Exponential Stabilization of Nonlinear Parabolic PDE Systems via Sampled-Data Fuzzy Control Approach
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- 英文论文题名：Exponential Stabilization of Nonlinear Parabolic PDE Systems via Sampled-Data Fuzzy Control Approach
- 论文作者：Zi-Peng Wang ; Huai-Ning Wu ; Han-Xiong Li
- 英文论文作者：Zi-Peng Wang ; Huai-Ning Wu ; Han-Xiong Li ; School of Electrical Engineering ; University of Jinan ; Science and Technology on Aircraft Control Laboratory ; School of Automation Science and Electrical Engineering ; Beihang University ; Department of Systems Engineering and Engineering Management ; City University of Hong Kong
- 年：2017
- 作者机构：School of Electrical Engineering,University of Jinan;Science and Technology on Aircraft Control Laboratory,School of Automation Science and Electrical Engineering,Beihang University;Department of Systems Engineering and Engineering Management,City University of Hong Kong;
- 英文论文关键词：Exponential Stability ; Sampled-Data Control ; Fuzzy control ; Parabolic PDE Systems ; Linear Matrix Inequality(LMI)
- 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：6
- 文件大小：304k
- 原文格式：D
- 会议级别：全国
摘要
This paper investigates the exponential stabilization problem of nonlinear parabolic partial differential equation(PDE)systems via sampled-data fuzzy control approach. Initially, the nonlinear PDE system is accurately represented by the TakagiSugeno(T-S) fuzzy PDE model. Then, based on the fuzzy PDE model, a novel time-dependent Lyapunov functional is used to design a sampled-data fuzzy controller such that the closed-loop fuzzy PDE system is exponentially stable with a given decay rate. The stabilization condition is presented in terms of a set of linear matrix inequalities(LMIs). Finally, simulation results on the temperature profile of a catalytic rod show that the proposed design method is effective.
This paper investigates the exponential stabilization problem of nonlinear parabolic partial differential equation(PDE)systems via sampled-data fuzzy control approach. Initially, the nonlinear PDE system is accurately represented by the TakagiSugeno(T-S) fuzzy PDE model. Then, based on the fuzzy PDE model, a novel time-dependent Lyapunov functional is used to design a sampled-data fuzzy controller such that the closed-loop fuzzy PDE system is exponentially stable with a given decay rate. The stabilization condition is presented in terms of a set of linear matrix inequalities(LMIs). Finally, simulation results on the temperature profile of a catalytic rod show that the proposed design method is effective.
This paper investigates the exponential stabilization problem of nonlinear parabolic partial differential equation(PDE)systems via sampled-data fuzzy control approach. Initially, the nonlinear PDE system is accurately represented by the TakagiSugeno(T-S) fuzzy PDE model. Then, based on the fuzzy PDE model, a novel time-dependent Lyapunov functional is used to design a sampled-data fuzzy controller such that the closed-loop fuzzy PDE system is exponentially stable with a given decay rate. The stabilization condition is presented in terms of a set of linear matrix inequalities(LMIs). Finally, simulation results on the temperature profile of a catalytic rod show that the proposed design method is effective.
引文
[1]W.-H.Ray,Advanced Process Control.New York:Mc GrawHill,1981.
[2]P.-D.Christofides,Nonlinear and Robust Control of PDE Systems:Methods and Applications to Transport-Reaction Processes.Boston,MA:Birkh¨aser,2001.
[3]H.-X.Li,H.Deng,and J.Zhong,“Model-based integration of control and supervision for one kind of curing process,”IEEE Transactions on Electronics Packaging Manufacturing,vol.27,no.3,pp.177–186,2004.
[4]G.Hagen,I.Mezic,and B.Bamieh,“Distributed control design for parabolic evolution equations:application to compressor stall control,”IEEE Transactions on Automatic Control,vol.49,no.8,pp.1247–1258,2004.2004.
[5]A.Smyshlyaev and M.Krstic,Adaptive Control of Parabolic PDEs.Princeton,NJ:Princeton Univ.Press,2010.
[6]M.A.Demetriou,“Guidance of mobile actuator-plus-sensor networks for improved control and estimation of distributed parameter systems,”IEEE Transactions on Automatic Control,vol.55,no.7,pp.1570–1584,2010.
[7]P.Naghshtabrizi,J.Hespanha,and A.Teel,“Exponential stability of impulsive systems with application to uncertain sampled-data systems,”System&Control Letters,vol.57,no.5,pp.378–385,2008.
[8]H.Fujioka,“A discrete-time approach to stability analysis of systems with aperiodic sample-and-hold devices,”IEEE Transactions on Automatic Control,vol.54,no.9,pp.2440–2445,2009.
