Hamilton-Jacobi equations for optimal control on multidimensional junctions with entry costs

被引：0

作者：

Dao, Manh-Khang ^{[1
]}

Djehiche, Boualem ^{[1
]}

机构：

[1] KTH Royal Inst Technol, Dept Math, S-10044 Stockholm, Sweden

来源：

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS | 2020年 / 27卷 / 02期

基金：

瑞典研究理事会;

关键词：

Optimal control; Multidimensional junctions; Hamilton-Jacobi equation; Viscosity solutions; Switching cost; VISCOSITY SOLUTIONS; EIKONAL EQUATIONS; BELLMAN APPROACH; WELL-POSEDNESS;

D O I：

10.1007/s00030-020-0625-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider an infinite horizon control problem for dynamics constrained to remain on a multidimensional junction with entry costs. We derive the associated system of Hamilton-Jacobi equations (HJ), prove the comparison principle and that the value function of the optimal control problem is the unique viscosity solution of the HJ system. This is done under the usual strong controllability assumption and also under a weaker condition, coined 'moderate controllability assumption'.

引用

页数：42

共 50 条

[1] Hamilton–Jacobi equations for optimal control on multidimensional junctions with entry costs
Manh-Khang Dao
Boualem Djehiche
Nonlinear Differential Equations and Applications NoDEA, 2020, 27
[2] HAMILTON-JACOBI EQUATIONS FOR OPTIMAL CONTROL ON NETWORKS WITH ENTRY OR EXIT COSTS
Manh Khang Dao
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2019, 25
[3] HAMILTON-JACOBI EQUATIONS FOR OPTIMAL CONTROL ON JUNCTIONS AND NETWORKS
Achdou, Yves
Oudet, Salome
Tchou, Nicoletta
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2015, 21 (03) : 876 - 899
[4] Hamilton-Jacobi equations for optimal control on junctions with unbounded running cost functions
Phan Trong Tien
Tran Van Bang
APPLICABLE ANALYSIS, 2021, 100 (07) : 1397 - 1413
[5] SEMICONCAVE FUNCTIONS, HAMILTON-JACOBI EQUATIONS, AND OPTIMAL CONTROL
Maslowski, Bohdan
MATHEMATICA BOHEMICA, 2007, 132 (02): : 220 - 220
[6] Semiconcave Functions, Hamilton-Jacobi equations and Optimal Control
Pascu, Mihai
REVUE ROUMAINE DE MATHEMATIQUES PURES ET APPLIQUEES, 2007, 52 (05): : 592 - 594
[7] Semiconcave Functions, Hamilton-Jacobi Equations, and Optimal Control
Pascu, Mihai
REVUE ROUMAINE DE MATHEMATIQUES PURES ET APPLIQUEES, 2007, 52 (01): : 121 - 122
[8] Central schemes for multidimensional Hamilton-Jacobi equations
Bryson, S
Levy, D
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2003, 25 (03): : 767 - 791
[9] HAMILTON-JACOBI EQUATIONS FOR OPTIMAL CONTROL ON JUNCTIONS AND NETWORKS (vol 21, pg 876, 2015)
Achdou, Yves
Oudet, Salome
Tchou, Nicoletta
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2016, 22 (02) : 539 - 542
[10] THE NONCONVEX MULTIDIMENSIONAL RIEMANN PROBLEM FOR HAMILTON-JACOBI EQUATIONS
BARDI, M
OSHER, S
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1991, 22 (02) : 344 - 351

← 1 2 3 4 5 →