On critical stability of discrete-time adaptive nonlinear control

CSpace

	On critical stability of discrete-time adaptive nonlinear control
	Guo, L
	1997-11-01
发表期刊	IEEE TRANSACTIONS ON AUTOMATIC CONTROL
ISSN	0018-9286
卷号	42 期号:11 页码:1488-1499
摘要	In this paper, we examine the global stability and instability problems for a class of discrete-time adaptive nonlinear stochastic control, The systems to be controlled may exhibit chaotic behavior and are assumed to be linear in unknown parameters hut nonlinear in output dynamics, which are characterized by a nonlinear function [say, f(x)]. It is found and proved that in the scalar parameter case there is a critical stability phenomenon for least squares (LS)-based adaptive control systems. To be specific, let the growth rate of f(x) be f(x) = O(parallel to x parallel to(b)) with b greater than or equal to 0, then it is found that b = 4 is a critical value for global stability, i.e., the closed-loop adaptive system is globally stable if b < 4 and is unstable in general if b greater than or equal to 4. As a consequence, we find an interesting phenomenon that the linear case does not have: for some LS-based certainty equivalence adaptive controls, even if the LS parameter estimates are strongly consistent, the closed-loop systems may still be unstable, This paper also indicates that adaptive nonlinear stochastic control that is designed based on, e.g., Taylor expansion (or Weierstrass approximation) for nonlinear models, may not be feasible in general.
关键词	adaptive control discrete-time global stability instability least squares nonlinear system random noises
语种	英语
WOS研究方向	Automation & Control Systems ; Engineering
WOS类目	Automation & Control Systems ; Engineering, Electrical & Electronic
WOS记录号	WOS:A1997YF51800001
出版者	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/28989
专题	中国科学院数学与系统科学研究院
通讯作者	Guo, L
作者单位	CHINESE ACAD SCI,INST SYST SCI,BEIJING 100080,PEOPLES R CHINA
推荐引用方式 GB/T 7714	Guo, L. On critical stability of discrete-time adaptive nonlinear control[J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL,1997,42(11):1488-1499.
APA	Guo, L.(1997).On critical stability of discrete-time adaptive nonlinear control.IEEE TRANSACTIONS ON AUTOMATIC CONTROL,42(11),1488-1499.
MLA	Guo, L."On critical stability of discrete-time adaptive nonlinear control".IEEE TRANSACTIONS ON AUTOMATIC CONTROL 42.11(1997):1488-1499.