Courses Taught in Georgia Institute of Technology

ECE6559: Advanced Linear Systems
Fall 2008

Linear systems are often the first used to verify and inspire new thoughts in systems theory and control.  This course introduces advanced linear systems theory associated with robust control where, due to the greater challenges in nonlinear systems, general results are mostly restricted to linear systems.  This course reviews and extends the knowledge of basic linear systems theory, and introduces essential techniques for investigating robustness of linear systems. 

“A Course in Robust Control Theory”  by Geir E. Dullerud, Fernando Paganini
The following books serve as references (not required):
“Linear Systems” by Thomas  Kailath
“Essentials of Robust Control” by Kemin Zhou and John C. Doyle.

1. Review and extension of basic systems theory.
2. Introduction to functional spaces and norms.
3. Co-Prime factorization. Stabilizing controller design.
4. Small gain theorem and unstructured uncertainty.
5. Algebraic Ricatti equations and Linear Matrix Inequalities.
6. H2 synthesis and H-infinity Synthesis.
7. Structured singular value and mu synthesis.

Work load:
There will be 1 midterm (30%), 1 final (30%), 4 homework sets (40%), and 1 optional final report.
The exams are going to be open book, open notes.  The final report is used to replace a bad score in either of the exams, and to help interested students to start their own research project. Note that final report should not be more than 6 single column pages with font size not smaller than 10pt .

ECE 6558: Stochastic Systems and Control
Summer 2008, Fall 2009

The goals of this course are two-fold: 1. to introduce stochastic system methods to graduate students who are preparing for MS or PHD research projects; 2. to give an overview of stochastic methods. Topics include stochastic differential equations, nonlinear filtering, stochastic control, and simulation based methods.

Self-contained lecture notes by Prof. Roger Brockett. The notes will be available free of charge thanks to Prof. Brockett.
The following books serve as references (not required):
Stochastic Processes and Filtering Theory. Jazwinski.
Optimal Estimation. Simon.
Applied Optimal Control: Optimization, Estimation, and Control. Bryson and Ho.
Stochastic Approximation and Recursive Algorithms and Applications. Kushner and Yin.
Dynamic Programming and Optimal Control. Bertsekas, Vol 1.

1. Review and extension of probability theory.
2. Poisson counters, jump processes and differential equations.
3. Stochastic differential equations, Ito rule, Fokker-Planck equation, convergence.
4. Introduction to linear system theory.
5. Estimation theory: linear filtering, Wonham equation, nonlinear filtering.
6. Stochastic control: linear quadratic Gaussian problem, stochastic control with noisy observation.
7. Introduction to Dynamic Programming with full state information and partial state information

Work load:
There is 1 midterm (30%), 1 final (30%), 4 homework sets (40%), and 1 optional final report.
The exams are open book, open notes.  The final report is used to replace a bad score in either of the exams, and to help interested students to start their own research project.

ECE 4560: Introduction to Robotics and Automation
Spring 2008, 2009, 2010, 2011

In this course, three important components of modern robotics are introduced: mechanics, control, and computer engineering. These components are organized to analysis, design, and control robotic manipulators (such as robotic arms) and mobile robots (such as robotic cars).
You are expected to learn: (1) how to construct robot arms and mobile robots (2) how to use mathematical methods to model robotic manipulators and mobile robots and plan their motion; (3) how to design a linear feedback control law to correct for errors; and (4) how to implement your algorithms through computer software systems.

You will be performing experiments on robotic manipulators and mobile robots to test your knowledge. You will perform a final project designing and implementing a robot mission using the robot arms and mobile robots you build.

John J. Craig "Introduction to Robotics: Mechanics and Control," 3rd Ed. Prentice Hall, 2005.
R. Siegwart and I. R. Nourbakhsh "Introduction to Autonomous Mobile Robots," MIT press, 2004.

Lynx 5 robot arms

Lynx 6 robotic arm

Vex Robotic Kit

Vex Robot

Courses Taught in Princeton University

Spring 2007: MAE 306 Engineering Mathematics (junior level)

The first half of the course introduces the theory of complex variables leading to its application for evaluating integrals by methods of contour integration, and using conformal mapping techniques to solve harmonic problems. The second half of the course is an introduction to partial differential equations with emphasis on their solution by separation of variables and transform methods.

Fall 2006: MAE 501 Advanced Engineering Analysis I (graduate level)

Methods of mathematical analysis for the solution of problems in physics and engineering. Topics include an introduction to functional analysis, linear analysis & eigenvalue problems for matrices & operators, Sturm-Liouville theory, Green's functions for the solution of linear ordinary differential equations and Poisson's equation, and the calculus of variations, and the inverse and implicit function theorems.