Robust adaptive control for nonlinear uncertain systems
type: Item
instance of: scholarly article
title: Robust adaptive control for nonlinear uncertain systems
zbMATH Open document ID: 1012.93056
DOI: 10.1016/S0005-1098(02)00244-3
author: Wassim M. Haddad
author: Tomohisa Hayakawa
author: VijaySekhar Chellaboina
published in: Automatica
publication date: 2003-04-27T00:00:00Z
review text: The authors develop a direct robust adaptive control framework for nonlinear uncertain systems \[ \dot x(t)= f(x(t)) + \Delta f(x(t)) + G(x(t))u(t),\qquad x(0)=x_0,\quad t\geq 0, \] where \(x(t)\in\mathbb R^n\) is the state vector, \(u(t)\in\mathbb R^m\) is the control input, \(f:\mathbb R^n \to\mathbb R^n\) and satisfies \(f(0) = 0\), \(\Delta f:\mathbb R^n \to\mathbb R^n\) and satisfies \(\Delta f(0) = 0\), and \(G:\mathbb R^n \to\mathbb R^{n\times m}\), \(t\geqslant 0\). It is assumed that \(f(\cdot)\) and \(\Delta f(\cdot)\) are uncertain. In particular, the uncertainty in \(f(\cdot)\) is captured by a constant linearly parametrized system uncertainty model of a known structure but unknown variation, while \(\Delta f(\cdot)\) denotes structured (possibly nonlinear) parametric uncertainty with bounded variation. The structured uncertainty \(\Delta f(\cdot)\) can effectively capture the residual approximation error inherent in the linear parametrization of the system uncertainty \(f(\cdot)\) as well as capture structured nonlinear (possibly state-dependent) uncertainty in the system of known bounded variation. The proposed framework is Lyapunov-based and guarantees partial asymptotic robust stability of the closed-loop system; that is, asymptotic robust stability with respect to part of the closed-loop system states associated with the plant. A numerical example is provided to demonstrate the efficacy of the proposed approach.
Mathematics Subject Classification ID: 93D21
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 93C73
zbMATH DE Number: 1900996
zbMATH Keywords: direct robust adaptive control
zbMATH Keywords: nonlinear uncertain systems
zbMATH Keywords: parametric uncertainty
zbMATH Keywords: state-dependent uncertainty
zbMATH Keywords: robust stabilization
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1900996