A new critical theorem for adaptive nonlinear stabilization

doi:10.1016/j.automatica.2010.03.008

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	A new critical theorem for adaptive nonlinear stabilization
	Li, Chanying; Guo, Lei
	2010-06-01
发表期刊	AUTOMATICA
ISSN	0005-1098
卷号	46 期号:6 页码:999-1007
摘要	It is fairly well known that there are fundamental differences between adaptive control of continuous-time and discrete-time nonlinear systems. In fact, even for the seemingly simple single-input single-output control system y(t+1) = theta(t)f(y(t)) + ut + w(t+1) with a scalar unknown parameter theta(t) and noise disturbance in {w(t)}, and with a known function f(.) having possible nonlinear growth rate characterized by vertical bar f(x)vertical bar = Theta(vertical bar x vertical bar(b)) with b >= 1, the necessary and sufficient condition for the system to be globally stabilizable by adaptive feedback is b < 4. This was first found and proved by Guo (1997) for the Gaussian white noise case, and then proved by Li and Xie (2006) for the bounded noise case. Subsequently, a number of other types of "critical values" and "impossibility theorems" on the maximum capability of adaptive feedback were also found, mainly for systems with known control parameter as in the above model. In this paper, we will study the above basic model again but with additional unknown control parameter theta(2), i.e., u(t) is replaced by theta(2)u(t) in the above model. Interestingly, it turns out that the system is globally stabilizable if and only if b < 3. This is a new critical theorem for adaptive nonlinear stabilization, which has meaningful implications for the control of more general uncertain nonlinear systems. (C) 2010 Elsevier Ltd. All rights reserved.
关键词	Discrete time Nonlinear systems Globally stabilizability Stochastic imbedding
DOI	10.1016/j.automatica.2010.03.008
语种	英语
资助项目	National Natural Science Foundation of China[60821091] ; CAS[KJCX3-SYW-S01]
WOS研究方向	Automation & Control Systems ; Engineering
WOS类目	Automation & Control Systems ; Engineering, Electrical & Electronic
WOS记录号	WOS:000278675500005
出版者	PERGAMON-ELSEVIER SCIENCE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/10000
专题	系统科学研究所国家数学与交叉科学中心
通讯作者	Guo, Lei
作者单位	Chinese Acad Sci, ISS, Acad Math & Syst Sci, Key Lab Syst & Control, Beijing, Peoples R China
推荐引用方式 GB/T 7714	Li, Chanying,Guo, Lei. A new critical theorem for adaptive nonlinear stabilization[J]. AUTOMATICA,2010,46(6):999-1007.
APA	Li, Chanying,&Guo, Lei.(2010).A new critical theorem for adaptive nonlinear stabilization.AUTOMATICA,46(6),999-1007.
MLA	Li, Chanying,et al."A new critical theorem for adaptive nonlinear stabilization".AUTOMATICA 46.6(2010):999-1007.