Adaptive output regulation for wave PDEs with a nonlocal term and unknown harmonic disturbances
In this paper, we apply internal model principle (IMP) and the adaptive frequency estimation strategy to achieve output tracking for a one-dimensional wave equation with velocity recirculation and unknown harmonic disturbances. The disturbances are present in all channels, and both the disturbances...
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| Published in | Systems & control letters Vol. 197; p. 106043 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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Elsevier B.V
01.03.2025
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| ISSN | 0167-6911 |
| DOI | 10.1016/j.sysconle.2025.106043 |
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| Abstract | In this paper, we apply internal model principle (IMP) and the adaptive frequency estimation strategy to achieve output tracking for a one-dimensional wave equation with velocity recirculation and unknown harmonic disturbances. The disturbances are present in all channels, and both the disturbances and the reference trajectory have an unknown sinusoidal form. We first construct an auxiliary system and a proper trajectory such that total disturbances appear only in the output of the auxiliary. As a result, we obtain a dynamic estimation of the total disturbances by constructing an internal model dynamics. An adaptive method is proposed to determine the uncertain parameters. In order to realize exponential output tracking, the proposed error-based adaptive dynamic compensator is employed. Finally, some simulation examples are carried out to validate the results. |
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| AbstractList | In this paper, we apply internal model principle (IMP) and the adaptive frequency estimation strategy to achieve output tracking for a one-dimensional wave equation with velocity recirculation and unknown harmonic disturbances. The disturbances are present in all channels, and both the disturbances and the reference trajectory have an unknown sinusoidal form. We first construct an auxiliary system and a proper trajectory such that total disturbances appear only in the output of the auxiliary. As a result, we obtain a dynamic estimation of the total disturbances by constructing an internal model dynamics. An adaptive method is proposed to determine the uncertain parameters. In order to realize exponential output tracking, the proposed error-based adaptive dynamic compensator is employed. Finally, some simulation examples are carried out to validate the results. |
| ArticleNumber | 106043 |
| Author | Peng, Ning Wang, Jun-Min Liu, Jun-Jun |
| Author_xml | – sequence: 1 givenname: Jun-Jun orcidid: 0000-0002-6567-2137 surname: Liu fullname: Liu, Jun-Jun email: liujunjun@tyut.edu.cn organization: School of Mathematics, Taiyuan University of Technology, Taiyuan, Shanxi, 030024, China – sequence: 2 givenname: Ning surname: Peng fullname: Peng, Ning email: pnlx1232022@163.com organization: School of Mathematics, Taiyuan University of Technology, Taiyuan, Shanxi, 030024, China – sequence: 3 givenname: Jun-Min surname: Wang fullname: Wang, Jun-Min email: jmwang@bit.edu.cn organization: School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China |
