Adaptive boundary observer for Euler–Bernoulli beam equations with nonlinear dynamics and parameter uncertainties
This paper focuses on designing boundary adaptive observers for systems that can be modeled as Euler–Bernoulli beams and are represented by fourth-order partial differential equations. Specifically, the objective is to estimate the entire state of the beam solely based on measurements taken at its b...
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| Published in: | Systems & control letters Vol. 201; p. 106096 |
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| Format: | Journal Article |
| Language: | English |
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Elsevier B.V
01.07.2025
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| ISSN: | 0167-6911 |
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| Abstract | This paper focuses on designing boundary adaptive observers for systems that can be modeled as Euler–Bernoulli beams and are represented by fourth-order partial differential equations. Specifically, the objective is to estimate the entire state of the beam solely based on measurements taken at its boundaries. The difficulty of this study lies not only in the uncertain parameters contained in the boundary and domain of the beam but also in taking into account the interior nonlinearity in-domain. Unlike many observers in adaptive control frameworks that do not require accurate estimation of unknown parameters, our approach is dedicated to accurately estimating both the system state and the unknown parameters. The crucial element in the design process of the adaptive observer is the introduction of a kind of finite-dimensional backstepping-like transformation, based on which we can transform the observer error system into the desired system. Then, we can use common parameter estimation methods, allowing the design of the parameter adaptive law to be decoupled from the choice of the state estimator. Using Lyapunov stability analysis, we show that the observer converges exponentially under persistent excitation conditions. Numerical simulations also demonstrate the effectiveness of the observer.
•A novel adaptive boundary observer is developed for a class of Euler–Bernoulli beam equations with unknown parameters and interior nonlinearity.•The adaptive boundary observer for the Euler–Bernoulli beam system is designed based on the finite-dimensional backstepping-like transformation.•The proposed observer consists of three main parts: a state observer; a parameter adaptive update law; and an auxiliary filter. The exponential convergence of the estimation errors is obtained. |
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| AbstractList | This paper focuses on designing boundary adaptive observers for systems that can be modeled as Euler–Bernoulli beams and are represented by fourth-order partial differential equations. Specifically, the objective is to estimate the entire state of the beam solely based on measurements taken at its boundaries. The difficulty of this study lies not only in the uncertain parameters contained in the boundary and domain of the beam but also in taking into account the interior nonlinearity in-domain. Unlike many observers in adaptive control frameworks that do not require accurate estimation of unknown parameters, our approach is dedicated to accurately estimating both the system state and the unknown parameters. The crucial element in the design process of the adaptive observer is the introduction of a kind of finite-dimensional backstepping-like transformation, based on which we can transform the observer error system into the desired system. Then, we can use common parameter estimation methods, allowing the design of the parameter adaptive law to be decoupled from the choice of the state estimator. Using Lyapunov stability analysis, we show that the observer converges exponentially under persistent excitation conditions. Numerical simulations also demonstrate the effectiveness of the observer.
•A novel adaptive boundary observer is developed for a class of Euler–Bernoulli beam equations with unknown parameters and interior nonlinearity.•The adaptive boundary observer for the Euler–Bernoulli beam system is designed based on the finite-dimensional backstepping-like transformation.•The proposed observer consists of three main parts: a state observer; a parameter adaptive update law; and an auxiliary filter. The exponential convergence of the estimation errors is obtained. |
