TY - JOUR
T1 - Boundary feedback control of linear hyperbolic systems
T2 - Application to the Saint-Venant–Exner equations
AU - Prieur, Christophe
AU - Winkin, Joseph J.
N1 - Funding Information:
This work was supported by the PHC Tournesol FR 2012 , project 27310WK , and by HYCON2 Network of Excellence “Highly-Complex and Networked Control Systems” , grant agreement 257462 . The material in this paper was not presented at any conference. This paper was recommended for publication in revised form by Associate Editor Rafael Vazquez under the direction of Editor Miroslav Krstic.
Funding Information:
This paper presents research results of the Belgian network DYSCO (Dynamical Systems, Control and Optimization), funded by the Interuniversity Attraction Poles Programme ( IAP VII/19 ), initiated by the Belgian state, Science Policy Office (BELSPO). The scientific responsibility rests with its authors.
Publisher Copyright:
© 2017 Elsevier Ltd
Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2018/3/1
Y1 - 2018/3/1
N2 - Distributed parameter systems modeled by hyperbolic partial differential equations are considered in this paper. The dynamic models include a source term and heterodirectional velocities. A boundary control problem is introduced and it is first shown that it is well-posed (in the sense of Tucsnak and Weiss), under appropriate assumptions coupling the boundary conditions and the source term. Then a sufficient exponential stability condition is derived using operator theory. This condition is written in terms of Linear Matrix Inequalities that are numerically tractable and that allow an optimization program. Connections with another classical stability condition are given. This approach is applied to the Saint-Venant–Exner equation describing the dynamics of the water level, of the water flow and of the sediment inside of a channel. The effect of the friction and of the slope are taken into account in the application model.
AB - Distributed parameter systems modeled by hyperbolic partial differential equations are considered in this paper. The dynamic models include a source term and heterodirectional velocities. A boundary control problem is introduced and it is first shown that it is well-posed (in the sense of Tucsnak and Weiss), under appropriate assumptions coupling the boundary conditions and the source term. Then a sufficient exponential stability condition is derived using operator theory. This condition is written in terms of Linear Matrix Inequalities that are numerically tractable and that allow an optimization program. Connections with another classical stability condition are given. This approach is applied to the Saint-Venant–Exner equation describing the dynamics of the water level, of the water flow and of the sediment inside of a channel. The effect of the friction and of the slope are taken into account in the application model.
UR - http://www.scopus.com/inward/record.url?scp=85038087409&partnerID=8YFLogxK
U2 - 10.1016/j.automatica.2017.11.028
DO - 10.1016/j.automatica.2017.11.028
M3 - Article
AN - SCOPUS:85038087409
SN - 0005-1098
VL - 89
SP - 44
EP - 51
JO - Automatica
JF - Automatica
ER -