Nonlinear and Adaptive Control with Unmodeled Dynamics

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The wide diversity of applications, from aero and automotive engines to micro and nano systems, requires a diversity of nonlinear feedback designs, which remain an important research direction. However, the increased availability of nonlinear design methods must be accompanied with a fuller understanding of their robustness properties with respect to unmodeled dynamics, ubiquitous in all engineering applications. Strong nonlinearities interacting with unmodeled dynamics may cause instability phenomena that cannot be handled by linear robust control methods. New nonlinear robustness analysis and compensation methods are needed to increase the applicability of nonlinear designs. The two main themes in this proposal are, first, analysis of the behavior of nonlinear feedback systems caused by significant dynamics not included in their nominal design models, and, second, static and dynamic compensation methods to improve stability properties and performance in the presence of unmodeled dynamics. After a brief overview of the accomplishments under the current grant in Part One, the effects of unmodeled dynamics and possible remedies are introduced through simple examples in Part Two. The research plan, described in Part Three, proposes an in-depth analysis and characterization of systems with minimum and nonminimum phase unmodeled dynamics. It then suggests promising directions for performance improvement by compensation and structure specific robust redesigns.