| ArticleNumber | 106096 |
| Author | Xu, Xiaodong Xiao, Yu Wu, Ruixin |
| Author_xml | – sequence: 1 givenname: Ruixin surname: Wu fullname: Wu, Ruixin email: RuixinWu@csu.edu.cn – sequence: 2 givenname: Yu surname: Xiao fullname: Xiao, Yu email: yu_xiao@csu.edu.cn – sequence: 3 givenname: Xiaodong orcidid: 0000-0003-4795-9967 surname: Xu fullname: Xu, Xiaodong email: xx1@ualberta.ca |
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| Cites_doi | 10.1109/TSMC.2022.3213477 10.1016/j.automatica.2020.109295 10.1109/TAC.2013.2239003 10.1016/j.automatica.2009.02.004 10.1109/TAC.2017.2700387 10.1109/TSMCB.2012.2198813 10.1093/imamci/dnt030 10.1007/s11424-018-7182-0 10.1109/TAC.2016.2643442 10.1051/cocv/2017080 10.1016/j.automatica.2007.02.014 10.1137/22M1501805 10.1080/00036811.2022.2037572 10.1016/j.automatica.2018.01.031 10.1016/j.automatica.2007.02.015 10.1016/j.automatica.2016.04.034 10.1016/j.automatica.2016.06.006 10.1016/j.automatica.2019.108507 10.1016/j.sysconle.2008.02.004 10.3182/20140824-6-ZA-1003.02365 10.1049/iet-cta.2011.0593 10.1007/BF03323104 10.1137/S0363012995279717 10.1109/TAC.2015.2500237 10.1002/nme.624 10.1109/TAC.2017.2767378 10.1109/9.989154 10.1016/j.sysconle.2023.105504 10.1109/TMECH.2014.2313876 10.1016/j.jsv.2010.05.005 10.1016/j.sysconle.2023.105552 10.1016/j.automatica.2011.01.064 10.1177/1077546304038103 10.1109/TAC.2012.2228035 10.1109/TAC.2018.2884677 10.1137/18M1172727 10.1002/asjc.677 10.1016/j.automatica.2017.01.015 10.1007/s00498-021-00298-8 10.1016/j.automatica.2014.09.001 10.1109/TAC.2008.927798 10.1109/TAC.2016.2530624 10.1016/j.automatica.2014.10.123 |
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| Keywords | Nonlinear dynamics Euler–Bernoulli beam Adaptive observer Parameter uncertainty |
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| References | Zhang, Liu (b4) 2013; 7 Smyshlyaev, Krstic (b29) 2007; 43 Krstic, Smyshlyaev (b30) 2008; 53 Anfinsen, Diagne, Aamo, Krstic (b44) 2016; 61 Jin, Guo (b16) 2015; 52 Guo, Zhao (b28) 2023; 61 Yang, Li, Li (b8) 2012; 43 Han, Xu (b13) 2014; 31 Zhou, Feng (b19) 2018; 91 Guo, Wang, Yang (b11) 2008; 57 Ahmed-Ali, Giri, Krstic, Burlion, Lamnabhi-Lagarrigue (b39) 2016; 72 Fan, Kou (b22) 2023; 102 Bin, Di Meglio (b43) 2016; 62 Guo, Zhou (b27) 2019; 57 Delavari, Lanusse, Sabatier (b3) 2013; 15 Choi, Hong, Yang (b2) 2004; 10 Karagiannis, Radisavljevic-Gajic (b18) 2018; 64 Guo, Yang (b10) 2009; 45 Benabdelhadi, Giri, Ahmed-Ali, Krstic, El Fadil, Chaoui (b25) 2021; 123 Di Meglio, Bresch-Pietri, Aarsnes (b42) 2014; 47 He, Ge, How, Choo, Hong (b1) 2011; 47 Guo, Meng (b50) 2021; 33 Schröck, Meurer, Kugi (b15) 2011 He, Ge (b23) 2014; 20 Gnedin (b49) 1992; 22 Wang, Wu, Wang, Lou, Görges (b24) 2022 Koh, Ong, Chua, Feng (b6) 2003; 56 Jing, Ma, Wu, He, Sun (b20) 2022; 53 Böhm, Demetriou, Reich, Rosen (b9) 1998; 36 Mei, Peng (b17) 2023; 177 Smyshlyaev, Krstic (b32) 2010 Wu, Shang (b48) 2019; 32 Jin, Guo (b7) 2019; 109 Ahmed-Ali, Giri, Krstic, Burlion, Lamnabhi-Lagarrigue (b41) 2015 Yang, Wang (b12) 2019; 25 Yang, Li, Zhang (b14) 2015; 75 Aamo (b34) 2012; 58 Anfinsen, Aamo (b36) 2017; 63 Smyshlyaev, Krstic (b31) 2007; 43 Krstic (b38) 2009 Bernard, Krstic (b37) 2014; 50 Hasanov, Baysal (b21) 2016; 71 Ahmed-Ali, Giri, Krstic, Lamnabhi-Lagarrigue, Burlion (b40) 2015; 61 Rahn, Rahn (b51) 2001 Hardy, Littlewood, Pólya (b52) 1952 Anfinsen, Diagne, Aamo, Krstic (b45) 2017; 79 Zhang (b47) 2002; 47 Guo, Guo (b33) 2013; 58 Nguyen, Tran (b5) 2010; 329 Ioannou, Sun (b53) 1996 Wu, Wang, Kang (b26) 2023; 175 Anfinsen, Aamo (b35) 2017; 62 Xu, Yuan, Dubljevic, Yin (b46) 2023 Ahmed-Ali (10.1016/j.sysconle.2025.106096_b41) 2015 He (10.1016/j.sysconle.2025.106096_b23) 2014; 20 Schröck (10.1016/j.sysconle.2025.106096_b15) 2011 Di Meglio (10.1016/j.sysconle.2025.106096_b42) 2014; 47 Koh (10.1016/j.sysconle.2025.106096_b6) 2003; 56 Guo (10.1016/j.sysconle.2025.106096_b27) 2019; 57 Hardy (10.1016/j.sysconle.2025.106096_b52) 1952 Delavari (10.1016/j.sysconle.2025.106096_b3) 2013; 15 Zhou (10.1016/j.sysconle.2025.106096_b19) 