[9]E.Fridman,“A refined input delay approach to sampled-data control,”Automatica,vol.46,no.2,pp.421–427,2010.
[10]W.-H.Chen,Z.-P.Wang,and X.Lu,“On sampled-data control for master-slave synchronization of chaotic Lur’e systems,”IEEE Transactions on Circuits and Systems II,vol.59,no.8,pp.515–519,2012.
[11]Y.Sun,S.Ghantasala,and N.H.El-Farra,“Networked control of spatially distributed processes with sensor-controller communication constraints,”in Proceedings of American Control Conference,2009,pp.2490–2494.
[12]S.Ghantasala and N.H.El-Farra,“Active fault-tolerant control of sampled-data nonlinear distributed parameter systems,”International Journal of Robust and Nonlinear Control,vol.22,no.1,pp.24–42,2012.
[13]E.Fridman and A.Blighovsky,“Robust sampled-data control of a class of semilinear parabolic systems,”Automatica,vol.48,no.5,pp.826–836,2012.
[14]E.Fridman and N.B.Am,“Sampled-data distributed H∞control of transport reaction systems,”SIAM Journal on Control and Optimization,vol.51,no.2,1500–1527,2013.
[15]K.Tanaka and H.O.Wang,Fuzzy Control Systems Design and Analysis:A Linear Matrix Inequality Approach.New York:Wiley,2001.
[16]G.Feng,Analysis and Synthesis of Fuzzy Control Systems:A Model Based Approach.Boca Raton:CRC Press,2010.
[17]H.-N.Wu and H.-X.Li,“Finite-dimensional constrained fuzzy control of a class of nonlinear distributed process systems,”IEEE Transactions on Systems,Man,Cybernetics-Part B:Cybernetics,vol.37,no.5,pp.1422–1430,2007.
[18]Y.-T.Chang,S.-J.Ho,and B.-S.Chen,“Robust stabilization design of nonlinear stochastic partial differential systems:fuzzy approach,”Fuzzy Sets and Systems,vol.248,pp.61–85,2014.
[19]H.-N.Wu,J.-W.Wang,and H.-X.Li,“Exponential stabilization for a class of nonlinear parabolic PDE systems via fuzzy control approach,”IEEE Transactions on Fuzzy Systems,vol.20,no.2,pp.318–329,2012.
[20]H.-N.Wu,J.-W.Wang,and H.-X.Li,“Fuzzy boundary control design for a class of nonlinear parabolic distributed parameter systems,”IEEE Transactions on Fuzzy Systems,vol.22,no.3,pp.642–652,2014.
[21]H.Gao and T.Chen,“Stabilization of nonlinear systems under variable sampling:a fuzzy control approach,”IEEE Transactions on Fuzzy Systems,vol.15,no.5,pp.972–983,2007.
[22]H.K.Lam and L.D.Seneviratne,“Chaotic synchronization using sampled-data fuzzy controller based on fuzzy-modelbased approach,”IEEE Transactions on Circuits and Systems I,vol.55,no.3,pp.883–892,2008.
[23]X.-L.Zhu,B.Chen,D.Yue,and Y.Wang,“An improved input delay approach to stabilization of fuzzy systems under variable sampling,”IEEE Transactions on Fuzzy Systems,vol.20,no.2,pp.330–341,2012.
[24]Z.-G.Wu,P.Shi,H.Su,and J.Chu,“Sampled-data fuzzy control of chaotic systems based on T-S fuzzy model,”IEEE Transactions on Fuzzy Systems,vol.22,no.1,pp.153–163,2014.
[25]Z.-P.Wang and H.-N.Wu,“On fuzzy sampled-data control of chaotic systems via a time-dependent Lyapunov functional approach,”IEEE transactions on cybernetics,vol.45,no.4,pp.819–829,2015.
[26]Z.-P.Wang and H.-N.Wu,“Finite dimensional guaranteed cost sampled-data fuzzy control for a class of nonlinear distributed parameter systems,”Information Sciences,vol.327,no.10,pp.21–39,2016.
[2]P.-D.Christofides,Nonlinear and Robust Control of PDE Systems:Methods and Applications to Transport-Reaction Processes.Boston,MA:Birkh¨aser,2001.
[3]H.-X.Li,H.Deng,and J.Zhong,“Model-based integration of control and supervision for one kind of curing process,”IEEE Transactions on Electronics Packaging Manufacturing,vol.27,no.3,pp.177–186,2004.
[4]G.Hagen,I.Mezic,and B.Bamieh,“Distributed control design for parabolic evolution equations:application to compressor stall control,”IEEE Transactions on Automatic Control,vol.49,no.8,pp.1247–1258,2004.2004.
[5]A.Smyshlyaev and M.Krstic,Adaptive Control of Parabolic PDEs.Princeton,NJ:Princeton Univ.Press,2010.
