Adaptive backstepping neural control of state‐delayed nonlinear systems with full‐state constraints and unmodeled dynamics. (18th June 2017)

• Record Type: Journal Article
• Authors: Zhang, Tianping; Xia, Meizhen; Zhu, Jiaming
• Is Part Of: International journal of adaptive control and signal processing. Volume 31:Number 11(2017)
• Page Start: 1704
• Page End: 1722
• Publication Date: 2017-06-18
• Subjects: adaptive control -- distributed time‐varying delay -- neural networks -- nonlinear systems -- state constraints -- unmodeled dynamics; Adaptive control systems -- Periodicals; Adaptive signal processing -- Periodicals; 629.836
• DOI: 10.1002/acs.2795
• Languages: English
• ISSNs: 0890-6327

Abstract

Summary: In this paper, the problem of adaptive neural control is discussed for a class of strict‐feedback time‐varying delays nonlinear systems with full‐state constraints and unmodeled dynamics, as well as distributed time‐varying delays. The considered nonlinear system with full‐state constraints is transformed into a nonlinear system without state constraints by introducing a one‐to‐one asymmetric nonlinear mapping. Based on modified backstepping design and using radial basis function neural networks to approximate the unknown smooth nonlinear function and using a dynamic signal to handle dynamic uncertainties, a novel adaptive backstepping control is developed for the transformed system without state constraints. The uncertain terms produced by state time delays and distributed time delays are compensated for by constructing appropriate Lyapunov‐Krasovskii functionals. All signals in the closed‐loop system are proved to be semiglobally uniformly ultimately bounded. A numerical example is provided to illustrate the effectiveness of the proposed design scheme.