Feedback Design for Nonlinear Systems

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A principal objective of this mathematical sciences project is the development of methods for the systematic design of feedback laws leading to the ability to shape, or at least influence, the steady state response of systems exhibiting complex dynamical behavior. In particular, the research program focuses on feedback design methods for problems of asymptotic tracking, disturbance rejection, and output regulation for nonlinear distributed parameter systems. A primary objective of this mathematical sciences project is the development of a methodology to systematically control or influence nonlinear effects which arise in a variety of physical phenomena. This goal is motivated in part by problems in combustion control, where nonlinear effects actually can improve mixing and hence can , in principle, improve the engine performance of automobiles, for example. Another example of the potential impact of nonlinear control in flluid flow problems is in the control of instabilities in aerodynamic applications, which have been experimentally shown to greatly influence stall and lift behavior of aircraft and which are known to lead to reduction in the life cycle of aircraft parts. Other applications are to active noise control of various devises, such as compressors.