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| Cites_doi | 10.1109/9.895561 10.1016/j.automatica.2021.109637 10.1007/s11432-019-2893-y 10.1016/j.automatica.2022.110159 10.1016/j.automatica.2020.108808 10.1016/j.automatica.2019.108796 10.1137/0327028 10.1002/rnc.4234 10.1109/TAC.2023.3333797 10.1109/TAC.2012.2218669 10.1109/TIE.2018.2884172 10.1137/120873212 10.1109/TAC.2022.3159292 10.1109/TAC.2017.2688128 10.1016/j.automatica.2011.08.033 10.1016/j.automatica.2014.10.117 10.1137/18M1172727 10.1109/TAC.2021.3056599 10.1115/1.3023128 10.1109/TAC.2019.2937727 10.1016/S0005-1098(03)00192-4 10.1016/j.automatica.2015.04.008 10.1137/22M1501805 10.1137/050623000 10.1016/j.automatica.2023.111202 10.1016/j.ejcon.2015.02.002 10.1016/j.cnsns.2023.107659 10.1109/TAC.2014.2326491 10.1016/j.sysconle.2023.105504 10.1017/S0956792500001133 10.1137/130921362 10.1109/9.553684 |
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| References | Wang, Krstic (b12) 2021; 129 Su, Guo, Wang, Krstic (b27) 2017; 62 Khalil (b36) 2002 Wang, Liu, Ren, Chen (b15) 2015; 52 Guo, Zhao (b7) 2022; 138 Liu, Guo (b10) 2022; 67 Guo, Guo (b16) 2013; 51 Tucsnak, Weiss (b33) 2009 Byrnes, Lauko, Gilliam, Shubov (b1) 2000; 45 Ioannou, Sun (b35) 1996 Krstic (b28) 2009 Weiss, Curtain (b34) 1997; 42 Zhao, Guo (b14) 2015; 23 Rebarber, Weiss (b17) 2003; 39 Paunonen, Pohjolainen (b5) 2014; 52 Immonen, Pohjolainen (b4) 2006; 45 Guo, Zhou, Krstic (b20) 2018; 28 Wu, Wang, Wen (b24) 2023 Rao (b29) 1993; 4 Liu, Chen, Mei, Wu (b22) 2022; 65 Wu, Wang (b25) 2024; 69 Jin, Guo (b32) 2020; 113 Natarajan, Gilliam, Weiss (b31) 2014; 59 Huang, Jin (b26) 2024; 128 Guo, Zhou (b6) 2019; 57 Yilmaz, Basturk (b8) 2020; 113 Liu, Yao, Zhao (b23) 2023; 156 Weiss (b37) 1989; 27 Liu, Fu, He, Hui (b19) 2018; 66 Krstic, Magnis, Vazquez (b11) 2009; 131 Feng, Guo, Wu (b21) 2019; 65 Wang, Krstic (b9) 2023; 68 Deutscher (b3) 2015; 57 Guo, Jin (b13) 2013; 58 Deutscher (b2) 2011; 47 Guo, Zhao (b18) 2023; 61 Krstic, Smyshlyaev (b30) 2008 Wang (10.1016/j.sysconle.2025.106043_b12) 2021; 129 Natarajan (10.1016/j.sysconle.2025.106043_b31) 2014; 59 Rao (10.1016/j.sysconle.2025.106043_b29) 1993; 4 Guo (10.1016/j.sysconle.2025.106043_b20) 2018; 28 Liu (10.1016/j.sysconle.2025.106043_b22) 2022; 65 Huang (10.1016/j.sysconle.2025.106043_b26) 2024; 128 Jin (10.1016/j.sysconle.2025.106043_b32) 2020; 113 Guo (10.1016/j.sysconle.2025.106043_b7) 2022; 138 Liu (10.1016/j.sysconle.2025.106043_b23) 2023; 156 Guo (10.1016/j.sysconle.2025.106043_b6) 2019; 57 Zhao (10.1016/j.sysconle.2025.106043_b14) 2015; 23 Guo (10.1016/j.sysconle.2025.106043_b13) 2013; 58 Rebarber (10.1016/j.sysconle.2025.106043_b17) 2003; 39 Deutscher (10.1016/j.sysconle.2025.106043_b2) 2011; 47 Wang (10.1016/j.sysconle.2025.106043_b15) 2015; 52 Feng (10.1016/j.sysconle.2025.106043_b21) 2019; 65 Immonen (10.1016/j.sysconle.2025.106043_b4) 2006; 45 Wang (10.1016/j.sysconle.2025.106043_b9) 2023; 68 Deutscher (10.1016/j.sysconle.2025.106043_b3) 2015; 57 Liu (10.1016/j.sysconle.2025.106043_b19) 2018; 66 Wu (10.1016/j.sysconle.2025.106043_b25) 2024; 69 Yilmaz (10.1016/j.sysconle.2025.106043_b8) 2020; 113 Liu (10.1016/j.sysconle.2025.106043_b10) 2022; 67 Ioannou (10.1016/j.sysconle.2025.106043_b35) 1996 Byrnes (10.1016/j.sysconle.2025.106043_b1) 2000; 45 Khalil (10.1016/j.sysconle.2025.106043_b36) 2002 Weiss (10.1016/j.sysconle.2025.106043_b37) 1989; 27 Paunonen (10.1016/j.sysconle.2025.106043_b5) 2014; 52 Krstic (10.1016/j.sysconle.2025.106043_b11) 2009; 131 Krstic (10.1016/j.sysconle.2025.106043_b30) 2008 Wu (10.1016/j.sysconle.2025.106043_b24) 2023 Guo (10.1016/j.sysconle.2025.106043_b16) 2013; 51 Krstic (10.1016/j.sysconle.2025.106043_b28) 2009 Weiss (10.1016/j.sysconle.2025.106043_b34) 1997; 42 Guo (10.1016/j.sysconle.2025.106043_b18) 2023; 61 Tucsnak (10.1016/j.sysconle.2025.106043_b33) 2009 Su (10.1016/j.sysconle.2025.106043_b27) 2017; 62 |
