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Unmodeled Dynamics in Robust Nonlinear Control

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Technical Report

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University of California, Santa Barbara Santa Barbara United States

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Since it is common to employ reduced models for control design, robustness to unmodeled dynamics is a crucial design criterion. Recent advances in nonlinear control theory have led to a number of recursive design procedures for which applications and extensions are being reported at an increasing rate. However, the robustness of these designs in the presence of unmodeled dynamics has received very little attention. The purpose of this dissertation is to develop systematic redesign procedures that render nonlinear control laws robust against unmodeled dynamics. We consider classes of unmodeled dynamics characterized by their structural properties such as input-to-state stability, passivity, minimum phaseness, relative degree, and discuss their destabilizing effects on closed-loop stability. Using recently developed nonlinear feedback tools such as nonlinear small-gain theorems and feedback passivation, we develop redesign methods for each class of unmodeled dynamics considered. Part One of the dissertation presents robust redesigns under the assumption that the full state of the plant is available for measurement. Our redesigns start with nominal control laws such as those designed by backstepping and forwarding, and robustify them to achieve global asymptotic stability in the presence of unmodeled dynamics. Part Two addresses output-feedback design issues and presents a new nonlinear observer design. Compared to other areas of nonlinear control theory, progress innonlinear output-feedback design has been slower due to the absence of constructive observer design methods. For systems with monotonic nonlinearities, we introduce a new global observer design which results in a nonlinear observer error system represented as the feedback interconnection of a linear system and a time-varying multivariable sector nonlinearity.

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