Adaptive and Robust Nonlinear Control

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The ideal goal of feedback control theory, "to employ imperfect models and design perfect systems," critically depends on the characterizations of model imperfections and on the design methodology. If the uncertain nonlinearities can be characterized by a nonlinear bound or by a parametrization for which an adaptive design is a available, then, as some of our results show, the designed system may be "perfect" in the sense that the ideal tracking performance is achieved globally. In this research we introduce structural and parametric characterizations of model uncertainties and use them to develop adaptive and robust nonlinear feedback designs which reduce the effects of uncertainties on system performance. We plan to employ tuning functions to develop new adaptive output-feedback schemes with minimal parametrizations and reduced complexity. Our new partial-state-feedback schemes will exploit structural information to assess tradeoffs between additional measurements and stability augmentation. We will analyze robustness not only with respect to unmodeled dynamics and bound disturbance, but also with respect to unmodeled nonlinearities. The dead-zone and hysteresis characteristics are the representatives of the applications-motivated uncertain nonlinearities to be addressed in the second part of this research.