| References_xml | – volume: 66 start-page: 8648 year: 2018 end-page: 8658 ident: b19 article-title: Modeling and observer-based vibration control of a flexible spacecraft with external disturbances publication-title: IEEE Trans. Ind. Electron. – volume: 69 start-page: 2689 year: 2024 end-page: 2696 ident: b25 article-title: Adaptive output tracking for 1-D wave equations subject to unknown harmonic disturbances publication-title: IEEE Trans. Automat. Control – volume: 129 year: 2021 ident: b12 article-title: Adaptive event-triggered PDE control for load-moving cable systems publication-title: Automatica – volume: 113 year: 2020 ident: b8 article-title: Adaptive output regulator for wave PDEs with unknown harmonic disturbance publication-title: Automatica – volume: 51 start-page: 1679 year: 2013 end-page: 1706 ident: b16 article-title: Adaptive output feedback stabilization for one-dimensional wave equation with corrupted observation by harmonic disturbance publication-title: SIAM J. Control Optim. – volume: 65 start-page: 1841 year: 2019 end-page: 1854 ident: b21 article-title: Trajectory planning approach to output tracking for a 1-D wave equation publication-title: IEEE Trans. Automat. Control – year: 2009 ident: b33 article-title: Observation and Control for Operator Semigroups – volume: 39 start-page: 1555 year: 2003 end-page: 1569 ident: b17 article-title: Internal model based tracking and disturbance rejection for stable well-posed systems publication-title: Automatica – volume: 4 start-page: 303 year: 1993 end-page: 319 ident: b29 article-title: Decay estimates of solutions for a hybrid system of flexible structures publication-title: Eur. J. Appl. Math. – volume: 52 start-page: 3967 year: 2014 end-page: 4000 ident: b5 article-title: The internal model principle for systems with unbounded control and observation publication-title: SIAM J. Control Optim. – volume: 23 start-page: 62 year: 2015 end-page: 70 ident: b14 article-title: On active disturbance rejection control for nonlinear systems using time-varying gain publication-title: Eur. J. Control – volume: 58 start-page: 1269 year: 2013 end-page: 1275 ident: b13 article-title: Sliding mode and active disturbance rejection control to stabilization of one-dimensional antistable wave equations subject to disturbance in boundary input publication-title: IEEE Trans. Automat. Control – volume: 42 start-page: 4 year: 1997 end-page: 21 ident: b34 article-title: Dynamic stabilization of regular linear systems publication-title: IEEE Trans. Automat. Control – volume: 68 start-page: 1568 year: 2023 end-page: 1583 ident: b9 article-title: Event-triggered adaptive control of coupled hyperbolic PDEs with piecewise-constant inputs and identification publication-title: IEEE Trans. Automat. Control – volume: 131 year: 2009 ident: b11 article-title: Nonlinear control of the viscous Burgers equation: Trajectory generation, tracking, and observer design publication-title: J. Dyn. Syst. Meas. Control. – volume: 61 start-page: 2088 year: 2023 end-page: 2113 ident: b18 article-title: Output regulation for Euler–Bernoulli beam with unknown exosystem using adaptive internal model publication-title: SIAM J. Control Optim. – volume: 28 start-page: 4309 year: 2018 end-page: 4329 ident: b20 article-title: Adaptive error feedback regulation problem for 1-D wave equation publication-title: Internat. J. Robust Nonlinear Control – volume: 62 start-page: 4760 year: 2017 end-page: 4767 ident: b27 article-title: Boundary stabilization of wave equation with velocity recirculation publication-title: IEEE Trans. Automat. Control – volume: 47 start-page: 2468 year: 2011 end-page: 2473 ident: b2 article-title: Output regulation for linear distributed-parameter systems using finite-dimensional dual observers publication-title: Automatica – volume: 59 start-page: 2708 year: 2014 end-page: 2723 ident: b31 article-title: The state feedback regulator problem for regular linear systems publication-title: IEEE Trans. Automat. Control – volume: 67 start-page: 1120 year: 2022 end-page: 