Edwin L. Aguirre
Assoc. Prof. Tingshu Hu of the Department of Electrical and Computer Engineering has received a three-year $286,824 grant from the National Science Foundation (NSF) to analyze nonlinear oscillations using the Lyapunov approach.
“Nonlinear oscillations, also called nonlinear vibrations, are ubiquitous in physical systems,” explains Hu. “They have been observed in systems of various types in biology, chemistry, circuits, communications, biophysics, plasma physics, power electronics, etc. In many cases the oscillations are unwanted, and may cause undesirable effects and disasters such as vibrations in bridges, buildings, airplanes and all sorts of noises.”
Nonlinear oscillation is a highly interdisciplinary subject that is studied in almost all branches of science and engineering, she says.
“The mathematics behind nonlinear oscillation is very intriguing and challenging,” she says. “There are numerous books and journals dedicated to this subject. Most efforts are devoted to qualitative description of the complex behavior of nonlinear oscillation. However, there is no systematic method to evaluate the magnitude of the oscillations, which is an important aspect of nonlinear dynamics.”
Hu’s expertise is control systems, for which nonlinear stability is a fundamental issue. And the most powerful tool for studying stability is the Lyapunov theory, named after Russian mathematician Aleksandr Mikhailovich Lyapunov (1857ߝ1918).
“Before the 1990s, the Lyapunov theory was only a mathematical result,” Hu says. “Due to recent advancement in computation technology, the Lyapunov theory is numerically realized and has been gaining strength and popularity.”
One of her major research focuses in the past six years has been the investigation of existing Lyapunov functions and the development of new ones. Since 2003 she has published 25 papers in peer-reviewed journals on the development and application of different Lyapunov functions. Her ongoing research on constrained control systems is funded by a four-year $246,000 grant also from the NSF.
Hu’s new project is expected to promote cross-fertilization between control theory and other research fields, and yield revolutionary discovery in nonlinear dynamics.