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<p>Nonparametric model reference adaptive control (MRAC) theory studies a novel class of nonlinear control systems able to counter functional uncertainties for which no parameterization is selected <i>a priori</i>, and which are contained in a reproducing kernel Hilbert space (RKHS). This paper presents, for the first time, robust nonparametric MRAC systems that, employing barrier Lyapunov functions, enforce user-defined time-varying constraints, or feasible approximations thereof, on the tracking error at all times. The proposed results generalize parametric MRAC systems, that is, MRAC systems that require a regressor vector or an equivalent representation of the matched uncertainties, and existing nonparametric MRAC systems that, presently, rely on the strong assumption of <i>a priori</i> knowledge of some bounded region in which the closed-loop trajectory lies.</p>

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Barrier Lyapunov Functions and Model Reference Adaptive Control with Uncertainty in Native Spaces

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年6月8日

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  • Giorgio Antonio Orlando,
  • Haoran Wang,
  • Andrea L’Afflitto,
  • Andrew J. Kurdila

摘要

Nonparametric model reference adaptive control (MRAC) theory studies a novel class of nonlinear control systems able to counter functional uncertainties for which no parameterization is selected a priori, and which are contained in a reproducing kernel Hilbert space (RKHS). This paper presents, for the first time, robust nonparametric MRAC systems that, employing barrier Lyapunov functions, enforce user-defined time-varying constraints, or feasible approximations thereof, on the tracking error at all times. The proposed results generalize parametric MRAC systems, that is, MRAC systems that require a regressor vector or an equivalent representation of the matched uncertainties, and existing nonparametric MRAC systems that, presently, rely on the strong assumption of a priori knowledge of some bounded region in which the closed-loop trajectory lies.