Premium
A robust adaptive pole‐placement controller without strictly positive real condition
Author(s) -
Xie Xuejun,
Zhang Siying
Publication year - 2002
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.663
Subject(s) - control theory (sociology) , mathematics , bounded function , controller (irrigation) , truncation (statistics) , noise (video) , constant (computer programming) , infinity , adaptive control , stability (learning theory) , order (exchange) , full state feedback , mathematical analysis , combinatorics , control (management) , computer science , statistics , finance , artificial intelligence , machine learning , agronomy , economics , image (mathematics) , biology , programming language
This paper considers the adaptive pole‐placement control problem for system (1) with unmodelled dynamics η n dominated by a small constant ε multiplied by a quantity independent of ε but tending to infinity as the past input, output, and noise grow. Using bounded external excitation and randomly varying truncation techniques, we give a design method of adaptive pole‐placement controller. It is shown that the closed‐loop system is globally stable, the estimation error for the parameter contained in the modelled part is of order ε , and the closed‐loop system under the adaptive pole‐placement control law is suboptimal in the sense of $$\mathop{\lim\sup}\limits_{{n\to\infty }}{1\over n}\mathop{\sum}\limits_{i=0}^n{\left({A^{*}(z)y_{n}‐L(z)C(z)w_{n}‐B(z)R(z)y_{n}^{*}}\right)^{2}{\leq}O({\varepsilon}^{2})+\gamma^{2}\mathop{\sum}\limits_{j=1}^q{b_{j}^{2}}}$$\nopagenumbers\end while the SPR condition used usually in other papers is replaced by a stability condition. Copyright © 2001 John Wiley & Sons, Ltd.