Adaptive Regulation of High Order Nonholonomic Systems

MU Xiao-wu; YU Ji-min; CHENG Gui-fang

Volume 27 Issue 4

Turn off MathJax

Article Contents

Abstract

References

Article Navigation > Applied Mathematics and Mechanics > 2006 > 27(4): 447-453

MU Xiao-wu, YU Ji-min, CHENG Gui-fang. Adaptive Regulation of High Order Nonholonomic Systems[J]. Applied Mathematics and Mechanics, 2006, 27(4): 447-453.

Citation:

MU Xiao-wu, YU Ji-min, CHENG Gui-fang. Adaptive Regulation of High Order Nonholonomic Systems[J]. Applied Mathematics and Mechanics, 2006, 27(4): 447-453.

Citation:

MU Xiao-wu, YU Ji-min, CHENG Gui-fang. Adaptive Regulation of High Order Nonholonomic Systems[J]. Applied Mathematics and Mechanics, 2006, 27(4): 447-453.

PDF( 301 KB)

Adaptive Regulation of High Order Nonholonomic Systems

Department of Mathematics, Zhengzhou University, Zhengzhou 450052, P. R. China

Received Date: 2004-12-10
Rev Recd Date: 2005-12-10
Publish Date: 2006-04-15

Abstract

Abstract

The problem of adaptive regulation for a class of high-order parametric nonholonomic systems chained-form is discussed.Using adding a power integrator technique and state scaling with discontinuous projection technique,a discontinuous adaptive dynamic controller was constructed.The controller guarantees the estimated value of unknown parameter in the prescribed extent.
- nonholonomic system,
- adaptive control,
- triangular system

FullText(HTML)

References(6)

References

[1]	Brockett R W,Millman R S,Sussmann H J.Asymptotic stability and feedback stabilization[A].In:Brockett R W,Millman R S,Sussmann H J Eds.Differential Geometric Control Theory[C].Boston: Birkhuser,1983,181—191.
[2]	LIN Wei,Pongvuthithum Radom,QIAN Chun-jiang.Control of high-order nonholonomic systems in power chained form using discontinuous feedback[J].IEEE Trans Automatic Contr,2002,47(1):108—114. doi: 10.1109/9.981728
[3]	Jiang Z P,Pomet J B.Global stabilization of parametric chained-form systems by time-varying dynamic feedback[J].Internat　Journal of Adaptive Control and Signal Processing,1996,10(1):47—59. doi: 10.1002/(SICI)1099-1115(199601)10:1<47::AID-ACS385>3.0.CO;2-7
[4]	QIAN Chun-jiang,LIN Wei.Non-Lipschitz continuous stabilizers for nonlinear systems with uncontrollable unstable linearization[J].System and Control Letters,2001,42(3):185—200. doi: 10.1016/S0167-6911(00)00089-X
[5]	Goodwin G C,Mayne D Q.A parameter estimation perspective of continuous time model reference adaptive control[J].Automatica,1989,23(1):57—70.
[6]	Khalil H K.Nonlinear Systems[M].New York:Macmillan,1992.