2018; 91 Karagiannis (10.1016/j.sysconle.2025.106096_b18) 2018; 64 Yang (10.1016/j.sysconle.2025.106096_b14) 2015; 75 Krstic (10.1016/j.sysconle.2025.106096_b38) 2009 Jin (10.1016/j.sysconle.2025.106096_b7) 2019; 109 Guo (10.1016/j.sysconle.2025.106096_b50) 2021; 33 Wu (10.1016/j.sysconle.2025.106096_b26) 2023; 175 Smyshlyaev (10.1016/j.sysconle.2025.106096_b29) 2007; 43 Ahmed-Ali (10.1016/j.sysconle.2025.106096_b40) 2015; 61 Yang (10.1016/j.sysconle.2025.106096_b8) 2012; 43 Böhm (10.1016/j.sysconle.2025.106096_b9) 1998; 36 Zhang (10.1016/j.sysconle.2025.106096_b4) 2013; 7 He (10.1016/j.sysconle.2025.106096_b1) 2011; 47 Mei (10.1016/j.sysconle.2025.106096_b17) 2023; 177 Anfinsen (10.1016/j.sysconle.2025.106096_b35) 2017; 62 Han (10.1016/j.sysconle.2025.106096_b13) 2014; 31 Ahmed-Ali (10.1016/j.sysconle.2025.106096_b39) 2016; 72 Fan (10.1016/j.sysconle.2025.106096_b22) 2023; 102 Aamo (10.1016/j.sysconle.2025.106096_b34) 2012; 58 Jing (10.1016/j.sysconle.2025.106096_b20) 2022; 53 Wang (10.1016/j.sysconle.2025.106096_b24) 2022 Smyshlyaev (10.1016/j.sysconle.2025.106096_b32) 2010 Guo (10.1016/j.sysconle.2025.106096_b10) 2009; 45 Anfinsen (10.1016/j.sysconle.2025.106096_b44) 2016; 61 Ioannou (10.1016/j.sysconle.2025.106096_b53) 1996 Nguyen (10.1016/j.sysconle.2025.106096_b5) 2010; 329 Guo (10.1016/j.sysconle.2025.106096_b28) 2023; 61 Anfinsen (10.1016/j.sysconle.2025.106096_b36) 2017; 63 Hasanov (10.1016/j.sysconle.2025.106096_b21) 2016; 71 Jin (10.1016/j.sysconle.2025.106096_b16) 2015; 52 Bernard (10.1016/j.sysconle.2025.106096_b37) 2014; 50 Xu (10.1016/j.sysconle.2025.106096_b46) 2023 Choi (10.1016/j.sysconle.2025.106096_b2) 2004; 10 Gnedin (10.1016/j.sysconle.2025.106096_b49) 1992; 22 Smyshlyaev (10.1016/j.sysconle.2025.106096_b31) 2007; 43 Bin (10.1016/j.sysconle.2025.106096_b43) 2016; 62 Rahn (10.1016/j.sysconle.2025.106096_b51) 2001 Yang (10.1016/j.sysconle.2025.106096_b12) 2019; 25 Benabdelhadi (10.1016/j.sysconle.2025.106096_b25) 2021; 123 Anfinsen (10.1016/j.sysconle.2025.106096_b45) 2017; 79 Guo (10.1016/j.sysconle.2025.106096_b11) 2008; 57 Zhang (10.1016/j.sysconle.2025.106096_b47) 2002; 47 Wu (10.1016/j.sysconle.2025.106096_b48) 2019; 32 Guo (10.1016/j.sysconle.2025.106096_b33) 2013; 58 Krstic (10.1016/j.sysconle.2025.106096_b30) 2008; 53 |
| References_xml | – volume: 43 start-page: 1543 year: 2007 end-page: 1556 ident: b29 article-title: Adaptive boundary control for unstable parabolic PDEs-Part II: Estimation-based designs publication-title: Automatica – volume: 63 start-page: 2405 year: 2017 end-page: 2420 ident: b36 article-title: Model reference adaptive control of publication-title: IEEE Trans. Autom. Control – volume: 102 start-page: 2755 year: 2023 end-page: 2773 ident: b22 article-title: Output feedback stabilization of Euler–Bernoulli beam equation with general corrupted boundary observation publication-title: Appl. Anal. – volume: 7 start-page: 43 year: 2013 end-page: 51 ident: b4 article-title: Adaptive boundary control for flexible two-link manipulator based on partial differential equation dynamic model publication-title: IET Control Theory Appl. – volume: 25 start-page: 4 year: 2019 ident: b12 article-title: Pointwise feedback stabilization of an Euler-Bernoulli beam in observations with time delay publication-title: ESAIM Control Optim. Calc. Var. – volume: 50 start-page: 2692 year: 2014 end-page: 2699 ident: b37 article-title: Adaptive output-feedback stabilization of non-local hyperbolic PDEs publication-title: Automatica – volume: 32 start-page: 542 year: 2019 end-page: 556 ident: b48 article-title: Exponential stability of the Euler-Bernoulli beam equation with external disturbance and output feedback time-delay publication-title: J. Syst. Sci. Complex. – volume: 72 start-page: 115 year: 2016 end-page: 122 ident: b39 article-title: Adaptive boundary observer for parabolic PDEs subject to domain and boundary parameter uncertainties publication-title: Automatica – volume: 58 start-page: 1095 year: 2012 end-page: 1106 ident: b34 article-title: Disturbance rejection in 2 x 2 linear hyperbolic systems publication-title: IEEE Trans. Autom. Control – volume: 64 start-page: 3809 year: 2018 end-page: 3816 ident: b18 article-title: A backstepping boundary observer for a simply supported beam