山东师范大学学报(自然科学版)

参考文献

[ 1 ] Wang P K C.Control of distributed parameter systems[J].Advances in Control Systems,1964,1:75-172.

[ 2 ] Kaka? S,Yener Y,Naveira-Cotta C P.Heat conduction (5th ed.)[M].Boca Raton:CRC Press,2018.

[ 3 ] Kundu P K,Cohen I M,Dowling D R,et al.Fluid mechanics (7th ed.)[M].Amsterdam:Elsevier,2021.

[ 4 ] Jin G Y,Ye T G,Su Z.Structural vibration:A uniform accurate solution for laminated beams,plates and shells with general boundary conditions[M].Beijing:Science Press,2015.

[ 5 ] Mukhanov O A.Energy-efficient single flux quantum technology[J].IEEE Transactions on Applied Superconductivity,2011,21(3):760-769.

[ 6 ] Meseguer J,Pérez-Grande I,Sanz-Andrés A.Spacecraft thermal control[M].Cambridge:Elsevier,2012.

[ 7 ] Schubel P J,Crossley R J.Wind turbine blade design[J].Energies,2012,5(9):3425-3449.

[ 8 ] Evans L C.Partial differential equations[M].Providence:American Mathematical Society,2022.

[ 9 ] Kato T.Abstract differential equations and nonlinear mixed problems[M].Pisa:Scuola Normale Superiore,1985.

[ 10 ] Whalley R.The response of distributed-lumped parameter systems[J].Proceedings of the Institution of Mechanical Engineers,Part C:Journal of Mechanical Engineering Science,1988,202(6):421-429.

[ 11 ] Terrell W J.Stability and stabilization:An introduction[M].Princeton:Princeton University Press,2009.

[ 12 ] Huang J,Chen Z.A general framework for tackling the output regulation problem[J].IEEE Transactions on Automatic Control,2004,49(12):2203-2218.

[ 13 ] Bamieh B,Paganini F,Dahleh M A.Distributed control of spatially invariant systems[J].IEEE Transactions on Automatic Control,2002,47(7):1091-1107.

[ 14 ] Krstic M,Smyshlyaev A.Boundary control of PDEs:A course on backstepping designs[M].Philadelphia:Society for Industrial and Applied Mathematics,2008.

[ 15 ] Krstic M.Delay compensation for nonlinear,adaptive,and PDE systems[M].Boston:Birkh?user,2009.

[ 16 ] Kwapień J,Dro■d■ S.Physical approach to complex systems[J].Physics Reports,2012,515(3-4):115-226.

[ 17 ] Park P G,Ko J W.Stability and robust stability for systems with a time-varying delay[J].Automatica,2007,43(10):1855-1858.

[ 18 ] Wen C Y,Zhou J,Liu Z T,et al.Robust adaptive control of uncertain nonlinear systems in the presence of input saturation and external disturbance[J].IEEE Transactions on Automatic Control,2011,56(7):1672-1678.

[ 19 ] Johnson M A,Moradi M H.PID control[M].London:Springer,2005.

[ 20 ] Knospe C.PID control[J].IEEE Control Systems Magazine,2006,26(1):30-31.

[ 21 ] ?str?m K J,H?gglund T.The control handbook[M].Piscataway:IEEE Press,1996.

[ 22 ] ?str?m K J.Adaptive control[M].Heidelberg:Springer,1995.

[ 23 ] Gang T.Adaptive control design and analysis[M].New York:John Wiley & Sons,2003.

[ 24 ] Landau I D,Lozano R,M′Saad M,et al.Adaptive control:Algorithms,analysis and applications[M].Heidelberg:Springer,2011.

[ 25 ] Shtessel Y,Edwards C,Fridman L,et al.Sliding mode control and observation[M].New York:Springer,2014.

[ 26 ] Edwards C,Spurgeon S K.Sliding mode control:Theory and applications[M].Boca Raton:CRC Press,1998.

[ 27 ] Utkin V I.Sliding mode control:Mathematical tools,design and applications[M].Berlin:Springer-Verlag,2008.

