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山东大学学报(工学版) ›› 2015, Vol. 45 ›› Issue (6): 29-35.doi: 10.6040/j.issn.1672-3961.0.2015.201

• 控制科学与工程 • 上一篇    下一篇

分数阶非线性三角系统的状态反馈控制器设计

赵以阁, 王玉振   

  1. 山东大学控制科学与工程学院, 山东济南 250061
  • 收稿日期:2015-06-26 修回日期:2015-11-02 出版日期:2015-12-20 发布日期:2015-06-26
  • 通讯作者: 王玉振(1963-),男,山东泰安人,博士,教授,博士生导师,主要研究方向为非线性控制,Hamilton控制系统理论,逻辑动态网络,复杂系统.E-mail:yzwang@sdu.edu.cn E-mail:yzwang@sdu.edu.cn
  • 作者简介:赵以阁(1986-),男,山东济南人,博士研究生,主要研究方向为分数阶系统控制.E-mail:zhaoeager@126.com
  • 基金资助:
    国家自然科学基金资助项目(G61374065,G61374002);山东省泰山学者项目基金资助项目

State feedback controller design for fractional order system in the triangular form

ZHAO Yige, WANG Yuzhen   

  1. School of Control Science and Engineering, Shandong University, Jinan 250061, Shandong, China
  • Received:2015-06-26 Revised:2015-11-02 Online:2015-12-20 Published:2015-06-26

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摘要： 给出了Caputo分数阶导数的若干新性质,并利用这些性质,建立了分数阶非线性系统渐近稳定的一个充分条件。利用Backsteping方法,针对一类分数阶非线性三角系统,提出了一种状态反馈控制器的设计方法。最后用例子说明理论结果的有效性。

关键词: Caputo分数阶导数, 三角系统, Backsteping方法, 状态反馈, 分数阶系统

Abstract: Some new properties for Caputo fractional derivative were presented, and a sufficient condition of asymptotical stability for fractional order nonlinear systems was obtained based on the new properties. By using the Backstepping technique, the state feedback control design problem for fractional order nonlinear systems in the triangular form was investigated. Two illustrative examples were provided to illustrate the effectiveness of the main results.

Key words: fractional order system, state feedback, triangular system, Backstepping technique, Caputo fractional derivative

中图分类号: 

  • TP273
[1] PODLUBNY I. Fractional differential equations[M]. New York:Academic Press, 1999.
[2] KILBAS A A, SRIVASTAVA H H, TRUJILLO J J. Theory and applications of fractional differential equations[M]. Elsevier Science B V:Amsterdam, 2006.
[3] MILLER K S, ROSS B. An introduction to the fractional calculus and fractional differential equation[M]. New York:John Wiley, 1993.
[4] MANABE S. The non-integer integral and its application to control systems[J]. Electrotechnical Journal of Japan, 1961, 6(3-4):83-87.
[5] TAVAZOEI M S, HAERI M. A note on the stability of fractional order systems[J]. Mathematics and Computers in Simulation, 2009, 79(5):1566-1576.
[6] CHEN Y Q, MOORE K L. Analytical stability bound for a class of delayed fractional-order dynamic systems[J]. Nonlinear Dynamics, 2002, 29(1):191-200.
[7] AHN H S, CHEN Y Q, PODLUBNY I. Robust stability test of a class of linear time-invariant interval fractional-order system using Lyapunov inequality[J]. Applied Mathematics and Computation, 2007, 187(1):27-34.
[8] MOORNANI K A, HAERI M. On robust stability of linear time invariant fractional-order systems with real parametric uncertainties[J]. ISA Transactions, 2009, 48(4):484-490.
[9] CHEN Y Q, AHN H S, XUE D Y. Robust controllability of interval fractional order linear time invariant systems[J]. Signal Processing, 2006, 86(10):2794-2802.
[10] MOORNANI K A, HAERI M. Necessary and sufficient conditions for BIBO-stability of some fractional delay systems of neutral type[J]. IEEE Transactions on Automatic Control, 2011, 56(1):125-128.
[11] ABUSAKSAKA A B, PARTINGTON J R. BIBO stability of some classes of delay systems and fractional systems[J]. Systems & Control Letters, 2014, 64:43-46.
[12] LAZAREVIĆ M P. Finite time stability analysis of PDα fractional control of robotic time-delay systems[J]. Mechanics Research Communications, 2006, 33(2):269-279.
[13] LAZAREVIĆ M P, SPASIĆ A M. Finite-time stability analysis of fractional order time-delay systems:Gronwall's approach[J]. Mathematical and Computer Modelling, 2009, 49(3):475-481.
[14] KAMAL S, RAMAN A, BANDYOPADHYAY B. Finite-time stabilization of fractional order uncertain chain of integrator:an integral sliding mode approach[J]. IEEE Transactions on Automatic Control, 2013, 58(6):1597-1602.
[15] SHEN J, LAM J. Non-existence of finite-time stable equilibria in fractional-order nonlinear systems[J]. Automatica, 2014, 50(2):547-551.
[16] LAKSHMIKANTHAM V, LEELA S, SAMBANDHAM M. Lyapunov theory for fractional differential equations[J]. Communications in Applied Analysis, 2008, 12(4):365-376.
[17] BURTON T A. Fractional differential equations and Lyapunov functionals[J]. Nonlinear Analysis:Theory, Methods & Applications, 2011, 74(16):5648-5662.
[18] LI Y, CHEN Y Q, PODLUBNY I. Mittag-Leffler stability of fractional order nonlinear dynamic systems[J]. Automatica, 2009, 45(8):1965-1969.
[19] LI Y, CHEN Y Q, PODLUBNY I. Stability of fractional-order nonlinear dynamic systems:Lyapunov direct method and generalized Mittag-Leffler stability[J]. Computers and Mathematics with Applications, 2010, 59(5):1810-1821.
[20] SADATI S J, BALEANU D, RANJBAR A, et al. Mittag-Leffler stability theorem for fractional nonlinear systems with delay[J]. Abstract and Applied Analysis, 2010, 2010:1-7.
[21] AGUILA-CAMACHO N, DUARTE-MERMOUD M A, GALLEGOS J A. Lyapunov functions for fractional order systems[J]. Communications in Nonlinear Science and Numerical Simulation, 2014, 19(9):2951-2957.
[22] 韩正之, 陈鹏年, 陈树中. 自适应控制[M]. 北京:清华大学出版社, 2011.
[23] XIE X J, DUAN N, YU X. State-feedback control of high-order stochastic nonlinear systems with SiISS inverse dynamics[J]. IEEE Transactions on Automatic Control, 2011, 56(8):1921-1926.
[24] XIE X J, LIU L. A homogeneous domination approach to state feedback of stochastic high-order nonlinear systems with time-varying delay[J]. IEEE Transactions on Automatic Control, 2013, 58(2):494-499.
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