Chaos suppression of uncertain gyros in a given finite time

doi:10.1088/1674-1056/21/11/110505

中国物理B ›› 2012, Vol. 21 ›› Issue (11): 110505-110505.doi: 10.1088/1674-1056/21/11/110505

Chaos suppression of uncertain gyros in a given finite time

Mohammad Pourmahmood Aghababa^a, Hasan Pourmahmood Aghababa^{b c}

a Electrical Engineering Department, Urmia University of Technology, Urmia, Iran;
b Department of Mathematics, University of Tabriz, Tabriz, Iran;
c Research Center for Industrial Mathematics of University of Tabriz, Tabriz, Iran

收稿日期:2012-04-24 修回日期:2012-06-14 出版日期:2012-10-01 发布日期:2012-10-01

Chaos suppression of uncertain gyros in a given finite time

Mohammad Pourmahmood Aghababa^a, Hasan Pourmahmood Aghababa^{b c}

a Electrical Engineering Department, Urmia University of Technology, Urmia, Iran;
b Department of Mathematics, University of Tabriz, Tabriz, Iran;
c Research Center for Industrial Mathematics of University of Tabriz, Tabriz, Iran

Received:2012-04-24 Revised:2012-06-14 Online:2012-10-01 Published:2012-10-01
Contact: Mohammad Pourmahmood Aghababa E-mail:m.p.aghababa@ee.uut.ac.ir

摘要/Abstract

摘要： The gyro is one of the most interesting and everlasting nonlinear dynamical systems, which displays very rich and complex dynamics, such as sub-harmonic and chaotic behaviors. We study the chaos suppression of the chaotic gyros in a given finite time. Considering the effects of model uncertainties, external disturbances, and fully unknown parameters, we design a robust adaptive finite-time controller to suppress the chaotic vibration of the uncertain gyro as quickly as possible. Using the finite-time control technique, we given the exact value of the chaos suppression time. A mathematical theorem is presented to prove the finite-time stability of the proposed scheme. The numerical simulation shows the efficiency and usefulness of the proposed finite-time chaos suppression strategy.

关键词: chaos suppression, chaotic gyro, finite-time stability, robustness

Abstract: The gyro is one of the most interesting and everlasting nonlinear dynamical systems, which displays very rich and complex dynamics, such as sub-harmonic and chaotic behaviors. We study the chaos suppression of the chaotic gyros in a given finite time. Considering the effects of model uncertainties, external disturbances, and fully unknown parameters, we design a robust adaptive finite-time controller to suppress the chaotic vibration of the uncertain gyro as quickly as possible. Using the finite-time control technique, we given the exact value of the chaos suppression time. A mathematical theorem is presented to prove the finite-time stability of the proposed scheme. The numerical simulation shows the efficiency and usefulness of the proposed finite-time chaos suppression strategy.

Key words: chaos suppression, chaotic gyro, finite-time stability, robustness

中图分类号: (Nonlinear dynamics and chaos)

05.45.-a

05.45.Xt (Synchronization; coupled oscillators) 05.45.Gg (Control of chaos, applications of chaos) 05.45.Pq (Numerical simulations of chaotic systems)

Mohammad Pourmahmood Aghababa, Hasan Pourmahmood Aghababa . Chaos suppression of uncertain gyros in a given finite time[J]. 中国物理B, 2012, 21(11): 110505-110505.

Mohammad Pourmahmood Aghababa, Hasan Pourmahmood Aghababa. Chaos suppression of uncertain gyros in a given finite time[J]. Chin. Phys. B, 2012, 21(11): 110505-110505.

参考文献 20

[1]	Ott E, Grebogi C and Yorke J A 1990 Phys. Rev. Lett. 65 3215
[2]	Aghababa M P 2011 Nonlinear Dyn. 69 247
[3]	Lü L, Li G, Guo L, Meng L, Zou J R and Yang M 2010 Chin. Phys. B 19 080507
[4]	Liu Y Z, Jiang C S, Lin C S and Jiang Y M 2007 Chin. Phys. B 16 660
[5]	Aghababa M P 2011 Chin. Phys. B 20 090505
[6]	Hu J and Zhang Q J 2008 Chin. Phys. B 17 503
[7]	Aghababa M P 2012 Chin. Phys. B 21 030502
[8]	Bowong S 2007 Nonlinear Dyn. 49 59
[9]	Chen H K 2002 J. Sound Vibr. 255 719
[10]	Dooren R V 2008 J. Sound Vibr. 268 632
[11]	Tong X and Mrad N 2001 J. Appl. Mech. 68 681
[12]	Leipnik R B and NewtoT A 1981 Phys. Lett. A 86 63
[13]	Polo M F P and Molina M P 2007 Nonlinear Dyn. 48 129
[14]	Lei Y, Xu W and Zheng H 2005 Phys. Lett. A 343 153
[15]	Hung M, Yan J and Liao T 2008 Chaos Soliton. Fract. 35 181
[16]	Yau H 2007 Chaos Soliton. Fract. 34 1357
[17]	Yau H 2008 Mech. Syst. Signal Process. 22 408
[18]	Yan J, Hung M, Lin J and Liao T 2007 Mech. Syst. Signal Process. 21 2515
[19]	Wang H, Han Z, Xie Q and Zhang W 2009 Commun. Nonlinear Sci. Numer. Simulat. 14 2728
[20]	Edwards C, Spurgeon S K and Patton R J 2000 Automatica 36 541

