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ECE 1647 is an introduction to analysis of systems described by nonlinear differential and difference equations. The course is divided roughly into two parts. The first part covers the following state-space topics: vector fields and equilibria; existence and uniqueness of solutions; linearization; Liapunov stability theory; invariance theorems; center manifolds; regular and singular perturbations; integral manifolds. The second part of the course covers analysis from an input-output point of view. Topics include: input-output stability definitions and their relationship with state-space stability definitions; passivity; sector nonlinearities and describing functions; the circle and popov criteria. Examples are drawn from adaptive control, electro-mechanical systems such as induction motors, robotics, nonlinear circuit analysis, bioengineering, and chemical engineering. Emphasis is place upon application of the theory to systems of interest to the students.
Anyone with an interest in the applied analysis of nonlinear systems. Mechanical systems such as robotics are described by nonlinear equations. Biological systems such as bioreactors are also nonlinear. In chemical engineering, processes such as ph regulation are nonlinear. Power systems such as induction motors are nonlinear. Electronic circuits such as phase-locked loops are nonlinear. Aerospace systems such as satellite attitude dynamics are nonlinear. Thus, in the past, students from from the Institute for Aerospace Studies, the Institute of Biomedical Engineering, the Department of Mechanical & Industrial Engineering, the Department of Chemical Engineering, the ECE Power Group, the ECE Systems Control Group, the ECE Communications Group, and the ECE Electronics Group, have taken the course. (Thus, it is a very interdisciplinary course, focusing on applications of theory. Its not just for Systems Control Graduate Students!)
Hassan Khalil, Nonlinear Systems, Second Edition, 1996.
Meets Mondays, 1:00pm - 3:00pm, in room EG103.
