zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Adaptive state-feedback stabilization for a class of high-order nonlinear uncertain systems. (English) Zbl 1119.93061
Summary: For high-order nonlinear uncertain systems, there have been a lot of investigations under a strong assumption that the lower bounds of the unknown control coefficients should be exactly known. In this paper, this assumption is removed and a unified approach is developed to systematically construct a state-feedback adaptive stabilizing control law for a class of high-order nonlinear uncertain systems with unknown control coefficients. By using the method of the so-called adding a power integrator merging with adaptive technique, a recursive design procedure is provided to achieve a smooth adaptive state-feedback control law, which guarantees that the closed-loop system is globally uniformly stable while the original system states globally asymptotically converge to zero. Finally, a simulation example is given to illustrate the correctness of the theoretical results.

MSC:
93D21Adaptive or robust stabilization
93C10Nonlinear control systems
93C15Control systems governed by ODE
93C40Adaptive control systems
WorldCat.org
Full Text: DOI
References:
[1] Deng, H.; Krstić, M.: Output-feedback stochastic nonlinear stabilization. IEEE transactions on automatic control 44, 328-333 (1999) · Zbl 0958.93095
[2] Ezal, K.; Pan, Z.; Kokotović, P. V.: Locally optimal backstepping design. IEEE transactions on automatic control 45, 260-271 (2000) · Zbl 0973.93008
[3] Freeman, R. A.; Kokotović, P. V.: Robust nonlinear control design. (1996)
[4] Ge, S. S.; Wang, C.: Adaptive NN control of uncertain nonlinear pure-feedback systems. Automatica 38, 671-682 (2002) · Zbl 0998.93025
[5] Jiang, Z. P.; Mareels, I.; Hill, D. J.; Huang, J.: A unifying framework for global regulation via nonlinear output feedback: from ISS to IISS. IEEE transactions on automatic control 49, 549-562 (2004)
[6] Kanellakopoulos, I.; Kokotović, P. V.; Morse, S.: Systematic design of adaptive controllers for feedback linearizable systems. IEEE transactions on automatic control 36, 1241-1253 (1991) · Zbl 0768.93044
[7] Khalil, H. K.: Nonlinear systems. (2002) · Zbl 1003.34002
[8] Kokotović, P. V.; Arcak, M.: Constructive nonlinear control: A historical perspective. Automatica 37, 637-662 (2001) · Zbl 1153.93301
[9] Krstić, M.; Kanellakopoulos, I.; Kokotović, P. V.: Adaptive nonlinear control without overparameterization. Systems and control letters 19, 177-185 (1992) · Zbl 0763.93043
[10] Krstić, M.; Kanellakopoulos, I.; Kokotović, P. V.: Adaptive nonlinear control without overparameterization. IEEE transactions on automatic control 39, 738-752 (1994) · Zbl 0807.93036
[11] Krstić, M.; Kanellakopoulos, I.; Kokotović, P. V.: Nonlinear and adaptive control design. (1995) · Zbl 0763.93043
[12] Lin, W.; Qian, C.: Adaptive regulation of high-order lower-triangular systems: an adding a power integrator technique. Systems and control letters 39, 353-364 (2000) · Zbl 0948.93055
[13] Lin, W.; Qian, C.: Adding one power integrator: A tool for global stabilization of high-order lower-triangular systems. Systems and control letters 39, 339-351 (2000) · Zbl 0948.93056
[14] Lin, W.; Qian, C.: Adaptive control of nonlinear parameterized systems: the nonsmooth feedback framework. IEEE transactions on automatic control 47, 757-774 (2002)
[15] Lin, W.; Qian, C.: Adaptive control of nonlinear parameterized systems: the smooth feedback case. IEEE transactions on automatic control 47, 1249-1266 (2002)
[16] Liu, Y. G.; Pan, Z.; Shi, S.: Output feedback control design for strict-feedback stochastic nonlinear systems under a risk-sensitive cost. IEEE transactions on automatic control 48, 509-513 (2003)
[17] Liu, Y. G.; Zhang, J. F.: Practical output-feedback risk-sensitive control for stochastic nonlinear systems with stable zero-dynamics. SIAM journal on control and optimization 45, 885-926 (2006) · Zbl 1117.93067
[18] Pan, Z.; Başar, T.: Adaptive controller design for tracking and disturbance attenuation in parametric strict-feedback nonlinear systems. IEEE transactions on automatic control 43, 1066-1084 (1998) · Zbl 0957.93046
[19] Pan, Z.; Başar, T.: Backstepping controller design for nonlinear stochastic systems under a risk-sensitive cost criterion. SIAM journal on control and optimization 37, 957-995 (1999) · Zbl 0924.93046
[20] Qian, C.; Lin, W.: A continuous feedback approach to global strong stabilization of nonlinear systems. IEEE transactions on automatic control 46, 1061-1079 (2001) · Zbl 1012.93053
[21] Qian, C.; Lin, W.; Dayawansa, W. P.: Smooth feedback, global stabilization and disturbance attenuation of nonlinear systems with uncontrollable linearization. SIAM journal on control and optimization 40, 191-210 (2002) · Zbl 0995.93060
[22] Seto, D.; Annaswamy, A. M.; Baillieul, J.: Adaptive control of nonlinear systems with triangular structure. IEEE transactions on automatic control 39, 1411-1428 (1994) · Zbl 0806.93034
[23] Sun, Z. Y.; Liu, Y. G.: State-feedback stabilizing control design for a class of high-order nonlinear systems with unknown but identical virtual control coefficients. Acta automatica sinica 33, 331-334 (2007)
[24] Ye, X.; Jiang, J.: Adaptive nonlinear design without a priori knowledge of control directions. IEEE transactions on automatic control 43, 1617-1621 (1998) · Zbl 0957.93048
[25] Zhang, Y.; Wen, C. Y.; Soh, Y. C.: Adaptive backstepping control design for systems with unknown high frequency gain. IEEE transactions on automatic control 45, 2350-2354 (2000) · Zbl 0990.93061
[26] Zhou, J.; Wen, C. Y.; Zhang, Y.: Adaptive output control of nonlinear systems with uncertain dead-zone nonlinearity. IEEE transactions on automatic control 51, 504-511 (2006)