A strict Lyapunov function for boundary control of hyperbolic systems of conservation laws

被引：285

作者：

Coron, Jean-Michel ^{[1
]}

d'Andrea-Novel, Brigitte

Bastin, Georges

机构：

[1] Univ Paris Sud, Dept Math, F-91405 Orsay, France

[2] Ecole Mines, Ctr Robot, F-75272 Paris 06, France

[3] Catholic Univ Louvain, Ctr Syst Engn & Appl Mech CESAME, B-1348 Louvain, Belgium

来源：

IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2007年 / 52卷 / 01期

关键词：

boundary control; conservation laws; hyperbolic systems; Lyapunov function; partial differential equations;

D O I：

10.1109/TAC.2006.887903

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We present a strict Lyapunov function for hyperbolic systems of conservation laws that can be diagonalized with Riemann invariants. The time derivative of this Lyapunov function can be made strictly negative definite by an appropriate choice of the boundary conditions. It is shown that the derived boundary control allows to guarantee the local convergence of the state towards a desired set point. Furthermore, the control can be implemented as a feedback of the state only measured at the boundaries. The control design method is illustrated with an hydraulic application, namely the level and flow regulation in an horizontal open channel.

引用

页码：2 / 11

页数：10

共 19 条

[1] AAMO OM, 2006, P IFAC S ADV CONTR C, P53
[2] [Anonymous], 1973, C BOARD MATH SCI REG
[3] Resurrection of "second order" models of traffic flow
Aw, A
Rascle, M
[J]. SIAM JOURNAL ON APPLIED MATHEMATICS, 2000, 60 (03) : 916 - 938
[4] Gas flow in pipeline networks
Banda, Mapundi K.
Herty, Michael
Klar, Axel
[J]. NETWORKS AND HETEROGENEOUS MEDIA, 2006, 1 (01) : 41 - 56
[5] Bastin G, 2005, IEEE DECIS CONTR P, P1086
[6] Brezis H., 1983, COLLECTION MATH APPL
[7] Coron JM, 2002, IEEE DECIS CONTR P, P3010, DOI 10.1109/CDC.2002.1184315
[8] On the null asymptotic stabilization of the two-dimensional incompressible Euler equations in a simply connected domain
Coron, JM
[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1999, 37 (06) : 1874 - 1896
[9] CORON JM, 1999, P EUR CONTR C KARLR
[10] Boundary control design for cascades of hyperbolic 2 X 2 PDE systems via graph theory.
de Halleux, J
Prieur, C
Bastin, G
[J]. 2004 43RD IEEE CONFERENCE ON DECISION AND CONTROL (CDC), VOLS 1-5, 2004, : 3313 - 3318

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