Chaos suppression of uncertain gyros in a given finite time

Chaos suppression of uncertain gyros in a given finite time

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 20

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Yun Su(苏云), Teli Xi(席特立), and Xiaopeng Shao(邵晓鹏). Research on the model of high robustness computational optical imaging system[J]. 中国物理B, 2023, 32(2): 24202-024202.
[2]	Yun-Yun Yang(杨云云), Biao Feng(冯彪), Liao Zhang(张辽), Shu-Hong Xue(薛舒红), Xin-Lin Xie(谢新林), and Jian-Rong Wang(王建荣). Robustness measurement of scale-free networks based on motif entropy[J]. 中国物理B, 2022, 31(8): 80201-080201.
[3]	Rui-Qiong Ma(马瑞琼), Jian Shi(时坚), Lin Liu(刘琳), Meng Liang(梁猛), Zuo-Liang Duan(段作梁), Wei Gao(高伟), and Jun Dong(董军). High-fidelity resonant tunneling passage in three-waveguide system[J]. 中国物理B, 2022, 31(2): 24202-024202.
[4]	Xi-Kun Feng(冯希昆), Xiao-Feng Gu(顾晓峰), Qin-Ling Ma(马琴玲), Yan-Ni Yang(杨燕妮), and Hai-Lian Liang(梁海莲). Design and investigation of novel ultra-high-voltage junction field-effect transistor embedded with NPN[J]. 中国物理B, 2021, 30(7): 78502-078502.
[5]	Zi-Wei Yuan(袁紫薇), Chang-Chun Lv(吕长春), Shu-Bin Si(司书宾), and Dong-Li Duan(段东立). Dynamical robustness of networks based on betweenness against multi-node attack[J]. 中国物理B, 2021, 30(5): 50501-050501.
[6]	魏士慧, 郭奋卓, 李新慧, 温巧燕. Robustness self-testing of states and measurements in the prepare-and-measure scenario with 3→1 random access code[J]. 中国物理B, 2019, 28(7): 70304-070304.
[7]	李红梅, 郭苗迪, 张锐, 苏雪梅. Boundary states for entanglement robustness under dephasing and bit flip channels[J]. 中国物理B, 2019, 28(10): 100302-100302.
[8]	王小娟, 宋梅, 金磊, 王珍. The robustness of sparse network under limited attack capacity[J]. 中国物理B, 2017, 26(8): 88901-088901.
[9]	王建荣, 王建萍, 何振, 许海涛. Degree distribution and robustness of cooperativecommunication network with scale-free model[J]. 中国物理B, 2015, 24(6): 60101-060101.
[10]	张宇超, 鲍皖苏, 汪翔, 付向群. Effects of systematic phase errors on optimized quantum random-walk search algorithm[J]. 中国物理B, 2015, 24(6): 60304-060304.
[11]	唐绪兵, 高放, 王耀雄, 匡森, 双丰. Non-Gaussian quantum states generation and robust quantum non-Gaussianity via squeezing field[J]. , 2015, 24(3): 34208-034208.
[12]	张争珍, 许文俊, 曾上游, 林家儒. An effective method to improve the robustness of small-world networks under attack[J]. , 2014, 23(8): 88902-088902.
[13]	花丽丽, 徐宁, 杨庚. An encryption scheme based on phase-shifting digital holography and amplitude-phase disturbance[J]. 中国物理B, 2014, 23(6): 64201-064201.
[14]	肖延东, 老松杨, 侯绿林, 白亮. Optimization of robustness of network controllability against malicious attacks[J]. 中国物理B, 2014, 23(11): 118902-118902.
[15]	刘平. Robust finite-time stabilization of unified chaotic complex systems with certain and uncertain parameters[J]. 中国物理B, 2013, 22(7): 70501-070501.