Novel mean square exponential stability criterion of uncertain stochastic interval type-2 fuzzy neural networks with multiple time-varying delays
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- 英文论文题名：Novel mean square exponential stability criterion of uncertain stochastic interval type-2 fuzzy neural networks with multiple time-varying delays
- 论文作者：Deqiang Zeng ; Kaibo Shi ; Ruimei Zhang ; Shouming Zhong
- 英文论文作者：Deqiang Zeng ; Kaibo Shi ; Ruimei Zhang ; Shouming Zhong ; Data Recovery Key Laboratory of Sichuan Province ; College of Mathematics and Information Science ; Neijiang Normal University ; School of Information Sciences and Engineering ; Chengdu University ; School of Mathematics Sciences ; University of Electronic Science and Technology of China
- 年：2017
- 作者机构：Data Recovery Key Laboratory of Sichuan Province,College of Mathematics and Information Science,Neijiang Normal University;School of Information Sciences and Engineering,Chengdu University;School of Mathematics Sciences,University of Electronic Science and Technology of China;
- 英文论文关键词：Neural networks ; IT2 fuzzy systems ; Uncertain stochastic systems ; Mean square exponential stability
- 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（B）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（B）
- 语种：英文
- 分类号：TP183
- 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：6
- 文件大小：223k
- 原文格式：D
- 会议级别：全国
摘要
This paper investigates the problem of mean square exponential stability for uncertain stochastic interval type-2(IT2)fuzzy neural networks with multiple time-varying delays. First, IT2 fuzzy neural network is introduced, which takes time delays and parameter uncertainties into account. Compared with the existing results, our model is more applicable since time delays and parameter uncertainties are very common due to environmental and artificial factors. Then, on the basis of a LyapunovKrasovskii functional(LKF), stochastic analysis approach, and It o?'s differential formula, a new sufficient condition is derived to guarantee the mean square exponential stability of the considered IT2 fuzzy neural network. Finally, a numerical example is provided to show the effectiveness of the proposed criterion.
This paper investigates the problem of mean square exponential stability for uncertain stochastic interval type-2(IT2)fuzzy neural networks with multiple time-varying delays. First, IT2 fuzzy neural network is introduced, which takes time delays and parameter uncertainties into account. Compared with the existing results, our model is more applicable since time delays and parameter uncertainties are very common due to environmental and artificial factors. Then, on the basis of a LyapunovKrasovskii functional(LKF), stochastic analysis approach, and It o?'s differential formula, a new sufficient condition is derived to guarantee the mean square exponential stability of the considered IT2 fuzzy neural network. Finally, a numerical example is provided to show the effectiveness of the proposed criterion.
This paper investigates the problem of mean square exponential stability for uncertain stochastic interval type-2(IT2)fuzzy neural networks with multiple time-varying delays. First, IT2 fuzzy neural network is introduced, which takes time delays and parameter uncertainties into account. Compared with the existing results, our model is more applicable since time delays and parameter uncertainties are very common due to environmental and artificial factors. Then, on the basis of a LyapunovKrasovskii functional(LKF), stochastic analysis approach, and It o?'s differential formula, a new sufficient condition is derived to guarantee the mean square exponential stability of the considered IT2 fuzzy neural network. Finally, a numerical example is provided to show the effectiveness of the proposed criterion.
引文
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[3]C.Peng,and T.Yang,Event-triggered communication and H∞control co-design for networked control systems,Automatica,49:1326-1332,2013.
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[5]K.Shi,Y.Tang,X.Liu,and S.Zhong,Non-fragile sampleddata robust synchronization of uncertain delayed chaotic Lurie systems with randomly occurring controller gain fluctuation,ISA Transactions,66:185-199,2017.
[6]T.Zhang,B.Fang,Y.Tang,G.He,J.Wen,Topology preserving non-negative matrix factorization for face recognition,IEEE Trans.Image Processing.53:1025-1032,2008.
[7]Y.Tang,Z.Wang,H.Gao,H.Qiao,and J.Kurths,On controllability of neuronal networks with constraints on the average of control gains,IEEE Trans.Cybern.44(12):2670-2681,2014.
[8]Y.Tang,F.Qian,H.Gao,and J.Kurths,Synchronization in complex networks and its application-a survey of recent advances and challenges,Annu.Rev.Control,38(2):184-198,2014.
[9]Y.Tang,H.Gao,and J.Kurths,Multiobjective identification of controlling areas in neuronal networks,IEEE/ACM Trans.Comput.Biol.Bioinf.,10(3):708-720,2013.
