Model-reference adaptive control. A primer
type: Item
instance of: scholarly article
title: Model-reference adaptive control. A primer
zbMATH Open document ID: 1405.93001
DOI: 10.1007/978-3-319-56393-0
author: Nhan Nguyen
published in: Advanced Textbooks in Control and Signal Processing
publication date: 2017-11-27T00:00:00Z
review text: This book considers various adaptive control problems in the presence of uncertainty. Adaptive control is a promising technology that can improve the performance of control systems in the presence of uncertainty due to a variety of factors such as degradation and modeling uncertainty, as well as unforeseen internal changes in system dynamics or external disturbances. Various types of uncertainty are defined. Many of new adaptive control methods have added new capabilities in terms of improved performance and robustness and can be applied in aerospace flight control and other settings. It is shown that the adaptive approach is applied to construction of various nonlinear control methods that deal with systems with uncertainty. A brief overview of nonlinear systems is presented in this book. Nonlinear systems possess many complex behaviors that are not observed in linear systems. At the same time linearization can provide information on the local stability of a region about an equilibrium point. The existence and uniqueness of a solution of a nonlinear differential equation are stated in the book by the Cauchy theorem and the Lipschitz condition. Stability of nonlinear systems is discussed also. In particular, various stability concepts for autonomous and non-autonomous systems, such as local stability, asymptotic stability, exponential stability, uniform stability, and uniform boundedness are investigated. Applications of Lyapunov's direct method and LaSalle's invariant set theorem for analyzing stability of nonlinear systems; as well as uniform continuity concept and Barbalat's lemma for analyzing stability of non-autonomous systems are considered. This book presents the fundamental theories of least-squares function approximation and least-squares adaptive control of systems with unstructured uncertainty. The function approximation theory based on polynomials, in particular the Chebyshev orthogonal polynomials, and neural networks is presented. Both direct and indi…
Mathematics Subject Classification ID: 93-01
Mathematics Subject Classification ID: 93C40
Mathematics Subject Classification ID: 93C41
Mathematics Subject Classification ID: 93B18
Mathematics Subject Classification ID: 93B35
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 93C95
Mathematics Subject Classification ID: 93D05
Mathematics Subject Classification ID: 93D20
Mathematics Subject Classification ID: 93E12
Mathematics Subject Classification ID: 93E24
zbMATH DE Number: 6813244
zbMATH Keywords: model-reference adaptive control
zbMATH Keywords: uncertainty
zbMATH Keywords: nonlinear differential equations
zbMATH Keywords: nonlinear control
zbMATH Keywords: time-delay systems
zbMATH Keywords: stability
zbMATH Keywords: least-squares method
zbMATH Keywords: robustness
zbMATH Keywords: applications
reviewed by: Vyacheslav A. Vasiliev
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-3-319-56393-0
OpenAlex ID: W4296368948
description: scientific article; zbMATH DE number 6813244