[ 28 ] Perruquetti W,Barbot J P.Sliding mode control in engineering[M].New York:Marcel Dekker,2002.

[ 29 ] Levant A.Sliding order and sliding accuracy in sliding mode control[J].International Journal of Control,1993,58(6):1247-1263.

[ 30 ] Passino K M,Yurkovich S,Reinfrank M.Fuzzy control[M].Reading:Addison-Wesley,1998.

[ 31 ] Driankov D,Hellendoorn H,Reinfrank M.An introduction to fuzzy control[M].Berlin:Springer,2013.

[ 32 ] Zimmermann H J.Fuzzy set theory and its applications (4th ed.)[M].Dordrecht:Kluwer Academic Publishers,2001.

[ 33 ] Kandel A,Langholz G.Fuzzy control systems[M].Boca Raton:CRC Press,1993.

[ 34 ] Feng H,Guo B Z.Active disturbance rejection control:old and new results[J].Annual Reviews in Control,2017,44:238-248.

[ 35 ] Han J Q.From PID to active disturbance rejection control[J].IEEE Transactions on Industrial Electronics,2009,56(3):900-906.

[ 36 ] Huang Y,Xue W.Active disturbance rejection control:Methodology and theoretical analysis[J].ISA Transactions,2014,53(4):963-976.

[ 37 ] Guo B Z,Zhao Z L.Active disturbance rejection control for nonlinear systems:an introduction[M].Singapore:John Wiley & Sons,2017.

[ 38 ] Huang Y,Xue W C,Gao Z Q,et al.Active disturbance rejection control:methodology,practice and analysis[C].Proceedings of the 33rd Chinese Control Conference.IEEE,2014:1-5.

[ 39 ] Sun D.Comments on active disturbance rejection control[J].IEEE Transactions on Industrial Electronics,2007,54(6):3428-3429.

[ 40 ] Guo B Z,Zhao Z L.On the convergence of an extended state observer for nonlinear systems with uncertainty[J].Systems & Control Letters,2011,60(6):420-430.

[ 41 ] Xiong S F,Wang W H,Liu X D,et al.A novel extended state observer[J].ISA Transactions,2015,58:309-317.

[ 42 ] Guo B Z,Jin F F.Sliding mode and active disturbance rejection control to stabilization of one-dimensional anti-stable wave equations subject to disturbance in boundary input[J].IEEE Transactions on Automatic Control,2012,58(5):1269-1274.

[ 43 ] Feng H,Guo B Z.A new active disturbance rejection control to output feedback stabilization for a one-dimensional anti-stable wave equation with disturbance[J].IEEE Transactions on Automatic Control,2016,62(8):3774-3787.

[ 44 ] 郑应文.无穷维系统理论的发展[J].福州大学学报(自然科学版),1993,21(5):106-110.

[ 45 ] 郭宝珠，柴树根.无穷维线性系统控制理论[M].北京：科学出版社，2012.

[ 46 ] Lax P D.Hyperbolic partial differential equations[M].New York:American Mathematical Society,2006.

[ 47 ] Ladyzenskaya O A.On the linear andquasilinear parabolic equations[J].Differential Equations and Their Applications,1967:273-279.

[ 48 ] Wei J,Feng H,Guo B Z.Asymptotic stabilization for a wave equation with periodic disturbance[J].IMA Journal of Mathematical Control and Information,2020,37(3):894-917.

[ 49 ] Feng H,Guo B Z.Distributed disturbance estimator and application to stabilization for multi-dimensional wave equation with corrupted boundary observation[J].Automatica,2016,66:25-33.

[ 50 ] Li Y,Pan K W,Liao Y L,et al.Improved active disturbance rejection heading control for unmanned wave glider[J].Applied Ocean Research,2021,106:102438.

[ 51 ] Zhou H C,Guo B Z,Wu Z H.Output feedback stabilisation for a cascaded wave PDE-ODE system subject to boundary control matched disturbance[J].International Journal of Control,2016,89(12):2396-2405.