publication-title: IEEE Trans. Autom. Control – volume: 91 start-page: 79 year: 2018 end-page: 88 ident: b19 article-title: Disturbance estimator based output feedback exponential stabilization for Euler–Bernoulli beam equation with boundary control publication-title: Automatica – volume: 71 start-page: 106 year: 2016 end-page: 117 ident: b21 article-title: Identification of unknown temporal and spatial load distributions in a vibrating Euler–Bernoulli beam from Dirichlet boundary measured data publication-title: Automatica – volume: 61 start-page: 2088 year: 2023 end-page: 2113 ident: b28 article-title: Output regulation for Euler–Bernoulli beam with unknown exosystem using adaptive internal model publication-title: SIAM J. Control Optim. – start-page: 1505 year: 2009 end-page: 1510 ident: b38 article-title: Adaptive control of an anti-stable wave PDE publication-title: 2009 American Control Conference – volume: 123 year: 2021 ident: b25 article-title: Adaptive observer design for wave PDEs with nonlinear dynamics and parameter uncertainty publication-title: Automatica – year: 1996 ident: b53 publication-title: Robust Adaptive Control – volume: 52 start-page: 95 year: 2015 end-page: 102 ident: b16 article-title: Lyapunov approach to output feedback stabilization for the Euler–Bernoulli beam equation with boundary input disturbance publication-title: Automatica – volume: 61 start-page: 3979 year: 2016 end-page: 3990 ident: b44 article-title: An adaptive observer design for publication-title: IEEE Trans. Autom. Control – volume: 31 start-page: 533 year: 2014 end-page: 550 ident: b13 article-title: Output-based stabilization of Euler–Bernoulli beam with time-delay in boundary input publication-title: IMA J. Math. Control Inform. – volume: 20 start-page: 237 year: 2014 end-page: 244 ident: b23 article-title: Vibration control of a nonuniform wind turbine tower via disturbance observer publication-title: IEEE/ASME Trans. Mechatronics – start-page: 2776 year: 2011 end-page: 2781 ident: b15 article-title: Non-collocated feedback stabilization of a non-uniform Euler-Bernoulli beam with in-domain actuation publication-title: 2011 50th IEEE Conference on Decision and Control and European Control Conference – year: 2001 ident: b51 article-title: Mechatronic Control of Distributed Noise and Vibration – volume: 47 start-page: 722 year: 2011 end-page: 732 ident: b1 article-title: Robust adaptive boundary control of a flexible marine riser with vessel dynamics publication-title: Automatica – volume: 109 year: 2019 ident: b7 article-title: Boundary output tracking for an Euler–Bernoulli beam equation with unmatched perturbations from a known exosystem publication-title: Automatica – volume: 177 year: 2023 ident: b17 article-title: Exponential stabilization for an Euler–Bernoulli beam PDE-ODE cascade system publication-title: Systems Control Lett. – volume: 62 start-page: 6237 year: 2017 end-page: 6249 ident: b35 article-title: Adaptive stabilization of publication-title: IEEE Trans. Autom. Control – year: 1952 ident: b52 article-title: Inequalities – volume: 57 start-page: 1890 year: 2019 end-page: 1928 ident: b27 article-title: Adaptive error feedback regulation problem for an Euler–Bernoulli beam equation with general unmatched boundary harmonic disturbance publication-title: SIAM J. Control Optim. – start-page: 1 year: 2023 end-page: 8 ident: b46 article-title: Adaptive output regulation of a class of 1-D hyperbolic PDEs with unknown boundary scaled parameters publication-title: IEEE Trans. Autom. Control – start-page: 1343 year: 2015 end-page: 1348 ident: b41 article-title: Adaptive observer for parabolic PDEs with uncertain parameter in the boundary condition publication-title: 2015 European Control Conference – volume: 36 start-page: 33 year: 1998 end-page: 81 ident: b9 article-title: Model reference adaptive control of distributed parameter systems publication-title: SIAM J. Control Optim. – volume: 58 start-page: 1631 year: 2013 end-page: 1643 ident: b33 article-title: Parameter estimation and non-collocated adaptive stabilization for a wave equation subject to general boundary harmonic disturbance publication-title: IEEE Trans. Autom. Control – volume: 175 year: 2023 ident: b26 article-title: Non-collocated tracking for