CAREER: Robust Nonlinear Control: Problems and Challenges from Communication Networks

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It is widely recognized that linear control laws are inadequate to account forsevere nonlinearities and uncertainties that many physical systems possess.Two examples of such systems, that will be studied in this project,are underactuated mechanical systems and communication networks.The issue of designing performance-aimed nonlinear controllerswith robustness to significant uncertainties has drawn attention ofmany researchers in the last 20 years.Phase I of this project will continue the study of nonlinear systems withdynamic uncertainties, initiated in our earlier work, and provide furtherinsights into the inherent limitations on achievable performancecaused by (input) dynamic uncertainties.Despite many elegant results in the recent literature of nonlinear control,their direct application to decentralized nonlinear systems with complexinterconnecting structures seems to be limited from a practical point of view. On the basis of the new framework of nonlinear ISS (input-to-state stability) small-gain theorems, we will develop nonlinear feedback design tools for important classes of decentralized nonlinear systemswith applications to communication networks.Phase II of this project is to address some interesting nonlinearcontrol problems in communication networks. The study of hard saturationnonlinearities and time-varying uncertain propagation delays in such systemswill generate new decentralized/nonlinear control problems as applicationsfor the basic research in Phase I.We expect that our contributions from the nonlinear control perspectivewill enhance the NSF's existing investment in this active application area.The educational element of this CAREER development plan is closely linked tothe research work. We will enhance the current control curriculum at Polytechnicby incorporating ``nonlinear'' thinking into the classical feedback control courses where ``linear'' methods are now the focal point, and by developing Web-based educational tools and tutorials.The specific goals of the educational plan include:(1) developing a new graduate course {\em Nonlinear Systems Theory}to report on recent developments in nonlinear systems and control;(2) setting up a Laboratory for Robust Nonlinear Control for research and education,which strengthens the Department's activities in control;(3) promoting hands-on experiments and involving undergraduate students in research-oriented and application-driven projects; and(4) developing interactions with practicing engineers for technology transfer and dissemination of new theory through seminars, workshops and continuing education programs.