Combined backstepping and HOSM control design for a class of nonlinear MIMO systems. (14th July 2016)

• Record Type: Journal Article
• Authors: Estrada, Antonio; Fridman, Leonid; Iriarte, Rafael
• Is Part Of: International journal of robust and nonlinear control. Volume 27:Number 4(2017)
• Page Start: 566
• Page End: 581
• Publication Date: 2016-07-14
• Subjects: robust control -- sliding modes -- backstepping -- uncertain systems; Automatic control -- Periodicals; Control theory -- Periodicals; Nonlinear systems -- Periodicals; 629.836
• DOI: 10.1002/rnc.3590
• Languages: English
• ISSNs: 1049-8923

Abstract

Summary: This paper presents a control design algorithm that combines backstepping and high‐order sliding modes. It is known that backstepping can achieve asymptotic stability for nonlinear systems in strict‐feedback form in spite of parametric uncertainties. Nevertheless, when external perturbations are also present, only practical stability can be ensured. For the same aforementioned perturbed conditions, the combined design presented in this paper can achieve finite‐time exact tracking/regulation. At the same time, the semi‐global or global stability obtained through backstepping is preserved, and the gains of the high‐order sliding modes controller can be reduced with respect to its direct application. The design is based on recently reported combined designs that are based on the idea of virtual controls, which can contain terms based on high‐order sliding modes algorithms. The proposal also extends previous results to the multiple‐input–multiple‐output case. Copyright © 2016 John Wiley & Sons, Ltd.