Robust controller design of a class of uncertain fractional-order nonlinear systems
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- 英文论文题名：Robust controller design of a class of uncertain fractional-order nonlinear systems
- 论文作者：Heng Liu ; Xiulan Zhang ; Ning Li ; Hui Lv
- 英文论文作者：Heng Liu ; Xiulan Zhang ; Ning Li ; Hui Lv ; Department of Applied Mathematics ; Huainan Normal University ; College of Electronic Engineering ; Huainan Normal University
- 年：2017
- 作者机构：Department of Applied Mathematics,Huainan Normal University;College of Electronic Engineering,Huainan Normal University;
- 英文论文关键词：Fractional-order system ; parameter perturbation ; robust control
- 会议召开时间：2017-07-26
- 会议录名称：第36届中国控制会议论文集（A）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（A）
- 语种：英文
- 分类号：O231
- 学会代码：KZLL
- 会议名称：第36届中国控制会议
- 会议地点：中国辽宁大连
- 主办单位：中国自动化学会控制理论专业委员会
- 学会名称：中国自动化学会控制理论专业委员会
- 页数：5
- 文件大小：970k
- 原文格式：D
- 会议级别：全国
摘要
In this paper, a robust control method is proposed for a class of fractional-order nonlinear system with unknown system parameter based on Lyapunov direct method. The Caputo definition is used to describe the fractional-order dynamic system. The controller is simple and enables asymptotically stability to be achieved without the computation of the conditional Lyapunov exponents. Finally, simulation results are given to show the effectiveness of the proposed method.
In this paper, a robust control method is proposed for a class of fractional-order nonlinear system with unknown system parameter based on Lyapunov direct method. The Caputo definition is used to describe the fractional-order dynamic system. The controller is simple and enables asymptotically stability to be achieved without the computation of the conditional Lyapunov exponents. Finally, simulation results are given to show the effectiveness of the proposed method.
In this paper, a robust control method is proposed for a class of fractional-order nonlinear system with unknown system parameter based on Lyapunov direct method. The Caputo definition is used to describe the fractional-order dynamic system. The controller is simple and enables asymptotically stability to be achieved without the computation of the conditional Lyapunov exponents. Finally, simulation results are given to show the effectiveness of the proposed method.
引文
[1]I.Podlubny,Fractional Differential Equations,ser.Mathematics in Science and Engineering.New York:Academic Press,1999.
[2]S.Wang,Y.G.Yu and M.Diao.Hybrid projective synchronization of chaotic fractional-order systems with different dimensions.Physica A,vol.389,pp.4981-4988,2010.
[3]M.Ichise,Y.Nagayanagi and T.Kojima.An analog simulation of non-integer order transfer functions for analysis of electroder processes,J.Electroanal.Chem.vol.33 pp.253-265,1971.
[4]J.G.Lu and G.R.Chen,Robust Stability and Stabilization of Fractional-Order Interval Systems:An LMI Approach.IEEE Trans.Automat.Control,vol.54,no.6,pp.1294-1299,2009.
[5]R.C.Koeller.Applications of fractional calculus to the theory of viscoelasticity,J.Appl.Mech.,vol.51,pp.299-307,1984.
[6]M.Nakagava and K.Sorimachi,Basic characteristics of a fractance device,IEICE Trans.Fund.,vol.E75-A,no.12,pp.1814-1818,1992.
[7]S.Westerlund,Capacitor theory,IEEE Trans.Dielect.Electron.Insul.,vol.1,no.5,pp.826-839,1994.
[8]P.S.V.Nataraj,Computation of spectral sets for uncertain linear fractional-order systems using interval constraints propagation.Third IFAC Workshop on Fractional Differentiation and its Application,Ankara,2008
[9]S.Kuntanapreeda.Robust synchronization of fractional-order unified chaotic systems via linear control,Computers and Mathematics with Applications,vol.63,pp.183-190,2012.
[10]D.F.Wang,J.Y.Zhang and X.Y.Wang,Robust modified projective synchronization of fractional-order chaotic systems with parameters perturbation and external disturbance.Chin.Phys.B,vol.22,no.10,pp.100504,2013.
[11]A.C.Bartlett,C.V.Hollot and H.Lin,Root location of an entire polytope of polynomials:it suffices to check the edges.Math.Controls,Signals Syst.,vol.1,pp.61-71,1988.
[12]C.V.Hollot and R.Tempo,On the Nyquist envelope of an interval plant family,IEEE Trans.Autom.Control,vol.39,pp.391-396,1994.
[13]Y.Li,Y.Q.Chen and I.Podlubny,Mittag-Leffler stability of fractional order nonlinear dynamic systems,Automatica,vol.45,no.8,pp.1965-1969,2009.
[14]S.Dadra and H.R.Momeni,Fractional sliding mode observer design for a class of uncertain fractional order nonlinear systems.IEEE Conference on Decision and Control and Europena control Conference,Orlando,FL,USA,pp.6925-6930,2011.
[2]S.Wang,Y.G.Yu and M.Diao.Hybrid projective synchronization of chaotic fractional-order systems with different dimensions.Physica A,vol.389,pp.4981-4988,2010.
[3]M.Ichise,Y.Nagayanagi and T.Kojima.An analog simulation of non-integer order transfer functions for analysis of electroder processes,J.Electroanal.Chem.vol.33 pp.253-265,1971.
[4]J.G.Lu and G.R.Chen,Robust Stability and Stabilization of Fractional-Order Interval Systems:An LMI Approach.IEEE Trans.Automat.Control,vol.54,no.6,pp.1294-1299,2009.
[5]R.C.Koeller.Applications of fractional calculus to the theory of viscoelasticity,J.Appl.Mech.,vol.51,pp.299-307,1984.
[6]M.Nakagava and K.Sorimachi,Basic characteristics of a fractance device,IEICE Trans.Fund.,vol.E75-A,no.12,pp.1814-1818,1992.
[7]S.Westerlund,Capacitor theory,IEEE Trans.Dielect.Electron.Insul.,vol.1,no.5,pp.826-839,1994.
[8]P.S.V.Nataraj,Computation of spectral sets for uncertain linear fractional-order systems using interval constraints propagation.Third IFAC Workshop on Fractional Differentiation and its Application,Ankara,2008
[9]S.Kuntanapreeda.Robust synchronization of fractional-order unified chaotic systems via linear control,Computers and Mathematics with Applications,vol.63,pp.183-190,2012.
[10]D.F.Wang,J.Y.Zhang and X.Y.Wang,Robust modified projective synchronization of fractional-order chaotic systems with parameters perturbation and external disturbance.Chin.Phys.B,vol.22,no.10,pp.100504,2013.
[11]A.C.Bartlett,C.V.Hollot and H.Lin,Root location of an entire polytope of polynomials:it suffices to check the edges.Math.Controls,Signals Syst.,vol.1,pp.61-71,1988.
[12]C.V.Hollot and R.Tempo,On the Nyquist envelope of an interval plant family,IEEE Trans.Autom.Control,vol.39,pp.391-396,1994.
[13]Y.Li,Y.Q.Chen and I.Podlubny,Mittag-Leffler stability of fractional order nonlinear dynamic systems,Automatica,vol.45,no.8,pp.1965-1969,2009.
[14]S.Dadra and H.R.Momeni,Fractional sliding mode observer design for a class of uncertain fractional order nonlinear systems.IEEE Conference on Decision and Control and Europena control Conference,Orlando,FL,USA,pp.6925-6930,2011.