ON THE SEMI-GLOBAL STABILIZABILITY OF THE KORTEWEG-DE VRIES EQUATION VIA MODEL PREDICTIVE CONTROL

被引：5
作者：
Azmi, Behzad [1 ]
Boulanger, Anne-Celine [2 ]
Kunisch, Karl [1 ]
机构：
[1] Karl Franzens Univ Graz, Inst Math & Sci Comp, Heinrichstr 36, A-8010 Graz, Austria
[2] Tech Univ Munich, Munich, Germany
来源：
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS | 2018年 / 24卷 / 01期
基金：
奥地利科学基金会;
关键词：
Receding horizon control; model predictive control; asymptotic stability; infinite-dimensional systems; EXACT BOUNDARY CONTROLLABILITY; LEGENDRE-PETROV-GALERKIN; BURGERS-EQUATION; FINITE; STABILIZATION; DECAY; 3RD-ORDER;
D O I：
10.1051/cocv/2017001
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
Stabilization of the nonlinear Korteweg-de Vries (KdV) equation on a bounded interval by model predictive control (MPG) is investigated. This MPG strategy does not need any terminal cost or terminal constraint to guarantee the stability. The semi-global stabilizability is the key condition. Based on this condition, the suboptimality and exponential stability of the model predictive control are investigated. Finally, numerical experiment is presented which validates the theoretical results.
引用
收藏
页码：237 / 263
页数：27
相关论文
共 57 条
[1]  
Allgower F., 1999, Advances in Control. Highlights of ECC'99, P391
[2]  
[Anonymous], 2010, FUNCTIONAL ANAL
[3]  
[Anonymous], 1986, Annali di Matematica Pura ed Applicata, DOI [DOI 10.1007/BF01762360.MR916688, DOI 10.1007/BF01762360]
[4]  
[Anonymous], 2012, SEMIGROUPS LINEAR OP
[5]   A SUPERCONVERGENT FINITE-ELEMENT METHOD FOR THE KORTEWEG-DE VRIES EQUATION [J].
ARNOLD, DN ;
WINTHER, R .
MATHEMATICS OF COMPUTATION, 1982, 38 (157) :23-36
[6]   ON THE STABILIZABILITY OF THE BURGERS EQUATION BY RECEDING HORIZON CONTROL [J].
Azmi, Behzad ;
Kunisch, Karl .
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2016, 54 (03) :1378-1405
[7]   STRONGLY CONTINUOUS SEMIGROUPS, WEAK SOLUTIONS, AND VARIATION OF CONSTANTS FORMULA [J].
BALL, JM .
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1977, 63 (02) :370-373
[8]   2-POINT STEP SIZE GRADIENT METHODS [J].
BARZILAI, J ;
BORWEIN, JM .
IMA JOURNAL OF NUMERICAL ANALYSIS, 1988, 8 (01) :141-148
[9]  
Bensoussan A., 2007, Representation and Control of Infinite Dimensional Systems, Systems Control Found
[10]   A non-homogeneous boundary-value problem for the Korteweg-de Vries equation posed on a finite domain II [J].
Bona, Jerry L. ;
Sun, Shu Ming ;
Zhang, Bing-Yu .
JOURNAL OF DIFFERENTIAL EQUATIONS, 2009, 247 (09) :2558-2596
123456