In this paper, we consider the asymptotic boundary stabilisation of a one-dimensional wave equation subject to anti-damping at its free end and with control at the opposite one. The control action, implemented through a state feedback or a dynamic controller, is derived by using the port-Hamiltonian framework. More precisely, the standard energy-shaping approach plus damping assignment is adapted to cope with infinite dimensional systems with anti-damping boundary conditions. It is shown how to modify the equivalent dynamic controller to account for the instability propagation along the domain.
Macchelli, A., Le Gorrec, Y., Wu, Y., Ramirez, H. (2020). Energy-based control of a wave equation with boundary anti-damping. AMSTERDAM : Elsevier B.V. [10.1016/j.ifacol.2020.12.1527].
Energy-based control of a wave equation with boundary anti-damping
Macchelli A.
;
2020
Abstract
In this paper, we consider the asymptotic boundary stabilisation of a one-dimensional wave equation subject to anti-damping at its free end and with control at the opposite one. The control action, implemented through a state feedback or a dynamic controller, is derived by using the port-Hamiltonian framework. More precisely, the standard energy-shaping approach plus damping assignment is adapted to cope with infinite dimensional systems with anti-damping boundary conditions. It is shown how to modify the equivalent dynamic controller to account for the instability propagation along the domain.| File | Dimensione | Formato | |
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