[10]X.Liu,and S.Yuan,Robust fault detection filter design for a class of switched systems with time-varying delay,Chinese Control Conference,30:22-24,2011.
[11]K.Shi,H.Zhu,S.Zhong,Y.Zeng,and Y.Zhang.New stability analysis for neutral type neural networks with discrete and distributed delays using a multiple integral approach,Journal of the Franklin Institute,352:155-176,2015.
[12]Y.Liu,S.M.Lee,O.M.Kwon,and Ju H.Park,New approach to stability criteria for generalized neural networks with interval time-varying delays,Neurocomputing,149:1544-1551,2015.
[13]O.M.Kwon,M.J.Park,Ju H.Park,S.M.Lee,and E.J.Cha,New and improved results on stability of static neural networks with interval time-varying delays,Appl.Math.Comput.,239:346-357,2014.
[14]K.Mathiyalagan,R.Sakthivel,and S.Marshal Anthoni,Exponential stability result for discrete-time stochastic fuzzy uncertain neural networks,Phys.Lett.A,376:901-912,2012.
[15]R.Yang,Z.Zhang,and P.Shi,Exponential stability on stochastic neural networks with discrete interval and distributed delays,IEEE Trans.Neural Netw.,21(1):169-175,2010.
[16]M.Liu,X.Cao,and P.Shi,Fault estimation and tolerant control for fuzzy stochastic systems,IEEE Trans.Fuzzy Syst.,21(2):221-229,2013.
[17]Y.Liu,and S.M.Lee,Stability and stabilization of TakagiSugeno fuzzy systems via sampled-data and state quantized controller,IEEE Trans.Fuzzy Syst.,24(3):635-644,2016.
[18]H.Li,H.Liu,H.Gao,and P.Shi,Reliable fuzzy control for active suspension systems with actuator delay and fault,IEEETrans.Fuzzy Syst.,20(2):342-357,2012.
[19]H.Li,J.Yu,C.Hilton,and H.Liu,Adaptive sliding mode control for nonlinear active suspension vehicle systems using T-S fuzzy approach,IEEE Trans.Ind.Electron.,60(12):3328-3338,2013.
[20]M.Liu,X.Cao,and P.Shi,Fuzzy-model-based fault tolerant design for nonlinear stochastic systems against simultaneous sensor and actuator faults,IEEE Trans.Fuzzy Syst.,21(5):789-799,2013.
[21]H.Li,X.Jing,H.-K.Lam,and P.Shi,Fuzzy sampled-data control for uncertain vehicle suspension systems,IEEE Trans.Cybern.,44(7):1111-1126,2014.
[22]T.Takagi,and M.Sugeno,Fuzzy identification of systems and its applications to modeling and control,IEEE Trans.Syst.Man Cybern.,15(1):116-132,1985.
[23]J.Cheng,J.H.Park,Y.Liu,Z.Liu,and L.Tang,Finite-time H fuzzy control of nonlinear Markovian jump delayed systems with partly uncertain transition descriptions,Fuzzy Sets and Systems.,314:99-115,2017.
[24]J.Cheng,J.H.Park,L.Zhang,and Y.Zhu,An Asynchronous Operation Approach to Event-triggered Control for Fuzzy Markovian Jump Systems with General Switching Policies,IEEE Transactions on Fuzzy Systems.,DOI:10.1109/TFUZZ.2016.2633325.
[25]J.M.Mendel,R.I.John,and F.Liu,Interval type-2 fuzzy logic systems made simple,IEEE Trans.Fuzzy Syst.,14(6):808-821,2006.
[26]H.K.Lam,and L.D.Seneviratne,Stability analysis of interval type-2 fuzzy-model-based control systems,IEEE Trans.Syst.Man Cybern.Part B:Cybern.,38(3):617-628,2008.
[27]H.K.Lam,H.Li,C.Deters,H.Wuerdemann,E.Secco,and K.Althoefer,Control design for interval type-2 fuzzy systems under imperfect premise matching,IEEE Trans.Ind.Electron.,61(2):956-968,2014.
[28]X.Xing,Y.Pan,Q.Lu,and H.Cui,New mean square exponential stability condition of stochastic fuzzy neural networks,Neurocomputing,156:129-133,2015.
[29]Y.Wang,L.Xie,and C.E.D.Souza,Robust control of a class of uncertain nonlinear system,Systems Control Lett.,19:139-149,1992.