Relative Articles

[1]	SUN Fengqi. Stability Analysis of Discrete Time-Delay Singularly Perturbed Uncertainty Control Systems[J]. Applied Mathematics and Mechanics, 2021, 42(7): 696-703. doi: 10.21656/1000-0887.410208
[2]	SONG Duan. Dependence of Equilibrium Stability of First Order Lagrange Systems on Parameters[J]. Applied Mathematics and Mechanics, 2014, 35(6): 692-696. doi: 10.3879/j.issn.1000-0887.2014.06.011
[3]	LI Feng-ming, LIU Chun-chuan. Parametric Vibration Stability and Active Control of Nonlinear Beams[J]. Applied Mathematics and Mechanics, 2012, 33(11): 1284-1293. doi: 10.3879/j.issn.1000-0887.2012.11.004
[4]	V. Čović, M. Vesković, D. Djuri, A. Obradović. On the Stability of Equilibria of Nonholonomic Systems With Nonlinear Constraints[J]. Applied Mathematics and Mechanics, 2010, 31(6): 722-723. doi: 10.3879/j.issn.1000-0887.2010.06.009
[5]	MU Xiao-wu, CHENG Gui-fang, DING Zhi-shuai. On the Stability of Discontinuous Systems via Vector Liapunov Functions[J]. Applied Mathematics and Mechanics, 2007, 28(12): 1441-1447.
[6]	MU Xiao-wu, GUO Xiao-li, CHENG Gui-fang. Adaptive H-infinity Control of a Class of Uncertain Nonlinear Systems[J]. Applied Mathematics and Mechanics, 2006, 27(9): 1056-1064.
[7]	LI Zhi-bin, WANG Zhao-lin, WANG Tian-shu, LIU Ning. Model of Centrifugal Effect and Attitude Maneuver Stability of a Coupled Rigid-Flexible System[J]. Applied Mathematics and Mechanics, 2005, 26(5): 547-555.
[8]	SHEN Qi-hong, WEI Jun-jie. Stability and Bifurcation of a Human Respiratory System Model With Time Delay[J]. Applied Mathematics and Mechanics, 2004, 25(11): 1169-1181.
[9]	MU Xiao-wu, YU Ji-min, BI Wei-ping, CHENG Dai-zhan. Robust Adaptive Control of Nonholonomic Systems With Uncertainties[J]. Applied Mathematics and Mechanics, 2004, 25(3): 297-304.
[10]	XU Jian-guo, JIA Jun-guo. Study on Dynamics, Stability and Control of Multi-Body Flexible Structure System in Functional Space[J]. Applied Mathematics and Mechanics, 2001, 22(12): 1267-1277.
[11]	Xu Zhenduo, Liu Erlie. Equilibrium Stability of Generalized Birkhoff’s Autonomous System[J]. Applied Mathematics and Mechanics, 1999, 20(5): 531-534.
[12]	Li Gangchang, He Shiben. Lagrange’s Theorem for a Class of Nonholonomic Systems and Its Application[J]. Applied Mathematics and Mechanics, 1998, 19(2): 126-135.
[13]	Liang Lifu, Liang Zhonghong, Shi Zhifei. The Stationary Value Property of Hamilton’s Principle in Non-Holonomic Systems[J]. Applied Mathematics and Mechanics, 1997, 18(12): 1089-1096.
[14]	Liang Lifu, Wei Yang. On the Unification of the Hamilton Principles in Non-Holonomic System and in Holonomic System[J]. Applied Mathematics and Mechanics, 1996, 17(5): 439-444.
[15]	Li Junfeng, Wang Zhaolin. Stability of Non-Conservative Linear Gyroscopic Systems[J]. Applied Mathematics and Mechanics, 1996, 17(12): 1107-1111.
[16]	Liu Jie. nvariant Manifolds and Their Stability in a Three-Dimensional Measure-preserving Mapping System[J]. Applied Mathematics and Mechanics, 1995, 16(10): 879-888.
[17]	Zhu Haiping, Shi Rongchang, Mei Fengxiang. Stability for the Equilibrium State of Chaplygin’s systems[J]. Applied Mathematics and Mechanics, 1995, 16(7): 595-601.
[18]	Zhu Hai-ping, Mei Feng-xiang. On the Stability 0f Nonholonomic Mechanical Systems with Respect to Partial Variables[J]. Applied Mathematics and Mechanics, 1995, 16(3): 225-233.
[19]	Hou Gan-sheng. The Bounded Extermination and Stability of Mutual Interference System of Four-Dimensional Species[J]. Applied Mathematics and Mechanics, 1994, 15(11): 981-990.
[20]	Hu Chao-yuang. The Asymptotic Stability of the Linear Discrete Large Scale Systems[J]. Applied Mathematics and Mechanics, 1993, 14(1): 89-94.