TY - GEN
T1 - Backstepping stabilization of the linearized Saint-Venant-Exner Model
T2 - 54th IEEE Conference on Decision and Control, CDC 2015
AU - Diagne, Ababacar
AU - Diagne, Mamadou
AU - Tang, Shuxia
AU - Krstic, Miroslav
N1 - Funding Information:
ACKNOWLEDGMENT The first author was supported by grants from Lisa and Carl-Gustav Esseen foundation.
Publisher Copyright:
© 2015 IEEE.
PY - 2015/2/8
Y1 - 2015/2/8
N2 - We consider a coupled Saint-Venant-Exner (SVE) model introduced in a companion paper. This studied model describes the water dynamics in a sediment-filled canal with arbitrary values of canal bottom slope, friction, porosity, and water-sediment interaction under subcritical or supercritical flow regime. It consists of two rightward and one leftward convecting transport Partial Differential Equations (PDEs). A single boundary input control (with actuation located only at downstream) strategy is adopted and the backstepping approach developed for the first order linear hyperbolic PDEs is used. A full state feedback exponentially stabilizing controller is designed in the companion paper. In this paper, we first design an exponentially convergent Luenberger observer. Then, based on the full state controller and reconstruction of the distributed state from the observer, we achieve output feedback exponential stabilization of the model.
AB - We consider a coupled Saint-Venant-Exner (SVE) model introduced in a companion paper. This studied model describes the water dynamics in a sediment-filled canal with arbitrary values of canal bottom slope, friction, porosity, and water-sediment interaction under subcritical or supercritical flow regime. It consists of two rightward and one leftward convecting transport Partial Differential Equations (PDEs). A single boundary input control (with actuation located only at downstream) strategy is adopted and the backstepping approach developed for the first order linear hyperbolic PDEs is used. A full state feedback exponentially stabilizing controller is designed in the companion paper. In this paper, we first design an exponentially convergent Luenberger observer. Then, based on the full state controller and reconstruction of the distributed state from the observer, we achieve output feedback exponential stabilization of the model.
UR - http://www.scopus.com/inward/record.url?scp=84962019181&partnerID=8YFLogxK
U2 - 10.1109/CDC.2015.7402382
DO - 10.1109/CDC.2015.7402382
M3 - Conference contribution
AN - SCOPUS:84962019181
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 1248
EP - 1253
BT - 54rd IEEE Conference on Decision and Control,CDC 2015
PB - Institute of Electrical and Electronics Engineers Inc.
Y2 - 15 December 2015 through 18 December 2015
ER -