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.
Energy-based control of a wave equation with boundary anti-damping / Macchelli A.; Le Gorrec Y.; Wu Y.; Ramirez H.. - STAMPA. - 53:2(2020), pp. 7740-7745. (Intervento presentato al convegno 21st IFAC World Congress 2020 tenutosi a Berlin nel 2020) [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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
