Backstepping control of a wave PDE with unstable source terms and dynamic boundary
Authors: C. Roman, D. Bresch-Pietri, E. Cerpa, C. Prieur and O. Sename, IEEE Control Systems Letters, Vol. 2, No. 3, pp. 459 - 464, July 2018, DOI: 10.1109/LCSYS.2018.2841898
This letter presents the design of an exponentially stabilizing controller for a one-dimensional wave partial differential equation. The control is acting on a Robin's boundary condition while the opposite boundary satisfies an unstable dynamic. The wave is also subject to unstable in-domain source terms. Closed-loop exponential stabilization is obtained via a full-state backstepping controller. The existence and uniqueness of this backstepping transformation is proven, using the method of successive approximations.
BibTeX:
@Article{,
author = {C. Roman, D. Bresch-Pietri, E. Cerpa, C. Prieur and O. Sename},
title = {Backstepping control of a wave PDE with unstable source terms and dynamic boundary},
journal = {IEEE Control Systems Letters},
volume = {2},
number = {3},
pages = {459 – 464},
year = {2018},
abstract = {This letter presents the design of an exponentially stabilizing controller for a one-dimensional wave partial differential equation. The control is acting on a Robin’s boundary condition while the opposite boundary satisfies an unstable dynamic. The wave is also subject to unstable in-domain source terms. Closed-loop exponential stabilization is obtained via a full-state backstepping controller. The existence and uniqueness of this backstepping transformation is proven, using the method of successive approximations.}, }
This letter presents the design of an exponentially stabilizing controller for a one-dimensional wave partial differential equation. The control is acting on a Robin's boundary condition while the opposite boundary satisfies an unstable dynamic. The wave is also subject to unstable in-domain source terms. Closed-loop exponential stabilization is obtained via a full-state backstepping controller. The existence and uniqueness of this backstepping transformation is proven, using the method of successive approximations.
BibTeX:
@Article{,
author = {C. Roman, D. Bresch-Pietri, E. Cerpa, C. Prieur and O. Sename},
title = {Backstepping control of a wave PDE with unstable source terms and dynamic boundary},
journal = {IEEE Control Systems Letters},
volume = {2},
number = {3},
pages = {459 – 464},
year = {2018},
abstract = {This letter presents the design of an exponentially stabilizing controller for a one-dimensional wave partial differential equation. The control is acting on a Robin’s boundary condition while the opposite boundary satisfies an unstable dynamic. The wave is also subject to unstable in-domain source terms. Closed-loop exponential stabilization is obtained via a full-state backstepping controller. The existence and uniqueness of this backstepping transformation is proven, using the method of successive approximations.}, }