Geodesic
Predictor control for wave PDE / nonlinear ODE cascaded system with boundary value-dependent propagation speed
Kybernetika, Tome 58 (2022) no. 3, pp. 400-425.

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This paper investigates predictor control for wave partial differential equation (PDE) and nonlinear ordinary differential equation (ODE) cascaded system with boundary value-dependent propagation speed. A predictor control is designed first. A two-step backstepping transformation and a new time variable are employed to derive a target system whose stability is established using Lyapunov arguments. The equivalence between stability of the target and the original system is provided using the invertibility of the backstepping transformations. Stability of the closed-loop system is established by Lyapunov arguments.
DOI : 10.14736/kyb-2022-3-0400
Classification : 93Cxx, 93Dxx
Keywords: cascaded system; wave dynamics; boundary value-dependent; predictor control; backstepping transformation 
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     author = {Cai, Xiushan and Lin, Yuhang and Zhang, Junfeng and Lin, Cong},
     title = {Predictor control for wave {PDE} / nonlinear {ODE} cascaded system with boundary value-dependent propagation speed},
     journal = {Kybernetika},
     pages = {400--425},
     publisher = {mathdoc},
     volume = {58},
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     url = {http://geodesic.mathdoc.fr/articles/10.14736/kyb-2022-3-0400/}
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Cai, Xiushan; Lin, Yuhang; Zhang, Junfeng; Lin, Cong. Predictor control for wave PDE / nonlinear ODE cascaded system with boundary value-dependent propagation speed. Kybernetika, Tome 58 (2022) no. 3, pp. 400-425. doi : 10.14736/kyb-2022-3-0400. http://geodesic.mathdoc.fr/articles/10.14736/kyb-2022-3-0400/

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