[6]M.A.Demetriou,“Guidance of mobile actuator-plus-sensor networks for improved control and estimation of distributed parameter systems,”IEEE Transactions on Automatic Control,vol.55,no.7,pp.1570–1584,2010.
[7]P.Naghshtabrizi,J.Hespanha,and A.Teel,“Exponential stability of impulsive systems with application to uncertain sampled-data systems,”System&Control Letters,vol.57,no.5,pp.378–385,2008.
[8]H.Fujioka,“A discrete-time approach to stability analysis of systems with aperiodic sample-and-hold devices,”IEEE Transactions on Automatic Control,vol.54,no.9,pp.2440–2445,2009.
[9]E.Fridman,“A refined input delay approach to sampled-data control,”Automatica,vol.46,no.2,pp.421–427,2010.
[10]W.-H.Chen,Z.-P.Wang,and X.Lu,“On sampled-data control for master-slave synchronization of chaotic Lur’e systems,”IEEE Transactions on Circuits and Systems II,vol.59,no.8,pp.515–519,2012.
[11]Y.Sun,S.Ghantasala,and N.H.El-Farra,“Networked control of spatially distributed processes with sensor-controller communication constraints,”in Proceedings of American Control Conference,2009,pp.2490–2494.
[12]S.Ghantasala and N.H.El-Farra,“Active fault-tolerant control of sampled-data nonlinear distributed parameter systems,”International Journal of Robust and Nonlinear Control,vol.22,no.1,pp.24–42,2012.
[13]E.Fridman and A.Blighovsky,“Robust sampled-data control of a class of semilinear parabolic systems,”Automatica,vol.48,no.5,pp.826–836,2012.
[14]E.Fridman and N.B.Am,“Sampled-data distributed H∞control of transport reaction systems,”SIAM Journal on Control and Optimization,vol.51,no.2,1500–1527,2013.
[15]K.Tanaka and H.O.Wang,Fuzzy Control Systems Design and Analysis:A Linear Matrix Inequality Approach.New York:Wiley,2001.
[16]G.Feng,Analysis and Synthesis of Fuzzy Control Systems:A Model Based Approach.Boca Raton:CRC Press,2010.
[17]H.-N.Wu and H.-X.Li,“Finite-dimensional constrained fuzzy control of a class of nonlinear distributed process systems,”IEEE Transactions on Systems,Man,Cybernetics-Part B:Cybernetics,vol.37,no.5,pp.1422–1430,2007.
[18]Y.-T.Chang,S.-J.Ho,and B.-S.Chen,“Robust stabilization design of nonlinear stochastic partial differential systems:fuzzy approach,”Fuzzy Sets and Systems,vol.248,pp.61–85,2014.
[19]H.-N.Wu,J.-W.Wang,and H.-X.Li,“Exponential stabilization for a class of nonlinear parabolic PDE systems via fuzzy control approach,”IEEE Transactions on Fuzzy Systems,vol.20,no.2,pp.318–329,2012.
[20]H.-N.Wu,J.-W.Wang,and H.-X.Li,“Fuzzy boundary control design for a class of nonlinear parabolic distributed parameter systems,”IEEE Transactions on Fuzzy Systems,vol.22,no.3,pp.642–652,2014.
[21]H.Gao and T.Chen,“Stabilization of nonlinear systems under variable sampling:a fuzzy control approach,”IEEE Transactions on Fuzzy Systems,vol.15,no.5,pp.972–983,2007.
[22]H.K.Lam and L.D.Seneviratne,“Chaotic synchronization using sampled-data fuzzy controller based on fuzzy-modelbased approach,”IEEE Transactions on Circuits and Systems I,vol.55,no.3,pp.883–892,2008.
[23]X.-L.Zhu,B.Chen,D.Yue,and Y.Wang,“An improved input delay approach to stabilization of fuzzy systems under variable sampling,”IEEE Transactions on Fuzzy Systems,vol.20,no.2,pp.330–341,2012.
[24]Z.-G.Wu,P.Shi,H.Su,and J.Chu,“Sampled-data fuzzy control of chaotic systems based on T-S fuzzy model,”IEEE Transactions on Fuzzy Systems,vol.22,no.1,pp.153–163,2014.
[25]Z.-P.Wang and H.-N.Wu,“On fuzzy sampled-data control of chaotic systems via a time-dependent Lyapunov functional approach,”IEEE transactions on cybernetics,vol.45,no.4,pp.819–829,2015.
[26]Z.-P.Wang and H.-N.Wu,“Finite dimensional guaranteed cost sampled-data fuzzy control for a class of nonlinear distributed parameter systems,”Information Sciences,vol.327,no.10,pp.21–39,2016.