STABILIZATION OF A MULTI-DIMENSIONAL SYSTEM OF HYPERBOLIC BALANCE LAWS

被引：3
作者：
Herty, Michael [1 ]
Thein, Ferdinand [1 ]
机构：
[1] IGPM RWTH Aachen, Templergraben 55, D-52056 Aachen, Germany
来源：
MATHEMATICAL CONTROL AND RELATED FIELDS | 2024年 / 14卷 / 03期
关键词：
Lyapunov stability; Control of PDEs; IBVP for hyperbolic PDE systems; DISSIPATIVE BOUNDARY-CONDITIONS; LYAPUNOV STABILITY; NUMERICAL DISCRETIZATION; FEEDBACK STABILIZATION; VENANT EQUATIONS; CAUCHY-PROBLEM; GAS-FLOW; CONTROLLABILITY; NETWORKS; SCHEMES;
D O I：
10.3934/mcrf.2023033
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
. We are interested in the feedback stabilization of systems described by Hamilton-Jacobi type equations in R-n. A reformulation leads to a stabilization problem for a multi-dimensional system of n hyperbolic partial differential equations. Using a novel Lyapunov function taking into account the multi-dimensional geometry we show stabilization in L(2 )for the arising system using a suitable feedback control. We further present examples of such systems partially based on a forming process.
引用
收藏
页码：1033 / 1047
页数：15
相关论文
共 39 条
  • [1] [Anonymous], 2010, AIMS series on applied mathematics
  • [2] Gas flow in pipeline networks
    Banda, Mapundi K.
    Herty, Michael
    Klar, Axel
    [J]. NETWORKS AND HETEROGENEOUS MEDIA, 2006, 1 (01) : 41 - 56
  • [3] NUMERICAL DISCRETIZATION OF STABILIZATION PROBLEMS WITH BOUNDARY CONTROLS FOR SYSTEMS OF HYPERBOLIC CONSERVATION LAWS
    Banda, Mapundi K.
    Herty, Michael
    [J]. MATHEMATICAL CONTROL AND RELATED FIELDS, 2013, 3 (02) : 121 - 142
  • [4] Bardos C., 1979, COMMUN PART DIFF EQ, V4, P1017, DOI DOI 10.1080/03605307908820117
  • [5] Lyapunov stability analysis of networks of scalar conservation laws
    Bastin, G.
    Haut, B.
    Coron, J-M.
    D'Andrea-Novel, B.
    [J]. NETWORKS AND HETEROGENEOUS MEDIA, 2007, 2 (04) : 751 - 759
  • [6] Bastin G, 2016, PROG NONLINEAR DIFFE, V88, P1, DOI 10.1007/978-3-319-32062-5
  • [7] Exponential boundary feedback stabilization of a shock steady state for the inviscid Burgers equation
    Bastin, Georges
    Coron, Jean-Michel
    Hayat, Amaury
    Shang, Peipei
    [J]. MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2019, 29 (02) : 271 - 316
  • [8] Bastin G, 2008, IEEE DECIS CONTR P, P1454
  • [9] ON LYAPUNOV STABILITY OF LINEARISED SAINT-VENANT EQUATIONS FOR A SLOPING CHANNEL
    Bastin, Georges
    Coron, Jean-Michel
    d'Andrea-Novel, Brigitte
    [J]. NETWORKS AND HETEROGENEOUS MEDIA, 2009, 4 (02) : 177 - 187
  • [10] BRENNER P, 1966, MATH SCAND, V19, P27
1234