Energy-based Control of a Wave Equation with Boundary Anti-damping. Issue 2 (2020)

• Record Type: Journal Article
• Authors: Macchelli, A.; Gorrec, Y. Le; Wu, Y.; Ramírez, H.
• Is Part Of: IFAC-PapersOnLine. Volume 53:Issue 2(2020)
• Page Start: 7740
• Page End: 7745
• Publication Date: 2020
• Subjects: distributed parameter systems -- port-Hamiltonian systems -- unstable wave equation -- passivity-based control; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2020.12.1527
• Languages: English
• ISSNs: 2405-8963

Abstract

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.