[30]W.Chen,and X.Lu,Mean square exponential stability of uncertain stochastic delayed neural networks,Phys Lett A,372:1061-1069,2008.
[31]K.Gu,V.L.Kharitonov,and J.Chen,Stability of Time Delay Systems,Birk¨ahuser,Boston,2003.
[32]S.Boyd,L.E.Ghauoi,E.Feron,and V.Balakrishnan,Linear Matrix Inequalities in System and Control Theory,SIAM,Philadelphia,PA,1994.
[33]Y.Liu,Z.Wang,and X.Liu,Global exponential stability of generalized recurrent neural networks with discrete and distributed delays,Neural Networks,19(5):667-675,2006.
[34]J.M.Mendel,Type-2 fuzzy sets and systems:an overview,IEEE Comput.Intell.Mag.,2(1):20-29,2007.
[35]H.Li,C.Wu,L.Wu,H.-K.Lam,and Y.Gao,Filtering of interval type-2 fuzzy systems with intermittent measurements,IEEE Trans.Cybern.,46(3):668-678,2016.
[36]H.Li,Y.Pan,and Q.Zhou,Filter design for interval type-2 fuzzy systems with D stability constraints under a unified frame,IEEE Trans.Fuzzy Syst.,23(3):719-725,2015.
[37]Y.Pan,H.Li,and Q.Zhou,Fault detection for interval type-2 fuzzy systems with sensor nonlinearities,Neurocomputing,145:488-494,2014.
[2]K.Shi,X.Liu,Y.Tang,H.Zhu,and S.Zhong,Some novel approaches on state estimation of delayed neural networks,Information Sciences,372:313-331,2016.
[3]C.Peng,and T.Yang,Event-triggered communication and H∞control co-design for networked control systems,Automatica,49:1326-1332,2013.
[4]X.M.Zhang,and Q.-L.Han,Event-triggered dynamic output feedback control for networked control systems,IET Control Theory and Appl.,8(4):226-234,2014.
[5]K.Shi,Y.Tang,X.Liu,and S.Zhong,Non-fragile sampleddata robust synchronization of uncertain delayed chaotic Lurie systems with randomly occurring controller gain fluctuation,ISA Transactions,66:185-199,2017.
[6]T.Zhang,B.Fang,Y.Tang,G.He,J.Wen,Topology preserving non-negative matrix factorization for face recognition,IEEE Trans.Image Processing.53:1025-1032,2008.
[7]Y.Tang,Z.Wang,H.Gao,H.Qiao,and J.Kurths,On controllability of neuronal networks with constraints on the average of control gains,IEEE Trans.Cybern.44(12):2670-2681,2014.
[8]Y.Tang,F.Qian,H.Gao,and J.Kurths,Synchronization in complex networks and its application-a survey of recent advances and challenges,Annu.Rev.Control,38(2):184-198,2014.
[9]Y.Tang,H.Gao,and J.Kurths,Multiobjective identification of controlling areas in neuronal networks,IEEE/ACM Trans.Comput.Biol.Bioinf.,10(3):708-720,2013.
[10]X.Liu,and S.Yuan,Robust fault detection filter design for a class of switched systems with time-varying delay,Chinese Control Conference,30:22-24,2011.
[11]K.Shi,H.Zhu,S.Zhong,Y.Zeng,and Y.Zhang.New stability analysis for neutral type neural networks with discrete and distributed delays using a multiple integral approach,Journal of the Franklin Institute,352:155-176,2015.
[12]Y.Liu,S.M.Lee,O.M.Kwon,and Ju H.Park,New approach to stability criteria for generalized neural networks with interval time-varying delays,Neurocomputing,149:1544-1551,2015.
[13]O.M.Kwon,M.J.Park,Ju H.Park,S.M.Lee,and E.J.Cha,New and improved results on stability of static neural networks with interval time-varying delays,Appl.Math.Comput.,239:346-357,2014.
[14]K.Mathiyalagan,R.Sakthivel,and S.Marshal Anthoni,Exponential stability result for discrete-time stochastic fuzzy uncertain neural networks,Phys.Lett.A,376:901-912,2012.
[15]R.Yang,Z.Zhang,and P.Shi,Exponential stability on stochastic neural networks with discrete interval and distributed delays,IEEE Trans.Neural Netw.,21(1):169-175,2010.
[16]M.Liu,X.Cao,and P.Shi,Fault estimation and tolerant control for fuzzy stochastic systems,IEEE Trans.Fuzzy Syst.,21(2):221-229,2013.
