Nonsmooth adaptive control design for a large class of uncertain high-order stochastic nonlinear systems
type: Item
instance of: scholarly article
title: Nonsmooth adaptive control design for a large class of uncertain high-order stochastic nonlinear systems
zbMATH Open document ID: 1264.93194
DOI: 10.1155/2012/808035
author: Jian Zhang
author: Yungang Liu
published in: Mathematical Problems in Engineering
publication date: 2013-06-11T00:00:00Z
review text: Summary: We investigate the problem of the global stabilization via partial-state feedback and adaptive technique for a class of high-order stochastic nonlinear systems with more uncertainties/unknowns and stochastic zero dynamics. First of all, two stochastic stability concepts are slightly extended to allow the systems with more than one solution. To solve the problem, a lot of substantial technical difficulties should be overcome since the presence of severe uncertainties/unknowns, unmeasurable zero dynamics, and stochastic noise. By introducing the suitable adaptive updated law for an unknown design parameter and appropriate control Lyapunov function, and by using the method of adding a power integrator, an adaptive continuous (nonsmooth) partial-state feedback controller without overparameterization is successfully designed, which guarantees that the closed-loop states are bounded and the original system states eventually converge to zero, both with probability one. A simulation example is provided to illustrate the effectiveness of the proposed approach.
Mathematics Subject Classification ID: 93D05
Mathematics Subject Classification ID: 93C40
Mathematics Subject Classification ID: 93B51
zbMATH DE Number: 6173593
Wikidata QID: Q58912009
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/808035
OpenAlex ID: W2041595107
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description: scientific article; zbMATH DE number 6173593