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arXiv · 1306.3432

Supporting Lemmas for RISE-based Control Methods

Rushikesh Kamalapurkar·Joel A. Rosenfeld·Justin Klotz·Ryan J. Downey·Warren E. Dixon
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Abstract

A class of continuous controllers termed Robust Integral of the Signum of the Error (RISE) have been published over the last decade as a means to yield asymptotic convergence of the tracking error for classes of nonlinear systems that are subject to exogenous disturbances and/or modeling uncertainties. The development of this class of controllers relies on a property related to the integral of the signum of an error signal. A proof for this property is not available in previous literature. The stability of some RISE controllers is analyzed using differential inclusions. Such results rely on the hypothesis that a set of points is Lebesgue negligible. This paper states and proves two lemmas related to the properties.

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Rushikesh Kamalapurkar, Joel A. Rosenfeld, Justin Klotz, Ryan J. Downey, Warren E. Dixon. 2013-06-14. Supporting Lemmas for RISE-based Control Methods. https://arxiv.org/abs/1306.3432

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