Robust learning control for a class of nonlinear systems with periodic and aperiodic uncertainties.
type: Item
instance of: scholarly article
title: Robust learning control for a class of nonlinear systems with periodic and aperiodic uncertainties.
zbMATH Open document ID: 1051.93039
DOI: 10.1016/S0005-1098(03)00205-X
author: Yu-Ping Tian
author: Xinghuo Yu
published in: Automatica
publication date: 2004-01-26T00:00:00Z
review text: The authors consider the output tracking problem for a nonlinear system having a triangular form \[ \begin{cases} \dot x_1= x_2+ w_1(x_1, t)+ \phi^T_1(x_1)\gamma(t)\\ \dot x_2= x_3+ w_2(x_1,x_2, t)+ \phi^T_2(x_1, x_2)\gamma(t)\\ \vdots\\ \dot x_n= u+ w_n(x_1,\dots, x_n, t)+ \phi^T_n(x_1,\dots, x_n)\gamma(t)\\ y= x_1\end{cases} \] where the functions \(w_i\) represent bounded (with known bounds) unstructured uncertainties, the functions \(\phi_i\) are known, and the function \(\gamma\) is unknown but periodic. The signal to be tracked is generated by a linear stable system. The method proposed by the authors is a combination of robust learning control and the backstepping procedure. A control law (consisting of three terms) is constructed in order to learn and approximate the unknown periodic function (by the use of a repetitive learning mechanism) and to suppress the unstructured bounded uncertainties (by using a robust control technique). The proposed control law is applied to the control of a chaotic Van der Pol attractor.
Mathematics Subject Classification ID: 93B51
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 93D15
zbMATH DE Number: 2032784
zbMATH Keywords: Iterative learning
zbMATH Keywords: Robust control
zbMATH Keywords: Nonlinear systems
zbMATH Keywords: Time-varying system
zbMATH Keywords: Control synthesis
zbMATH Keywords: Output tracking
zbMATH Keywords: Backstepping
zbMATH Keywords: Periodic function
reviewed by: Andrea Bacciotti
MaRDI profile type: Publication
cites work: Nonlinear repetitive control
cites work: Systematic design of adaptive controllers for feedback linearizable systems
cites work: Constructive nonlinear control: a historical perspective
cites work: Adaptive nonlinear control without overparametrization
cites work: Iterative learning control for deterministic systems
cites work: Adaptive learning control of uncertain robotic systems
cites work: Analysis of iterative learning control for a class of nonlinear discrete-time systems
cites work: Robust iterative learning control for a class of nonlinear systems.
cites work: Robust learning control for robotic manipulators with an extension to a class of non-linear systems
cites work: Relationships between internal and external stability for infinite-dimensional systems with applications to a servo problem
description: scientific article; zbMATH DE number 2032784