[ 52 ] Guo W,Guo B Z.Parameter estimation and stabilisation for a one-dimensional wave equation with boundary output constant disturbance and non-collocated control[J].International Journal of Control,2011,84(2):381-395.

[ 53 ] Wu Z H,Zhou H C,Guo B Z,et al.Review and new theoretical perspectives on active disturbance rejection control for uncertain finite-dimensional and infinite-dimensional systems[J].Nonlinear Dynamics,2020,101(2):935-959.

[ 54 ] 赵志良，郭宝珠.自抗扰控制对具边界扰动和区间内反阻尼的波动方程的镇定[J].控制理论与应用，2013,30(12):1553-1563.

[ 55 ] 张亚超，刘军军.带有非线性边界和扰动输入的波动方程的输出反馈控制[J].控制理论与应用，2024,41(8):1459-1468.

[ 56 ] 王帅，王建立，李洪文，等.光电跟踪系统力矩波动的自抗扰控制[J].光电工程，2012,39(4):7-13.

[ 57 ] 杨坤一.边界含有界扰动的一维波动方程的滑模控制及自抗扰控制[J].系统科学与数学，2025,45(3):696-707.

[ 58 ] 梅占东，竺迪.带边界非线性干扰的反稳定波方程的镇定[J].控制理论与应用，2023,40(8):1331-1338.

[ 59 ] 张亚超，刘军军.带有非线性边界和扰动输入的波动方程的输出反馈控制[J].控制理论与应用，2024,41(8):1459-1468.

[ 60 ] 孟巍.一类边界带有不确定干扰的一维波动方程的输出反馈镇定[J].山西大学学报(自然科学版),2014,37(2):161-164.

[ 61 ] 冯红银萍.双曲系统自抗扰控制及非线性波方程解的性质[D].山西大学，2013.

[ 62 ] 郭春丽，胡蓉.反阻尼一维波动方程的稳定性(英文)[J].控制理论与应用，2022,39(11):2161-2167.

[ 63 ] Li R C,Jin F F.Boundary output feedback stabilization for a cascaded wave PDE-ODE system with velocity recirculation and matched disturbance[J].Applied Mathematics and Computation,2023,444:127827.

[ 64 ] Chen J,Wang J M.A kind of observer-based active disturbance rejection control method for the stabilization of a class of Timoshenko beams[J].Evolution Equations and Control Theory,2025,14(5):1055-1068.

[ 65 ] Tavasoli A.Active disturbance rejection boundary control of Timoshenko beam with tip mass[J].ISA Transactions,2018,80:221-231.

[ 66 ] Wang S,Han Z J,Zhao Z X,et al.Saturated boundary feedback stabilization for a nonuniform Timoshenko beam with disturbances and uncertainties[J].IEEE Transactions on Automatic Control,2023,69(5):3230-3237.

[ 67 ] Liu D Y,Zhang L P,Xu G Q.Stabilisation of Timoshenko beam system with a tip payload under the unknown boundary external disturbances[J].International Journal of Control,2015,88(9):1830-1840.

[ 68 ] Fan X R,Xu C Z,Xu X,et al.Stabilization of a Timoshenko beam system with boundary matched disturbances by designing novel disturbance estimator[J].Mathematical Control and Related Fields,2025,15(2):690-711.

[ 69 ] Liu D Y,Chen Y N,Shang Y F,et al.Stabilization of a Timoshenko beam with disturbance observer-based time varying boundary controls[J].Asian Journal of Control,2018,20(5):1869-1880.

[ 70 ] Guo W,Chen Y L,Feng H.Output feedback stabilization for a Kirchhoff-type nonlinear beam with general corrupted boundary observation[J].International Journal of Robust and Nonlinear Control,2017,27(16):3280-3295.

[ 71 ] Guo B Z,Zhou H C.Output feedback stabilization for multi-dimensional Kirchhoff plate with general corrupted boundary observation[J].European Journal of Control,2016,28:38-48.

[ 72 ] Guo B Z,Zhou H C.Active disturbance rejection control for rejecting boundary disturbance from multidimensional Kirchhoff plate via boundary control[J].SIAM Journal on Control and Optimization,2014,52(5):2800-2830.

