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- W3216848570 abstract "We consider the problem of exponential tracking and disturbance rejection for the nonlinear unstable gradient-dependent wave equation via boundary control without any geometrical conditions on the domain. By splitting the tracking problem into a linear exponentially stable wave equation and a nonlinear dynamical regulator wave equation, we construct an explicit feedback and feedforward boundary controller that involves the reference, the disturbance and the solutions of the two problems. If the controller is applied on the whole boundary and the nonlinearity is globally Lipschitz, then we prove that the wave average tracks a desired reference signal exponentially by using the wave Green's function and the Banach contraction fixed point theorem. If the controller is applied on only a part of the boundary, then the same result is proved for a linear unstable gradient-dependent wave equation, but it is open for the nonlinear wave equation. Furthermore, as a robust analysis, we prove that the change of tracking error continuously depends on the change of disturbance. As usual, the rate of convergence of tracking error is independent of the feedforward part of the controller. A numerical example is given to confirm our theoretical results." @default.
- W3216848570 created "2021-12-06" @default.
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- W3216848570 date "2022-04-01" @default.
- W3216848570 modified "2023-09-25" @default.
- W3216848570 title "The exponential tracking and disturbance rejection for the nonlinear wave equation via boundary control without any geometrical conditions on the domain" @default.
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- W3216848570 doi "https://doi.org/10.1016/j.jmaa.2021.125863" @default.
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