.

**ChE256:** Model Predictive Control (faculty: Doyle)

Prerequisites: Consent of instructor.

TBA

Past syllabus: Spring'03

**ChE154**: Engineering Approaches to Systems Biology (faculty: Doyle)

Prerequisites: ChE 171, Math 5A,B,C

Applications of engineering tools and methods to solve problems in systems biology. Emphasis is placed on integrated approaches that address multi-scale and multi-rate phenomena in biological regulation. Modeling, optimization, and sensitivity analysis tools are introduced.

Past syllabus: Spring'04

**ME225AF**: Distributed Dynamical Systems (4 units, faculty: Bamieh)

Prerequisites: ECE210A(???), ME243A/ECE230A and ME243B/ECE230B

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.

**Selected Control Applications** (faculty: Kokotovic, Hespanha)

Prerequisites: Consent of instructor.

TBA

Estimation, filtering, and classification

**ECE205A**: Information Theory (4 units, faculty: Rose)

Prerequisites: ECE140 or PStat120A-B.

Entropy, mutual information, and Shannon's coding theorems; lossless source coding, Huffman, Shannon-Fano-Elias, and arithmetic codes; channel capacity; rate-distortion theory, and lossy source coding; source-channel coding; algorithmic complexity and information; applications of information theory in various fields

**ECE277A**: Neural Networks Theory (Fall, 4 units, faculty: Rose)

Prerequisites: ECE130C and 140.

Discrete and continuous feedback (Hopfield) models. Feedforward models. Capacity bounds and estimates. Supervised learning: perceptrons, back-propagation, Boltzmann machine. Unsupervised learning: self-organization and hierarchical clustering by stochastic and deterministic methods. Generalizing from examples and the Vapnik-Chervonenkis dimension.

Biomedical

**ChE225**: Biomedical Engineering (4 units)

Engineering applied to medicine. Basic physiology, transducers and systems. Medical terminology. Biomaterials. Thermal and electrical applications. Diagnostic and therapeutic radiology and nuclear medicine. Radiation protection. Laser medicine. Ultrasound, nuclear magnetic resonance, other diagnostic techniques. Image processing.

Networks

**ECE246**: Data Networks (4 units)

Prerequisite: ECE140.

Layered network architectures; point to point protocols; queueing theory for data networks; multiaccess communications; switch design; routing in data networks; flow control

**ECE279B**: Queuing Theory and Applications (4 units, faculty: Moser)

Prerequisite: ECE140.

Discrete- and continuous-time Markov chains; birth-death processes; birth-death queuing systems in equilibrium; Markovian queues in equilibrium; results from M/G/1, G/M/1 queues (S)

Discrete-event systems

**ECE252A**: Sequential Machines and Automata Theory (Fall, 4 units, faculty: Cheng)

Prerequisite: ECE152A.

Structure of sequential machines; covers, partitions, decomposition, and synthesis of multiple machines; state identification and fault detection experiments; Petri nets; stochastic systems; memory characteristics of finite automata; linear sequential machines; finite automata and regular languages; retiming

Embedded system

**ECE 594:** Embedded System Design (faculty: Kastner)

Prerequisites: Consent of instructor.

The proliferation of digital systems has brought about the incorporation of computers into every aspect of our lives. Cars have complex digital systems which include microcontrollers, sensors, actuators and other various computing devices. A networked “smart” coffee machine, refrigerator, dishwasher, light bulb, etc, are no longer visions of the future; they are appearing in modern homes. It is rare to find a person that is not carrying a cell phone, PDA, MP3 players and other electronic gadgets. All of these devices fall into the realm of embedded systems. This class will look at some of the critical issues involving new and exciting research in embedded systems. In particular, the class will focus on different models of computations needed to specify an embedded system. Furthermore, we will look at different synthesis and optimization techniques for embedded systems including hardware/software partitioning, synthesis techniques that transform a programming language into hardware and behavioral level transformations and optimizations.

PDEs

**124A**: Partial Differential Equations (4 units)

Prerequisites: Mathematics 5A-B-C.

Wave, heat, and potential equations.

**246A-B-C**: Partial Differential Equations (4 units each)\

Prerequisites: Mathematics 201A-B-C.

First-order nonlinear equations; the Cauchy problem, elements of distribution theory and Sobolev spaces; the heat, wave, and Laplace equations; additional topics such as quasilinear symmetric hyperbolic systems, elliptic regularity theory.