[ 73 ] Guo B Z,Jin F F.Output feedback stabilization for one-dimensional wave equationsubject to boundary disturbance[J].IEEE Transactions on Automatic Control,2014,60(3):824-830.

[ 74 ] Liu J J,Wang J M.Boundary stabilization of a cascade of ODE-wave systems subject to boundary control matched disturbance[J].International Journal of Robust and Nonlinear Control,2017,27(2):252-280.

[ 75 ] Feng H,Guo B Z.Output feedback stabilization of an unstable wave equation with general corrupted boundary observation[J].Automatica,2014,50(12):3164-3172.

[ 76 ] Lang P H,Feng H.The active disturbance rejection control approach to output feedback stabilization of an anti-stable wave equation with corrupted boundary observation[J].Journal of Mathematical Analysis and Applications,2024,536(2):128194.

[ 77 ] Xie Y R,Xu G Q.Stabilization of a wave equation with a tip mass based on disturbance observer of time-varying gain[J].Journal of Dynamical and Control Systems,2017,23:667-677.

[ 78 ] Guo B Z,Zhou H C.The active disturbance rejection control to stabilization for multi-dimensional wave equation with boundary control matched disturbance[J].IEEE Transactions on Automatic Control,2014,60(1):143-157.

[ 79 ] Zhou H C,Weiss G.Output feedback exponential stabilization for one-dimensional unstable wave equations with boundary control matched disturbance[J].SIAM Journal on Control and Optimization,2018,56(6):4098-4129.

[ 80 ] Zhou H C,Guo W.Output feedback exponential stabilization of one-dimensional wave equation with velocity recirculation[J].IEEE Transactions on Automatic Control,2019,64(11):4599-4606.

[ 81 ] Mei Z D,Zhou H C.Output feedback exponential stabilization for a one-dimensional wave equation with control matched nonlinear disturbance[J].IEEE Transactions on Automatic Control,2020,66(5):2273-2280.

[ 82 ] Xiang Q M,Wu Z H,Zhou H C,et al.Disturbance estimator-based boundary control for a chaotic wave system with disturbance[J].IEEE Transactions on Automatic Control,2024,69(10):6762-6776.

[ 83 ] Feng X D,Zhang Z F.Output feedback stabilization for a wave-ODE cascaded system subject to uncertain disturbance[J].Asian Journal of Control,2024,26(2):974-988.

[ 84 ] Zhou H C,Guo B Z.Unknown input observer design and output feedback stabilization for multi-dimensional wave equation with boundary control matched uncertainty[J].Journal of Differential Equations,2017,263(4):2213-2246.

[ 85 ] Zhang X Y,Feng H,Chai S G.Performance output exponential tracking for a wave equation with a general boundary disturbance[J].Systems & Control Letters,2016,98:79-85.

[ 86 ] Zhou H C,Guo B Z.Performance output tracking for one-dimensional wave equation subject to unmatched general disturbance and non-collocated control[J].European Journal of Control,2018,39:39-52.

[ 87 ] Zhou H C.Output tracking and disturbance rejection for 1-D anti-stable wave equation[J].ESAIM:Control,Optimisation and Calculus of Variations,2019,25:69.

[ 88 ] Wei J,Feng H.Output tracking for one-dimensional wave equation with non-collocated control and output configuration[J].Journal of Systems Science and Complexity,2020,33(5):1469-1484.

[ 89 ] Guo B Z,Jin F F.The active disturbance rejection and sliding mode control approach to the stabilization of the Euler-Bernoulli beam equation with boundary input disturbance[J].Automatica,2013,49(9):2911-2918.

[ 90 ] Guo B Z,Zhou H C,Al-Fhaid A S,et al.Stabilization of Euler-Bernoulli beam equation with boundary moment control and disturbance by active disturbance rejection control and sliding mode control approaches[J].Journal of Dynamical and Control Systems,2014,20:539-558.

[ 91 ] Li Y,Xu G,Han Z.Stabilization of an Euler-Bernoulli beam system with a tip mass subject to non-uniform bounded disturbance[J].IMA Journal of Mathematical Control and Information,2017,34(4):1239-1254.

