{"title":"Asymptotic Stabilization for Uncertain Nonlinear Systems With Input Quantization","authors":"Fei Yan, Shuo Wang, Guoxiang Gu","doi":"10.1049/cth2.70009","DOIUrl":null,"url":null,"abstract":"<p>This paper investigates the problem of asymptotic stabilization for a class of uncertain nonlinear systems involving logarithmic quantization at the system input. Different from the existing results and approaches, a Lyapunov function candidate and an adaptive control law are developed to adaptively estimate the uncertain parameters and to asymptotically stabilize the uncertain nonlinear system, in which the control input also involves uncertain parameters, possibly in the nonlinear form. It is shown that asymptotic stabilization can be achieved under some mild conditions, even though the adaptively estimated parameters do not converge to the true system parameters. A sufficient condition is obtained for the asymptotic stabilizability, in terms of the quantization density and the multiplicative parameter error bound at the control input. More importantly, the proposed adaptive control law is suboptimal for the corresponding LQR control and achieves the <span></span><math>\n <semantics>\n <msub>\n <mi>H</mi>\n <mi>∞</mi>\n </msub>\n <annotation>${\\cal H}_{\\infty }$</annotation>\n </semantics></math>-norm to be strictly smaller than <span></span><math>\n <semantics>\n <mi>γ</mi>\n <annotation>$\\gamma$</annotation>\n </semantics></math>, provided that <span></span><math>\n <semantics>\n <mrow>\n <mi>γ</mi>\n <mo>></mo>\n <mn>1</mn>\n </mrow>\n <annotation>$\\gamma >1$</annotation>\n </semantics></math>, for the uncertain linearized closed-loop system, effectively suppressing energy bounded disturbances. Finally, two simulation examples are worked out to illustrate the effectiveness of the proposed method.</p>","PeriodicalId":50382,"journal":{"name":"IET Control Theory and Applications","volume":"19 1","pages":""},"PeriodicalIF":2.2000,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1049/cth2.70009","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"IET Control Theory and Applications","FirstCategoryId":"94","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1049/cth2.70009","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
This paper investigates the problem of asymptotic stabilization for a class of uncertain nonlinear systems involving logarithmic quantization at the system input. Different from the existing results and approaches, a Lyapunov function candidate and an adaptive control law are developed to adaptively estimate the uncertain parameters and to asymptotically stabilize the uncertain nonlinear system, in which the control input also involves uncertain parameters, possibly in the nonlinear form. It is shown that asymptotic stabilization can be achieved under some mild conditions, even though the adaptively estimated parameters do not converge to the true system parameters. A sufficient condition is obtained for the asymptotic stabilizability, in terms of the quantization density and the multiplicative parameter error bound at the control input. More importantly, the proposed adaptive control law is suboptimal for the corresponding LQR control and achieves the -norm to be strictly smaller than , provided that , for the uncertain linearized closed-loop system, effectively suppressing energy bounded disturbances. Finally, two simulation examples are worked out to illustrate the effectiveness of the proposed method.
期刊介绍:
IET Control Theory & Applications is devoted to control systems in the broadest sense, covering new theoretical results and the applications of new and established control methods. Among the topics of interest are system modelling, identification and simulation, the analysis and design of control systems (including computer-aided design), and practical implementation. The scope encompasses technological, economic, physiological (biomedical) and other systems, including man-machine interfaces.
Most of the papers published deal with original work from industrial and government laboratories and universities, but subject reviews and tutorial expositions of current methods are welcomed. Correspondence discussing published papers is also welcomed.
Applications papers need not necessarily involve new theory. Papers which describe new realisations of established methods, or control techniques applied in a novel situation, or practical studies which compare various designs, would be of interest. Of particular value are theoretical papers which discuss the applicability of new work or applications which engender new theoretical applications.