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On the basis properties of the functions arising in the boundary control problem of a string with a variable tension
1. | University of Alaska Fairbanks, Fairbanks, AK 99775-6660, United States |
2. | Department of Mathematics, University of Tennessee at Chattanooga, 615 McCallie Avenue, Chattanooga, TN 37403-2598, United States |
[1] |
Harry L. Johnson, David Russell. Transfer function approach to output specification in certain linear distributed parameter systems. Conference Publications, 2003, 2003 (Special) : 449-458. doi: 10.3934/proc.2003.2003.449 |
[2] |
Dominique Chapelle, Philippe Moireau, Patrick Le Tallec. Robust filtering for joint state-parameter estimation in distributed mechanical systems. Discrete and Continuous Dynamical Systems, 2009, 23 (1&2) : 65-84. doi: 10.3934/dcds.2009.23.65 |
[3] |
Scott W. Hansen, Rajeev Rajaram. Riesz basis property and related results for a Rao-Nakra sandwich beam. Conference Publications, 2005, 2005 (Special) : 365-375. doi: 10.3934/proc.2005.2005.365 |
[4] |
Getachew K. Befekadu, Eduardo L. Pasiliao. On the hierarchical optimal control of a chain of distributed systems. Journal of Dynamics and Games, 2015, 2 (2) : 187-199. doi: 10.3934/jdg.2015.2.187 |
[5] |
Libin Wang. Breakdown of $C^1$ solution to the Cauchy problem for quasilinear hyperbolic systems with characteristics with constant multiplicity. Communications on Pure and Applied Analysis, 2003, 2 (1) : 77-89. doi: 10.3934/cpaa.2003.2.77 |
[6] |
Kareem T. Elgindy. Optimal control of a parabolic distributed parameter system using a fully exponentially convergent barycentric shifted gegenbauer integral pseudospectral method. Journal of Industrial and Management Optimization, 2018, 14 (2) : 473-496. doi: 10.3934/jimo.2017056 |
[7] |
Marc Puche, Timo Reis, Felix L. Schwenninger. Funnel control for boundary control systems. Evolution Equations and Control Theory, 2021, 10 (3) : 519-544. doi: 10.3934/eect.2020079 |
[8] |
Domingo Tarzia, Carolina Bollo, Claudia Gariboldi. Convergence of simultaneous distributed-boundary parabolic optimal control problems. Evolution Equations and Control Theory, 2020, 9 (4) : 1187-1201. doi: 10.3934/eect.2020045 |
[9] |
Xavier Litrico, Vincent Fromion, Gérard Scorletti. Robust feedforward boundary control of hyperbolic conservation laws. Networks and Heterogeneous Media, 2007, 2 (4) : 717-731. doi: 10.3934/nhm.2007.2.717 |
[10] |
Gen Qi Xu, Siu Pang Yung. Stability and Riesz basis property of a star-shaped network of Euler-Bernoulli beams with joint damping. Networks and Heterogeneous Media, 2008, 3 (4) : 723-747. doi: 10.3934/nhm.2008.3.723 |
[11] |
Ngoc Minh Trang Vu, Laurent Lefèvre. Finite rank distributed control for the resistive diffusion equation using damping assignment. Evolution Equations and Control Theory, 2015, 4 (2) : 205-220. doi: 10.3934/eect.2015.4.205 |
[12] |
Volodymyr O. Kapustyan, Ivan O. Pyshnograiev, Olena A. Kapustian. Quasi-optimal control with a general quadratic criterion in a special norm for systems described by parabolic-hyperbolic equations with non-local boundary conditions. Discrete and Continuous Dynamical Systems - B, 2019, 24 (3) : 1243-1258. doi: 10.3934/dcdsb.2019014 |
[13] |
Serge Nicaise. Control and stabilization of 2 × 2 hyperbolic systems on graphs. Mathematical Control and Related Fields, 2017, 7 (1) : 53-72. doi: 10.3934/mcrf.2017004 |
[14] |
Barbara Kaltenbacher, William Rundell. On the identification of the nonlinearity parameter in the Westervelt equation from boundary measurements. Inverse Problems and Imaging, 2021, 15 (5) : 865-891. doi: 10.3934/ipi.2021020 |
[15] |
Atte Aalto, Jarmo Malinen. Compositions of passive boundary control systems. Mathematical Control and Related Fields, 2013, 3 (1) : 1-19. doi: 10.3934/mcrf.2013.3.1 |
[16] |
Xiaoqiang Dai, Chao Yang, Shaobin Huang, Tao Yu, Yuanran Zhu. Finite time blow-up for a wave equation with dynamic boundary condition at critical and high energy levels in control systems. Electronic Research Archive, 2020, 28 (1) : 91-102. doi: 10.3934/era.2020006 |
[17] |
C.P. Walkden. Solutions to the twisted cocycle equation over hyperbolic systems. Discrete and Continuous Dynamical Systems, 2000, 6 (4) : 935-946. doi: 10.3934/dcds.2000.6.935 |
[18] |
Gildas Besançon, Didier Georges, Zohra Benayache. Towards nonlinear delay-based control for convection-like distributed systems: The example of water flow control in open channel systems. Networks and Heterogeneous Media, 2009, 4 (2) : 211-221. doi: 10.3934/nhm.2009.4.211 |
[19] |
Zhiyong Sun, Toshiharu Sugie. Identification of Hessian matrix in distributed gradient-based multi-agent coordination control systems. Numerical Algebra, Control and Optimization, 2019, 9 (3) : 297-318. doi: 10.3934/naco.2019020 |
[20] |
Tomás Caraballo Garrido, Oleksiy V. Kapustyan, Pavlo O. Kasyanov, José Valero, Michael Zgurovsky. Preface to the special issue "Dynamics and control in distributed systems: Dedicated to the memory of Valery S. Melnik (1952-2007)". Discrete and Continuous Dynamical Systems - B, 2019, 24 (3) : i-v. doi: 10.3934/dcdsb.20193i |
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