1134 ident: b10 article-title: Robust tracking error feedback control for a one-dimensional Schrödinger equation publication-title: IEEE Trans. Automat. Control – year: 2023 ident: b24 article-title: Non-collocated tracking for an Euler–Bernoulli beam subject to disturbances with unknown frequencies publication-title: Systems Control Lett. – year: 2008 ident: b30 article-title: Boundary Control of PDEs: A Course on Backstepping Designs – volume: 113 year: 2020 ident: b32 article-title: Boundary state feedback exponential stabilization for a one-dimensional wave equation with velocity recirculation publication-title: Automatica – volume: 27 start-page: 527 year: 1989 end-page: 545 ident: b37 article-title: Admissibility of unbounded control operators publication-title: SIAM J. Control Optim. – volume: 52 start-page: 23 year: 2015 end-page: 34 ident: b15 article-title: Sliding mode control to stabilization of cascaded heat PDE-ODE systems subject to boundary control matched disturbance publication-title: Automatica – volume: 45 start-page: 1714 year: 2006 end-page: 1735 ident: b4 article-title: Feedback and feedforward output regulation of bounded uniformly continuous signals for infinite-dimensional systems publication-title: SIAM J. Control Optim. – volume: 57 start-page: 1890 year: 2019 end-page: 1928 ident: b6 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. – volume: 128 year: 2024 ident: b26 article-title: Adaptive error feedback regulator problem for a 1-D wave equation with velocity recirculation publication-title: Commun. Nonlinear Sci. Numer. Simul. – volume: 57 start-page: 56 year: 2015 end-page: 64 ident: b3 article-title: A backstepping approach to the output regulation of boundary controlled parabolic PDEs publication-title: Automatica – year: 2002 ident: b36 article-title: Nonlinear Systems – volume: 156 year: 2023 ident: b23 article-title: Distributed neural-based fault-tolerant control of multiple flexible manipulators with input saturations publication-title: Automatica – year: 1996 ident: b35 article-title: Robust Adaptive Control – volume: 65 year: 2022 ident: b22 article-title: Observer-based boundary control for an asymmetric output-constrained flexible robotic manipulator publication-title: Sci. China Inf. Sci. – volume: 45 start-page: 2236 year: 2000 end-page: 2252 ident: b1 article-title: Output regulation for linear distributed parameter systems publication-title: IEEE Trans. Automat. Control – year: 2009 ident: b28 article-title: Delay Compensation for Nonlinear, Adaptive, and PDE Systems – volume: 138 start-page: 11015 year: 2022 ident: b7 article-title: Output regulation for a heat equation with unknown exosystem publication-title: Automatica – volume: 45 start-page: 2236 year: 2000 ident: 10.1016/j.sysconle.2025.106043_b1 article-title: Output regulation for linear distributed parameter systems publication-title: IEEE Trans. Automat. Control doi: 10.1109/9.895561 – volume: 129 year: 2021 ident: 10.1016/j.sysconle.2025.106043_b12 article-title: Adaptive event-triggered PDE control for load-moving cable systems publication-title: Automatica doi: 10.1016/j.automatica.2021.109637 – year: 2008 ident: 10.1016/j.sysconle.2025.106043_b30 – volume: 65 issue: 3 year: 2022 ident: 10.1016/j.sysconle.2025.106043_b22 article-title: Observer-based boundary control for an asymmetric output-constrained flexible robotic manipulator publication-title: Sci. China Inf. Sci. doi: 10.1007/s11432-019-2893-y – year: 2002 ident: 10.1016/j.sysconle.2025.106043_b36 – volume: 138 start-page: 11015 year: 2022 ident: 10.1016/j.sysconle.2025.106043_b7 article-title: Output regulation for a heat equation with unknown exosystem publication-title: Automatica doi: 10.1016/j.automatica.2022.110159 – volume: 113 year: 2020 ident: 10.1016/j.sysconle.2025.106043_b8 article-title: Adaptive output regulator for wave PDEs with unknown harmonic disturbance publication-title: Automatica doi: 10.1016/j.automatica.2020.108808 – volume: 113 year: 2020 ident: 10.1016/j.sysconle.2025.106043_b32 article-title: Boundary state feedback exponential stabilization for a one-dimensional wave equation with velocity recirculation publication-title: Automatica doi: 10.1016/j.automatica.2019.108796 – volume: 27 start-page: 527 year: 1989 ident: 10.1016/j.sysconle.2025.106043_b37 article-title: Admissibility of unbounded control operators publication-title: SIAM J. Control Optim. doi: 10.1137/0327028 – year: 2009 ident: 10.1016/j.sysconle.2025.106043_b33 – volume: 28 start-page: 4309 issue: 15 year: 2018 ident: 10.1016/j.sysconle.2025.106043_b20 article-title: Adaptive error feedback regulation problem for 1-D wave equation publication-title: Internat. J. Robust Nonlinear Control doi: 10.1002/rnc.4234 – volume: 69 start-page: 2689 issue: 4 year: 2024 ident: 10.1016/j.sysconle.2025.106043_b25 article-title: Adaptive output tracking for 1-D wave equations subject to unknown harmonic disturbances publication-title: IEEE Trans. Automat. Control doi: 10.1109/TAC.2023.3333797 – volume: 58 start-page: 1269 year: 2013 ident: 10.1016/j.sysconle.2025.106043_b13 article-title: Sliding mode and active disturbance rejection control to stabilization of one-dimensional antistable wave equations subject to disturbance in boundary input publication-title: IEEE Trans. Automat. Control doi: 10.1109/TAC.2012.2218669 – volume: 66 start-page: 8648 issue: 11 year: 2018 ident: 10.1016/j.sysconle.2025.106043_b19 article-title: Modeling and observer-based vibration control of a flexible spacecraft with external disturbances publication-title: IEEE Trans. Ind. Electron. doi: 10.1109/TIE.2018.2884172 – volume: 51 start-page: 1679 year: 2013 ident: 10.1016/j.sysconle.2025.106043_b16 article-title: Adaptive output feedback stabilization for one-dimensional wave equation with corrupted observation by harmonic disturbance publication-title: SIAM J. Control Optim. doi: 10.1137/120873212 – volume: 68 start-page: 1568 year: 2023 ident: 10.1016/j.sysconle.2025.106043_b9 article-title: Event-triggered adaptive control of coupled hyperbolic PDEs with piecewise-constant inputs and identification publication-title: IEEE Trans. Automat. Control doi: 10.1109/TAC.2022.3159292 – volume: 62 start-page: 4760 issue: 9 year: 2017 ident: 10.1016/j.sysconle.2025.106043_b27 article-title: Boundary stabilization of wave equation with velocity recirculation publication-title: IEEE Trans. Automat. Control doi: 10.1109/TAC.2017.2688128 – volume: 47 start-page: 2468 year: 2011 ident: 10.1016/j.sysconle.2025.106043_b2 article-title: Output regulation for linear distributed-parameter systems using finite-dimensional dual observers publication-title: Automatica doi: 10.1016/j.automatica.2011.08.033 – volume: 52 start-page: 23 year: 2015 ident: 10.1016/j.sysconle.2025.106043_b15 article-title: Sliding mode control to stabilization of cascaded heat PDE-ODE systems subject to boundary control matched disturbance publication-title: Automatica doi: 10.1016/j.automatica.2014.10.117 – volume: 57 start-page: 1890 year: 2019 ident: 10.1016/j.sysconle.2025.106043_b6 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: 67 start-page: 1120 issue: 3 year: 2022 ident: 10.1016/j.sysconle.2025.106043_b10 article-title: Robust tracking error feedback control for a one-dimensional Schrödinger equation publication-title: IEEE Trans. Automat. Control doi: 10.1109/TAC.2021.3056599 – volume: 131 year: 2009 ident: 10.1016/j.sysconle.2025.106043_b11 article-title: Nonlinear control of the viscous