Exponential Stability with RISE Controllers

A class of continuous robust controllers termed Robust Integral of the Sign of the Error (RISE) have been published over the past two decades as a means to yield asymptotic tracking error convergence and asymptotic identification of time-varying uncertainties, for classes of nonlinear systems that a...

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Bibliographic Details
Published inIEEE control systems letters Vol. 6; p. 1
Main Authors Patil, Omkar Sudhir, Isaly, Axton, Xian, Bin, Dixon, Warren E.
Format Journal Article
LanguageEnglish
Published IEEE 01.01.2022
Subjects
Control theory
Convergence
Feedforward systems
Lyapunov methods
nonlinear control systems
Robust control
Stability criteria
Trajectory
Uncertainty
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Summary:A class of continuous robust controllers termed Robust Integral of the Sign of the Error (RISE) have been published over the past two decades as a means to yield asymptotic tracking error convergence and asymptotic identification of time-varying uncertainties, for classes of nonlinear systems that are subject to sufficiently smooth bounded exogenous disturbances and/or modeling uncertainties. Despite the wide application of RISE-based techniques, an open question that has eluded researchers during this time-span is whether the asymptotic tracking error convergence is also uniform or exponential. This question has remained open due to certain limitations in the traditional construction of a Lyapunov function for RISE-based error systems. In this paper, new insights on the construction of a Lyapunov function are used that result in an exponential stability result for RISE-based controllers. As an outcome of this breakthrough, the inherent learning capability of RISE-based controllers is shown to yield exponential identification of state-dependent disturbances/uncertainty.
ISSN:2475-1456
2475-1456
DOI:10.1109/LCSYS.2021.3127134