[ 92 ] Zhou H C,Feng H.Disturbance estimator based output feedback exponential stabilization for Euler-Bernoulli beam equation with boundary control[J].Automatica,2018,91:79-88.

[ 93 ] Zhou H C,Feng H.Stabilization for Euler-Bernoulli beam equation with boundary moment control and disturbance via a new disturbance estimator[J].Journal of Dynamical and Control Systems,2021,27:247-259.

[ 94 ] Mei Z D,Peng J G.Exponential stabilization for an Euler-Bernoulli beam PDE-ODE cascade system[J].Systems & Control Letters,2023,177:105552.

[ 95 ] Mei Z D.Stabilization for a flexible beam with tip mass and control matched disturbance[J].IEEE Transactions on Automatic Control,2023,69(5):3238-3245.

[ 96 ] Mei Z D.Disturbance estimator and servomechanism based performance output tracking for a 1-D Euler-Bernoulli beam equation[J].Automatica,2020,116:108925.

[ 97 ] Ladyzenskaya O A.On the linear and quasilinear parabolic equations[J].Differential Equations and Their Applications,1967:273-279.

[ 98 ] Zhao D,Li D H,Wang Y Q.A novel boundary control solution for unstable heat conduction systems based on active disturbance rejection control[J].Asian Journal of Control,2016,18(2):595-608.

[ 99 ] Zhang Y L,Zhu M,Li D,et al.ADRC dynamic stabilization of an unstable heat equation[J].IEEE Transactions on Automatic Control,2019,65(10):4424-4429.

[100] Wu Z H,Zhou H C,Deng F,et al.Disturbance observer-based boundary control for an antistable stochastic heat equation with unknown disturbance[J].IEEE Transactions on Automatic Control,2022,68(6):3604-3611.

[101] Feng H,Xu C Z,Yao P F.Observers and disturbance rejection control for a heat equation[J].IEEE Transactions on Automatic Control,2020,65(11):4957-4964.

[102] Wei C Z,Li J M.Prescribed-time stabilization of uncertain heat equation via boundary time-varying feedback and disturbance estimator[J].Systems & Control Letters,2023,171:105419.

[103] Zhao R X,Guo B Z,Hu Q Q.Active disturbance rejection control approach to the output tracking of PDEs with generaldisturbances:a new perspective[J].Automatica,2024,164:111608.

[104] Zheng G,Li J.Stabilization for the multi-dimensional heat equation with disturbance on the controller[J].Automatica,2017,82:319-323.

[105] Cai R Y,Zhou H C,Kou C H.Active disturbance rejection control for fractional reaction-diffusion equations with spatially varying diffusivity and time delay[J].Science China-Information Sciences,2022,65(2):129203.

[106] Zhou H C,Guo B Z.Boundary feedback stabilization for an unstable time fractional reaction diffusion equation[J].SIAM Journal on Control and Optimization,2018,56(1):75-101.

[107] Cai R Y,Kou C H.Mittag-Leffler stabilization for coupled fractional reaction-diffusion neural networks subjectto boundary matched disturbance[J].Mathematical Methods in the Applied Sciences,2023,46(3):3143-3156.

[108] Liu J J,Wang J M.Active disturbance rejection control and sliding mode control of one-dimensional unstable heat equation with boundary uncertainties[J].IMA Journal of Mathematical Control and Information,2015,32(1):97-117.

[109] Guo B Z,Liu J J,Al-Fhaid A S,et al.The active disturbance rejection control approach to stabilisation of coupled heat and ODE system subject to boundary control matched disturbance[J].International Journal of Control,2015,88(8):1554-1564.

[110] Kang W,Guo B Z.Stabilisation of unstable cascaded heat partial differential equation system subject to boundary disturbance[J].IET Control Theory & Applications,2016,10(9):1027-1039.

[111] Feng H,Guo B Z.New unknown input observer and output feedback stabilization for uncertain heat equation[J].Automatica,2017,86:1-10.