an Euler–Bernoulli beam subject to disturbances with unknown frequencies publication-title: Systems Control Lett. – year: 2022 ident: b24 article-title: Robust boundary control approaches to the stabilization of the Euler–Bernoulli beam under external disturbances publication-title: J. Vib. Control – volume: 53 start-page: 1575 year: 2008 end-page: 1591 ident: b30 article-title: Adaptive boundary control for unstable parabolic PDEs-Part I: Lyapunov design publication-title: IEEE Trans. Autom. Control – volume: 53 start-page: 2562 year: 2022 end-page: 2571 ident: b20 article-title: Backstepping control for vibration suppression of 2-D Euler–Bernoulli beam based on nonlinear saturation compensator publication-title: IEEE Trans. Syst. Man Cybern.: Syst. – volume: 43 start-page: 24 year: 2012 end-page: 36 ident: b8 article-title: Trajectory planning and optimized adaptive control for a class of wheeled inverted pendulum vehicle models publication-title: IEEE Trans. Cybern. – volume: 47 start-page: 525 year: 2002 end-page: 529 ident: b47 article-title: Adaptive observer for multiple-input-multiple-output (MIMO) linear time-varying systems publication-title: IEEE Trans. Autom. Control – volume: 79 start-page: 185 year: 2017 end-page: 197 ident: b45 article-title: Estimation of boundary parameters in general heterodirectional linear hyperbolic systems publication-title: Automatica – volume: 329 start-page: 4455 year: 2010 end-page: 4465 ident: b5 article-title: Multi-cracks detection of a beam-like structure based on the on-vehicle vibration signal and wavelet analysis publication-title: J. Sound Vib. – volume: 15 start-page: 783 year: 2013 end-page: 795 ident: b3 article-title: Fractional order controller design for a flexible link manipulator robot publication-title: Asian J. Control – volume: 10 start-page: 661 year: 2004 end-page: 682 ident: b2 article-title: Exponential stabilization of an axially moving tensioned strip by passive damping and boundary control publication-title: J. Vib. Control – volume: 57 start-page: 740 year: 2008 end-page: 749 ident: b11 article-title: Dynamic stabilization of an Euler–Bernoulli beam under boundary control and non-collocated observation publication-title: Systems Control Lett. – volume: 43 start-page: 1557 year: 2007 end-page: 1564 ident: b31 article-title: Adaptive boundary control for unstable parabolic PDEs-Part III: Output feedback examples with swapping identifiers publication-title: Automatica – volume: 22 start-page: 528 year: 1992 end-page: 544 ident: b49 article-title: Stabilization of Euler-Bernoulli beam by a boundary control publication-title: Results Math. – volume: 56 start-page: 1549 year: 2003 end-page: 1567 ident: b6 article-title: Moving element method for train-track dynamics publication-title: Internat. J. Numer. Methods Engrg. – volume: 62 start-page: 3890 year: 2016 end-page: 3904 ident: b43 article-title: Boundary estimation of boundary parameters for linear hyperbolic PDEs publication-title: IEEE Trans. Autom. Control – volume: 45 start-page: 1468 year: 2009 end-page: 1475 ident: b10 article-title: Dynamic stabilization of an Euler–Bernoulli beam equation with time delay in boundary observation publication-title: Automatica – volume: 61 start-page: 3083 year: 2015 end-page: 3090 ident: b40 article-title: Adaptive observer for a class of parabolic PDEs publication-title: IEEE Trans. Autom. Control – volume: 47 start-page: 11391 year: 2014 end-page: 11397 ident: b42 article-title: An adaptive observer for hyperbolic systems with application to underbalanced drilling publication-title: IFAC Proc. Vol. – volume: 33 start-page: 707 year: 2021 end-page: 754 ident: b50 article-title: Robust tracking error feedback control for output regulation of Euler–Bernoulli beam equation publication-title: Math. Control Signals Systems – volume: 75 start-page: 1 year: 2015 end-page: 14 ident: b14 article-title: Stabilization of Euler-Bernoulli beam equations with variable coefficients under delayed boundary output feedback publication-title: Electron. J. Differential Equations – year: 2010 ident: b32 article-title: Adaptive Control of Parabolic PDEs – volume: 53 start-page: 2562 issue: 5 year: 2022 ident: 10.1016/j.sysconle.2025.106096_b20 article-title: Backstepping control