Burgers equation: Trajectory generation, tracking, and observer design publication-title: J. Dyn. Syst. Meas. Control. doi: 10.1115/1.3023128 – volume: 65 start-page: 1841 year: 2019 ident: 10.1016/j.sysconle.2025.106043_b21 article-title: Trajectory planning approach to output tracking for a 1-D wave equation publication-title: IEEE Trans. Automat. Control doi: 10.1109/TAC.2019.2937727 – volume: 39 start-page: 1555 year: 2003 ident: 10.1016/j.sysconle.2025.106043_b17 article-title: Internal model based tracking and disturbance rejection for stable well-posed systems publication-title: Automatica doi: 10.1016/S0005-1098(03)00192-4 – volume: 57 start-page: 56 year: 2015 ident: 10.1016/j.sysconle.2025.106043_b3 article-title: A backstepping approach to the output regulation of boundary controlled parabolic PDEs publication-title: Automatica doi: 10.1016/j.automatica.2015.04.008 – volume: 61 start-page: 2088 year: 2023 ident: 10.1016/j.sysconle.2025.106043_b18 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 – volume: 45 start-page: 1714 year: 2006 ident: 10.1016/j.sysconle.2025.106043_b4 article-title: Feedback and feedforward output regulation of bounded uniformly continuous signals for infinite-dimensional systems publication-title: SIAM J. Control Optim. doi: 10.1137/050623000 – volume: 156 year: 2023 ident: 10.1016/j.sysconle.2025.106043_b23 article-title: Distributed neural-based fault-tolerant control of multiple flexible manipulators with input saturations publication-title: Automatica doi: 10.1016/j.automatica.2023.111202 – volume: 23 start-page: 62 year: 2015 ident: 10.1016/j.sysconle.2025.106043_b14 article-title: On active disturbance rejection control for nonlinear systems using time-varying gain publication-title: Eur. J. Control doi: 10.1016/j.ejcon.2015.02.002 – volume: 128 year: 2024 ident: 10.1016/j.sysconle.2025.106043_b26 article-title: Adaptive error feedback regulator problem for a 1-D wave equation with velocity recirculation publication-title: Commun. Nonlinear Sci. Numer. Simul. doi: 10.1016/j.cnsns.2023.107659 – year: 2009 ident: 10.1016/j.sysconle.2025.106043_b28 – year: 1996 ident: 10.1016/j.sysconle.2025.106043_b35 – volume: 59 start-page: 2708 year: 2014 ident: 10.1016/j.sysconle.2025.106043_b31 article-title: The state feedback regulator problem for regular linear systems publication-title: IEEE Trans. Automat. Control doi: 10.1109/TAC.2014.2326491 – year: 2023 ident: 10.1016/j.sysconle.2025.106043_b24 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: 4 start-page: 303 issue: 3 year: 1993 ident: 10.1016/j.sysconle.2025.106043_b29 article-title: Decay estimates of solutions for a hybrid system of flexible structures publication-title: Eur. J. Appl. Math. doi: 10.1017/S0956792500001133 – volume: 52 start-page: 3967 year: 2014 ident: 10.1016/j.sysconle.2025.106043_b5 article-title: The internal model principle for systems with unbounded control and observation publication-title: SIAM J. Control Optim. doi: 10.1137/130921362 – volume: 42 start-page: 4 year: 1997 ident: 10.1016/j.sysconle.2025.106043_b34 article-title: Dynamic stabilization of regular linear systems publication-title: IEEE Trans. Automat. Control doi: 10.1109/9.553684 |
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| Snippet | In this paper, we apply internal model principle (IMP) and the adaptive frequency estimation strategy to achieve output tracking for a one-dimensional wave... |
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| SubjectTerms | Adaptive output tracking Error feedback Internal model dynamic Wave equation |
| Title | Adaptive output regulation for wave PDEs with a nonlocal term and unknown harmonic disturbances |
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