[112] Wei C Z,Li J M.Prescribed-time stabilization of uncertain heat equation with Dirichlet boundary control[J].IMA Journal of Mathematical Control and Information,2023,40(3):445-473.

[113] Liu J J,Jia Y N.Stabilisation of a cascaded ODE-heat system with boundary input term incorporates both enforceable control and external unknown disturbance[J].International Journal of Control,2021,94(1):21-29.

[114] Cai R Y,Zhou H C.Boundary disturbance rejection for Caputo-Hadamard fractional heat equations via ADRC approach[J].Chaos,Solitons & Fractals,2024,189:115741.

[115] Liu D Z,Zong X J,Zheng Z Y.Output tracking control for the one-dimensional heat equation with unknown disturbance by the dirichlet boundary actuation[C].2019 Chinese Automation Congress (CAC).IEEE,2019:193-198.

[116] Jin F F,Guo B Z.Performance boundary output tracking for one-dimensional heat equation with boundary unmatched disturbance[J].Automatica,2018,96:1-10.

[117] Zhou H C,Guo B Z,Xiang S H.Performance output tracking for multidimensional heat equation subject to unmatched disturbance and noncollocated control[J].IEEE Transactions on Automatic Control,2019,65(5):1940-1955.

[118] Zhou H C,Wu Z H,Guo B Z,et al.Boundary stabilization and disturbance rejection for an unstable time fractional diffusion-wave equation[J].ESAIM:Control,Optimisation and Calculus of Variations,2022,28:7.

[119] Cai R Y,Kou C H.Mittag-Leffler stabilization for coupled fractional reaction-diffusion neural networks subject to boundary matched disturbance[J].Mathematical Methods in the Applied Sciences,2023,46(3):3143-3156.

[120] Wei C Z,Li J M,He C.Prescribed-time stabilisation for uncertain reaction-diffusion equations with Neumann boundary control[J].International Journal of Control,2023,96(9):2374-2383.

[121] Chen J,Zhou H C,Zhuang B,et al.Active disturbance rejection control to stabilization of coupled delayed time fractional-order reaction-advection-diffusion systems with boundary disturbances and spatially varying coefficients[J].Chaos,Solitons & Fractals,2023,170:113316.

[122] Zhang X Y,Feng H,Chai S G.Output feedback stabilization for an anti-stable Schr?dinger equation with internal unknown dynamic and external disturbance[J].Journal of the Franklin Institute,2018,355(13):5632-5648.

[123] Jia Y N,Liu J J.Output feedback stabilization of an ODE-Schr?dinger cascade system subject to boundary control matched unknown disturbance[J].Journal of Dynamical and Control Systems,2020,26:393-405.

[124] Zhou H C.Output-based disturbance rejection control for 1-D anti-stable Schr?dinger equation with boundary input matched unknown disturbance[J].International Journal of Robust and Nonlinear Control,2017,27(18):4686-4705.

[125] Guo B Z,Liu J J.Sliding mode control and active disturbance rejection control to the stabilization of one-dimensional Schr?dinger equation subject to boundary control matched disturbance[J].International Journal of Robust and Nonlinear Control,2014,24(16):2194-2212.

[126] Mei Z D,Lin Y Y.Stabilization for acascaded ODE-Schr?dinger system via a new transformation[C]// The 14th Asian Control Conference (ASCC).IEEE,2024:1015-1020.

[127] Guo Y P,Liu J J.Stabilization of ODE-Schr?dinger cascaded systems subject to boundary control matched disturbance[J].Electronic Journal of Differential Equations,2015,248:1-22.

[128] Zhang X Y,Chai S G.The stability of Schr?dinger equation with boundary control matched disturbance[J].Journal of Systems Science and Complexity,2017,30(6):1258-1269.

[129] 杨坤一.Dirichlet边界条件含有界扰动一维薛定谔方程的滑模控制及自抗扰控制[J].应用数学学报，2025,48(3):462-480.

[130] Kang W,Zhang J,Wang J M.Disturbance rejection approaches of Korteweg-de Vries-Burgers equation under event-triggering mechanism[J].Automatica,2024,169:111844.