for vibration suppression of 2-D Euler–Bernoulli beam based on nonlinear saturation compensator publication-title: IEEE Trans. Syst. Man Cybern.: Syst. doi: 10.1109/TSMC.2022.3213477 – volume: 123 year: 2021 ident: 10.1016/j.sysconle.2025.106096_b25 article-title: Adaptive observer design for wave PDEs with nonlinear dynamics and parameter uncertainty publication-title: Automatica doi: 10.1016/j.automatica.2020.109295 – year: 1952 ident: 10.1016/j.sysconle.2025.106096_b52 – volume: 58 start-page: 1631 issue: 7 year: 2013 ident: 10.1016/j.sysconle.2025.106096_b33 article-title: Parameter estimation and non-collocated adaptive stabilization for a wave equation subject to general boundary harmonic disturbance publication-title: IEEE Trans. Autom. Control doi: 10.1109/TAC.2013.2239003 – volume: 45 start-page: 1468 issue: 6 year: 2009 ident: 10.1016/j.sysconle.2025.106096_b10 article-title: Dynamic stabilization of an Euler–Bernoulli beam equation with time delay in boundary observation publication-title: Automatica doi: 10.1016/j.automatica.2009.02.004 – volume: 62 start-page: 6237 issue: 12 year: 2017 ident: 10.1016/j.sysconle.2025.106096_b35 article-title: Adaptive stabilization of 2times2 linear hyperbolic systems with an unknown boundary parameter from collocated sensing and control publication-title: IEEE Trans. Autom. Control doi: 10.1109/TAC.2017.2700387 – volume: 43 start-page: 24 issue: 1 year: 2012 ident: 10.1016/j.sysconle.2025.106096_b8 article-title: Trajectory planning and optimized adaptive control for a class of wheeled inverted pendulum vehicle models publication-title: IEEE Trans. Cybern. doi: 10.1109/TSMCB.2012.2198813 – volume: 31 start-page: 533 issue: 4 year: 2014 ident: 10.1016/j.sysconle.2025.106096_b13 article-title: Output-based stabilization of Euler–Bernoulli beam with time-delay in boundary input publication-title: IMA J. Math. Control Inform. doi: 10.1093/imamci/dnt030 – start-page: 2776 year: 2011 ident: 10.1016/j.sysconle.2025.106096_b15 article-title: Non-collocated feedback stabilization of a non-uniform Euler-Bernoulli beam with in-domain actuation – volume: 32 start-page: 542 year: 2019 ident: 10.1016/j.sysconle.2025.106096_b48 article-title: Exponential stability of the Euler-Bernoulli beam equation with external disturbance and output feedback time-delay publication-title: J. Syst. Sci. Complex. doi: 10.1007/s11424-018-7182-0 – volume: 62 start-page: 3890 issue: 8 year: 2016 ident: 10.1016/j.sysconle.2025.106096_b43 article-title: Boundary estimation of boundary parameters for linear hyperbolic PDEs publication-title: IEEE Trans. Autom. Control doi: 10.1109/TAC.2016.2643442 – volume: 25 start-page: 4 year: 2019 ident: 10.1016/j.sysconle.2025.106096_b12 article-title: Pointwise feedback stabilization of an Euler-Bernoulli beam in observations with time delay publication-title: ESAIM Control Optim. Calc. Var. doi: 10.1051/cocv/2017080 – volume: 43 start-page: 1543 issue: 9 year: 2007 ident: 10.1016/j.sysconle.2025.106096_b29 article-title: Adaptive boundary control for unstable parabolic PDEs-Part II: Estimation-based designs publication-title: Automatica doi: 10.1016/j.automatica.2007.02.014 – volume: 61 start-page: 2088 issue: 4 year: 2023 ident: 10.1016/j.sysconle.2025.106096_b28 article-title: Output regulation for Euler–Bernoulli beam with unknown exosystem using adaptive internal model publication-title: SIAM J. Control Optim. doi: 10.1137/22M1501805 – year: 2010 ident: 10.1016/j.sysconle.2025.106096_b32 – volume: 102 start-page: 2755 issue: 10 year: 2023 ident: 10.1016/j.sysconle.2025.106096_b22 article-title: Output feedback stabilization of Euler–Bernoulli beam equation with general corrupted boundary observation publication-title: Appl. Anal. doi: 10.1080/00036811.2022.2037572 – volume: 91 start-page: 79 year: 2018 ident: 10.1016/j.sysconle.2025.106096_b19 article-title: Disturbance estimator based output feedback exponential stabilization for Euler–Bernoulli beam equation with boundary control publication-title: Automatica doi: 10.1016/j.automatica.2018.01.031 – volume: 43 start-page: 1557 issue: 9 year: 2007 ident: 10.1016/j.sysconle.2025.106096_b31 article-title: Adaptive boundary control for unstable parabolic PDEs-Part III: Output feedback examples with swapping