摘要
本文研究了一类高阶不确定非线性系统的全局渐近稳定控制设计问题.不同于现有结果,本文所研究的高阶非线性系统具有两个控制输入通道,即控制输入直接作用于两个一维子系统.这导致已有的控制设计方法不能或难以用来解决该类控制设计问题,因此,寻求新的控制设计方法,用以解决多控制输入通道高阶非线性系统的控制设计问题,是一个很有意义的研究课题.本文首先引入一个有效的反馈变换,从而在非线性系统满足适当假设条件下,成功地将该类系统的控制设计问题转化为规范的单控制输入通道情况下的控制设计问题.进而借助于已有结果,特别是增加幂次积分方法,给出所研究非线性系统的全局渐近稳定控制器的设计方法.尽管本文所研究的系统是具有多控制输入通道高阶非线性系统的特殊情况,所得结果具有一定的局限性,但对更一般情况具有借鉴和指导作用.最后,仿真算例验证了本文理论结果的有效性.
A problem of globally asymptotically stable control design is investigated for a class of high-order uncertain nonlinear systems.These systems,unlike the existing results,have double control input channels;that is,the control input directly a-ects two one-dimensional subsystems.This makes the existing methods of control design inapplicable or the control design problem di-cult to solve,and therefore,it is of interest to explore a new control design method to solve the control design of high-order nonlinear systems with multiple control input channels.First,an e-ective feedback transformation is introduced.Hence,this control design problem under appropriate assumptions can be transformed into one with a single control input channel.Then,using existing results,particularly,the method of adding a power integrator,a methodology is proposed to design the globally asymptotically stable controller for the nonlinear systems under investigation.Although the systems studied in the paper are a special case of high-order nonlinear systems with multiple control input channels,the results obtained in the paper,while unavoidably having certain limitations,will provide a reference and guidance in tackling the general case.Finally,a simulation is provided to verify the e-ectiveness of the theoretical results obtained.
出处
《中国科学：信息科学》
CSCD
2013年第5期670-681,共12页
Scientia Sinica(Informationis)
基金
国家自然科学基金(批准号:60974003
61143011
61273084
61233014)
山东省自然科学杰出青年基金(批准号:JQ200919)
山东大学自主创新基金(批准号:2012JC014)资助项目
关键词
非线性系统
双控制输入通道
控制设计
增加幂积分
渐近稳定
nonlinear systems
double control input channels
control design
adding a power integrator
asymptotic stability
作者简介
ZHANG Jian was born in 1981. He received his Ph.D. degree in control theory and control engineering from Shandong University in 2012. Cur- rently, he is a Lecturer at Department of Mathematics, Zhengzhou University. His research interests include nonlinear control system theory, stochastic control, and adaptive control.
通信作者．E-mail：lygfr@sdu．edu．an LIU YunGang received his Ph.D. degree in control theory and applications from the Shanghai Jiaotong University in 2000. During 2001-2003, he worked as a Postdoctoral Researcher at the Academy of Mathematics and Systems Science. Since 2003 he has been with the School of Control Sciences and Engineering, Shandong University, where he is now a Professor. He currently serves as Associate Editor for Asian Journal of Control, Acta Automatica Sinica, and Archives of Control Sciences. He is a recipient of the Guan Zhao-Zhi Award （the Best Paper Award of 2004 China Control Conference）. His current research interests are adap- tive control, stochastic systems, optimal control, and observer design.
