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.

Selected research topics in process control.

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

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.

Feedback systems design, specifications in time and frequency domains. Analysis and synthesis of closed loop systems. Computer aided analysis and design.

Students are required to design, implement, and document a significant control systems project. The project is implemented in hardware or in high-fidelity numerical simulators. Lectures and laboratories cover special topics related to the practical implementation of control systems.

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.

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 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.

Modern compensator design. Disturbance localizations and decoupling. Least-squares control. Least-squares estimation; Kalman filters; smoothing. The separation theorem; LQG compensator design. Computational considerations. Selected additional topics.

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.

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 and the describing function method

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.

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.

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.

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.

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. Min-max problems and differential games. Extensive treatment of Linear Quadratic Problems.

Machine learning algorithms from a signal processing viewpoint; unsupervised learning (K-means, 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.

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.

Measure theory and integration. Point set topology. Principles of functional analysis. Lp-spaces. The Riesz representation theorem. Topics in real and functional analysis.

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.

An advanced lab course with experiments in dynamical systems and feedback control design. Students design, troubleshoot, and perform detailed, multi-session experiments.

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.

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.

Vectorial dynamics, conservation theorems, particle and rigid body motion; analytical dynamics, Lagrange equations, rigid body dynamics, normal modes of oscillations

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.

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.

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.

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

In this course, we will introduce key cases of pattern formation and self-organization 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.

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.

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.

Generating functions, discrete and continuous time Markov chains; random walks; branching processes; birth-death processes; Poisson processes, point processes.

Martingales, martingale convergence, stopping times, optional sampling, optional stopping theorems and applications, maximal inequalities. Brownian motion, introduction to diffusions.

social networks in social psychology