identifiers publication-title: Automatica doi: 10.1016/j.automatica.2007.02.015 – volume: 71 start-page: 106 year: 2016 ident: 10.1016/j.sysconle.2025.106096_b21 article-title: Identification of unknown temporal and spatial load distributions in a vibrating Euler–Bernoulli beam from Dirichlet boundary measured data publication-title: Automatica doi: 10.1016/j.automatica.2016.04.034 – volume: 72 start-page: 115 year: 2016 ident: 10.1016/j.sysconle.2025.106096_b39 article-title: Adaptive boundary observer for parabolic PDEs subject to domain and boundary parameter uncertainties publication-title: Automatica doi: 10.1016/j.automatica.2016.06.006 – volume: 109 year: 2019 ident: 10.1016/j.sysconle.2025.106096_b7 article-title: Boundary output tracking for an Euler–Bernoulli beam equation with unmatched perturbations from a known exosystem publication-title: Automatica doi: 10.1016/j.automatica.2019.108507 – volume: 57 start-page: 740 issue: 9 year: 2008 ident: 10.1016/j.sysconle.2025.106096_b11 article-title: Dynamic stabilization of an Euler–Bernoulli beam under boundary control and non-collocated observation publication-title: Systems Control Lett. doi: 10.1016/j.sysconle.2008.02.004 – volume: 47 start-page: 11391 issue: 3 year: 2014 ident: 10.1016/j.sysconle.2025.106096_b42 article-title: An adaptive observer for hyperbolic systems with application to underbalanced drilling publication-title: IFAC Proc. Vol. doi: 10.3182/20140824-6-ZA-1003.02365 – volume: 7 start-page: 43 issue: 1 year: 2013 ident: 10.1016/j.sysconle.2025.106096_b4 article-title: Adaptive boundary control for flexible two-link manipulator based on partial differential equation dynamic model publication-title: IET Control Theory Appl. doi: 10.1049/iet-cta.2011.0593 – start-page: 1505 year: 2009 ident: 10.1016/j.sysconle.2025.106096_b38 article-title: Adaptive control of an anti-stable wave PDE – volume: 22 start-page: 528 issue: 1–2 year: 1992 ident: 10.1016/j.sysconle.2025.106096_b49 article-title: Stabilization of Euler-Bernoulli beam by a boundary control publication-title: Results Math. doi: 10.1007/BF03323104 – volume: 36 start-page: 33 issue: 1 year: 1998 ident: 10.1016/j.sysconle.2025.106096_b9 article-title: Model reference adaptive control of distributed parameter systems publication-title: SIAM J. Control Optim. doi: 10.1137/S0363012995279717 – volume: 75 start-page: 1 year: 2015 ident: 10.1016/j.sysconle.2025.106096_b14 article-title: Stabilization of Euler-Bernoulli beam equations with variable coefficients under delayed boundary output feedback publication-title: Electron. J. Differential Equations – volume: 61 start-page: 3083 issue: 10 year: 2015 ident: 10.1016/j.sysconle.2025.106096_b40 article-title: Adaptive observer for a class of parabolic PDEs publication-title: IEEE Trans. Autom. Control doi: 10.1109/TAC.2015.2500237 – volume: 56 start-page: 1549 issue: 11 year: 2003 ident: 10.1016/j.sysconle.2025.106096_b6 article-title: Moving element method for train-track dynamics publication-title: Internat. J. Numer. Methods Engrg. doi: 10.1002/nme.624 – volume: 63 start-page: 2405 issue: 8 year: 2017 ident: 10.1016/j.sysconle.2025.106096_b36 article-title: Model reference adaptive control of 2times2 coupled linear hyperbolic PDEs publication-title: IEEE Trans. Autom. Control doi: 10.1109/TAC.2017.2767378 – volume: 47 start-page: 525 issue: 3 year: 2002 ident: 10.1016/j.sysconle.2025.106096_b47 article-title: Adaptive observer for multiple-input-multiple-output (MIMO) linear time-varying systems publication-title: IEEE Trans. Autom. Control doi: 10.1109/9.989154 – year: 2001 ident: 10.1016/j.sysconle.2025.106096_b51 – volume: 175 year: 2023 ident: 10.1016/j.sysconle.2025.106096_b26 article-title: Non-collocated tracking for an Euler–Bernoulli beam subject to disturbances with unknown frequencies publication-title: Systems Control Lett. doi: 10.1016/j.sysconle.2023.105504 – volume: 20 start-page: 237 issue: 1 year: 2014 ident: 10.1016/j.sysconle.2025.106096_b23 article-title: Vibration control of a nonuniform wind turbine tower via disturbance observer publication-title: IEEE/ASME Trans. Mechatronics doi: 10.1109/TMECH.2014.2313876 – volume: 329 start-page: 4455 issue: 21 year: 2010 ident: 10.1016/j.sysconle.2025.106096_b5 article-title: