Louisiana State University
Research in Nonlinear Control Systems Theory: Lyapunov Functions, Stabilization, and Engineering Applications
This research will provide new Lyapunov-based stability methods in mathematical control theory, which are based on the systematic use of generalized differentials, optimal control, and the input-to-state stability framework. In particular, the project will derive and apply new feedback stabilization techniques for nonautonomous systems and underactuated mechanical systems on manifolds that are not tractable by the existing theory. Other related lines of research to be pursued include: a) the explicit construction of time-varying control-Lyapunov functions, b) the analysis of bifurcation points of discontinuous feedbacks, c) approximation and regularity theory for Lyapunov functions, and d) the construction of state estimators for output stable systems. By developing powerful new engineering and mathematical techniques, this project will make it possible to analyze a large class of important stability problems across many disciplines using a single, systematic, user-friendly approach. Feedback stabilization is used in many areas, including engineering (e.g., control of autonomous air and surface vehicles for military surveillance and reconnaissance missions) and systems biology (e.g., analysis of cell receptors in models of viral infection). The research will promote learning by supporting graduate student research assistants, who will apply and validate the project methods in a mechanical engineering control system laboratory. The project will be carried out in an institution that traditionally attracts many minorities, and special efforts will be made to recruit research assistants from under-represented groups.