[17]Y.Liu,and S.M.Lee,Stability and stabilization of TakagiSugeno fuzzy systems via sampled-data and state quantized controller,IEEE Trans.Fuzzy Syst.,24(3):635-644,2016.
[18]H.Li,H.Liu,H.Gao,and P.Shi,Reliable fuzzy control for active suspension systems with actuator delay and fault,IEEETrans.Fuzzy Syst.,20(2):342-357,2012.
[19]H.Li,J.Yu,C.Hilton,and H.Liu,Adaptive sliding mode control for nonlinear active suspension vehicle systems using T-S fuzzy approach,IEEE Trans.Ind.Electron.,60(12):3328-3338,2013.
[20]M.Liu,X.Cao,and P.Shi,Fuzzy-model-based fault tolerant design for nonlinear stochastic systems against simultaneous sensor and actuator faults,IEEE Trans.Fuzzy Syst.,21(5):789-799,2013.
[21]H.Li,X.Jing,H.-K.Lam,and P.Shi,Fuzzy sampled-data control for uncertain vehicle suspension systems,IEEE Trans.Cybern.,44(7):1111-1126,2014.
[22]T.Takagi,and M.Sugeno,Fuzzy identification of systems and its applications to modeling and control,IEEE Trans.Syst.Man Cybern.,15(1):116-132,1985.
[23]J.Cheng,J.H.Park,Y.Liu,Z.Liu,and L.Tang,Finite-time H fuzzy control of nonlinear Markovian jump delayed systems with partly uncertain transition descriptions,Fuzzy Sets and Systems.,314:99-115,2017.
[24]J.Cheng,J.H.Park,L.Zhang,and Y.Zhu,An Asynchronous Operation Approach to Event-triggered Control for Fuzzy Markovian Jump Systems with General Switching Policies,IEEE Transactions on Fuzzy Systems.,DOI:10.1109/TFUZZ.2016.2633325.
[25]J.M.Mendel,R.I.John,and F.Liu,Interval type-2 fuzzy logic systems made simple,IEEE Trans.Fuzzy Syst.,14(6):808-821,2006.
[26]H.K.Lam,and L.D.Seneviratne,Stability analysis of interval type-2 fuzzy-model-based control systems,IEEE Trans.Syst.Man Cybern.Part B:Cybern.,38(3):617-628,2008.
[27]H.K.Lam,H.Li,C.Deters,H.Wuerdemann,E.Secco,and K.Althoefer,Control design for interval type-2 fuzzy systems under imperfect premise matching,IEEE Trans.Ind.Electron.,61(2):956-968,2014.
[28]X.Xing,Y.Pan,Q.Lu,and H.Cui,New mean square exponential stability condition of stochastic fuzzy neural networks,Neurocomputing,156:129-133,2015.
[29]Y.Wang,L.Xie,and C.E.D.Souza,Robust control of a class of uncertain nonlinear system,Systems Control Lett.,19:139-149,1992.
[30]W.Chen,and X.Lu,Mean square exponential stability of uncertain stochastic delayed neural networks,Phys Lett A,372:1061-1069,2008.
[31]K.Gu,V.L.Kharitonov,and J.Chen,Stability of Time Delay Systems,Birk¨ahuser,Boston,2003.
[32]S.Boyd,L.E.Ghauoi,E.Feron,and V.Balakrishnan,Linear Matrix Inequalities in System and Control Theory,SIAM,Philadelphia,PA,1994.
[33]Y.Liu,Z.Wang,and X.Liu,Global exponential stability of generalized recurrent neural networks with discrete and distributed delays,Neural Networks,19(5):667-675,2006.
[34]J.M.Mendel,Type-2 fuzzy sets and systems:an overview,IEEE Comput.Intell.Mag.,2(1):20-29,2007.
[35]H.Li,C.Wu,L.Wu,H.-K.Lam,and Y.Gao,Filtering of interval type-2 fuzzy systems with intermittent measurements,IEEE Trans.Cybern.,46(3):668-678,2016.
[36]H.Li,Y.Pan,and Q.Zhou,Filter design for interval type-2 fuzzy systems with D stability constraints under a unified frame,IEEE Trans.Fuzzy Syst.,23(3):719-725,2015.
[37]Y.Pan,H.Li,and Q.Zhou,Fault detection for interval type-2 fuzzy systems with sensor nonlinearities,Neurocomputing,145:488-494,2014.