Multi-cracks detection of a beam-like structure based on the on-vehicle vibration signal and wavelet analysis publication-title: J. Sound Vib. doi: 10.1016/j.jsv.2010.05.005 – volume: 177 year: 2023 ident: 10.1016/j.sysconle.2025.106096_b17 article-title: Exponential stabilization for an Euler–Bernoulli beam PDE-ODE cascade system publication-title: Systems Control Lett. doi: 10.1016/j.sysconle.2023.105552 – volume: 47 start-page: 722 issue: 4 year: 2011 ident: 10.1016/j.sysconle.2025.106096_b1 article-title: Robust adaptive boundary control of a flexible marine riser with vessel dynamics publication-title: Automatica doi: 10.1016/j.automatica.2011.01.064 – volume: 10 start-page: 661 issue: 5 year: 2004 ident: 10.1016/j.sysconle.2025.106096_b2 article-title: Exponential stabilization of an axially moving tensioned strip by passive damping and boundary control publication-title: J. Vib. Control doi: 10.1177/1077546304038103 – volume: 58 start-page: 1095 issue: 5 year: 2012 ident: 10.1016/j.sysconle.2025.106096_b34 article-title: Disturbance rejection in 2 x 2 linear hyperbolic systems publication-title: IEEE Trans. Autom. Control doi: 10.1109/TAC.2012.2228035 – volume: 64 start-page: 3809 issue: 9 year: 2018 ident: 10.1016/j.sysconle.2025.106096_b18 article-title: A backstepping boundary observer for a simply supported beam publication-title: IEEE Trans. Autom. Control doi: 10.1109/TAC.2018.2884677 – year: 2022 ident: 10.1016/j.sysconle.2025.106096_b24 article-title: Robust boundary control approaches to the stabilization of the Euler–Bernoulli beam under external disturbances publication-title: J. Vib. Control – start-page: 1343 year: 2015 ident: 10.1016/j.sysconle.2025.106096_b41 article-title: Adaptive observer for parabolic PDEs with uncertain parameter in the boundary condition – volume: 57 start-page: 1890 issue: 3 year: 2019 ident: 10.1016/j.sysconle.2025.106096_b27 article-title: Adaptive error feedback regulation problem for an Euler–Bernoulli beam equation with general unmatched boundary harmonic disturbance publication-title: SIAM J. Control Optim. doi: 10.1137/18M1172727 – volume: 15 start-page: 783 issue: 3 year: 2013 ident: 10.1016/j.sysconle.2025.106096_b3 article-title: Fractional order controller design for a flexible link manipulator robot publication-title: Asian J. Control doi: 10.1002/asjc.677 – volume: 79 start-page: 185 year: 2017 ident: 10.1016/j.sysconle.2025.106096_b45 article-title: Estimation of boundary parameters in general heterodirectional linear hyperbolic systems publication-title: Automatica doi: 10.1016/j.automatica.2017.01.015 – volume: 33 start-page: 707 issue: 4 year: 2021 ident: 10.1016/j.sysconle.2025.106096_b50 article-title: Robust tracking error feedback control for output regulation of Euler–Bernoulli beam equation publication-title: Math. Control Signals Systems doi: 10.1007/s00498-021-00298-8 – year: 1996 ident: 10.1016/j.sysconle.2025.106096_b53 – volume: 50 start-page: 2692 issue: 10 year: 2014 ident: 10.1016/j.sysconle.2025.106096_b37 article-title: Adaptive output-feedback stabilization of non-local hyperbolic PDEs publication-title: Automatica doi: 10.1016/j.automatica.2014.09.001 – start-page: 1 year: 2023 ident: 10.1016/j.sysconle.2025.106096_b46 article-title: Adaptive output regulation of a class of 1-D hyperbolic PDEs with unknown boundary scaled parameters publication-title: IEEE Trans. Autom. Control – volume: 53 start-page: 1575 issue: 7 year: 2008 ident: 10.1016/j.sysconle.2025.106096_b30 article-title: Adaptive boundary control for unstable parabolic PDEs-Part I: Lyapunov design publication-title: IEEE Trans. Autom. Control doi: 10.1109/TAC.2008.927798 – volume: 61 start-page: 3979 issue: 12 year: 2016 ident: 10.1016/j.sysconle.2025.106096_b44 article-title: An adaptive observer design for n+1 coupled linear hyperbolic PDEs based on swapping publication-title: IEEE Trans. Autom. Control doi: 10.1109/TAC.2016.2530624 – volume: 52 start-page: 95 year: 2015 ident: 10.1016/j.sysconle.2025.106096_b16 article-title: Lyapunov approach to output feedback stabilization for the Euler–Bernoulli beam equation with boundary input disturbance publication-title: Automatica doi: 10.1016/j.automatica.2014.10.123 |
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