### University of Notre Dame

Aerospace and Mechanical Engineering

# AME 698: Course Syllabus

### Course Outline:

- Nonlinear systems introduction - subtleties, complexities and examples;
- Mathematical preliminaries;
- Dynamical systems overview;
- Lyapunov theory and control applications;
- Bifurcations and control applications;
- Basic differential geometry;
- Linearization by state feedback;
- Design examples using linearization;
- Controllability and observability;
- Steering drift-free systems;
- Application to stratified systems, legged robotic locomotion and robotic manipulation.

### Grading:

The final grade will be based on homework sets, a midterm exam,a final
exam and one class presentation.
- Homework (40%)

Homework sets will be handed out weekly and will be due before
the beginning of class on Thursdays. *Late homework will not be
accepted without ***prior** permission from the instructor.
- Presentation: (15%)

Each registered student will give one class presentation on an
application of a topic covered in the course. Typically, this
will be a summary of a relevant research publication.
- Midterm exam (20%): Wednesday, October 13, 1999.
- Final exam (25%)

### Homework policy:

Collaboration on homework assignments in encouraged. You may
consult outside reference materials, other students or the
instructor. However, all solutions that are handed in should
reflect your understanding of the subject matter at the time of
writing.
### Course text and references:

The required text for the course is:
- S. Shankar Sastry,
*Nonlinear Systems: Stability, Analysis
and Controls,* Springer-Verlag, 1999.

The following text will be useful as well, and has been placed on reserve
in the engineering library:
- Alberto Isidori,
*Nonlinear Control Systems,*third
edition, Springer-Verlag, 1995.

### Software:

Mathematica is a very useful tool for many computations and
simulations necessary to complete the homeworks in this class.
You are strongly encourage to learn how to use it, if necessary,
and to regularly use it for the homework assignments. The
following are a few resources to help you become familiar with
Mathematica:
Return to the AME 698 Homepage.

*Last updated: August 26, 1999*

B. Goodwine (*jgoodwin@nd.edu*)