Verification theorems for Hamilton-Jacobi-Bellman equations

被引：1
|
作者：
Garavello, M [1 ]
机构：
[1] SISSA, ISAS, I-34014 Trieste, Italy
来源：
SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2003年 / 42卷 / 05期
关键词：
verification theorem; optimal control; HJB equation; value function; viscosity solution;
D O I：
10.1137/S0363012902392688
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 study an optimal control problem in Bolza form, and we consider the value function associated to this problem. We prove two verification theorems which ensure that, if a function W satisfies some suitable weak continuity assumptions and a Hamilton-Jacobi-Bellman inequality outside a countably H-n-rectifiable set, then it is lower than or equal to the value function. These results can be used for optimal synthesis approach.
引用
收藏
页码：1623 / 1642
页数：20
相关论文
共 50 条
  • [21] Adaptive spline interpolation for Hamilton-Jacobi-Bellman equations
    Bauer, Florian
    Gruene, Lars
    Semmler, Willi
    APPLIED NUMERICAL MATHEMATICS, 2006, 56 (09) : 1196 - 1210
  • [22] VISCOSITY SOLUTIONS OF STOCHASTIC HAMILTON-JACOBI-BELLMAN EQUATIONS
    Qiu, Jinniao
    SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2018, 56 (05) : 3708 - 3730
  • [23] LOWER SEMICONTINUOUS SOLUTIONS OF HAMILTON-JACOBI-BELLMAN EQUATIONS
    FRANKOWSKA, H
    SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1993, 31 (01) : 257 - 272
  • [24] Hamilton-Jacobi-Bellman equations for quantum optimal control
    Gough, J.
    Belavkin, V. A.
    Smolyanov, O. G.
    PROCEEDINGS OF THE INTERNATIONAL CONFERENCE DAYS ON DIFFRACTION 2006, 2006, : 293 - 297
  • [25] Optimal soaring via Hamilton-Jacobi-Bellman equations
    Almgren, Robert
    Tourin, Agnes
    OPTIMAL CONTROL APPLICATIONS & METHODS, 2015, 36 (04): : 475 - 495
  • [26] SOBOLEV WEAK SOLUTIONS OF THE HAMILTON-JACOBI-BELLMAN EQUATIONS
    Wei, Lifeng
    Wu, Zhen
    Zhao, Huaizhong
    SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2014, 52 (03) : 1499 - 1526
  • [27] Policy Iteration for Exploratory Hamilton-Jacobi-Bellman Equations
    Tran, Hung Vinh
    Wang, Zhenhua
    Zhang, Yuming Paul
    APPLIED MATHEMATICS AND OPTIMIZATION, 2025, 91 (02):
  • [28] Improved Patchy Solution to the Hamilton-Jacobi-Bellman Equations
    Hunt, Thomas
    Krener, Arthur J.
    49TH IEEE CONFERENCE ON DECISION AND CONTROL (CDC), 2010, : 5835 - 5839
  • [29] NUMERICAL-ANALYSIS OF HAMILTON-JACOBI-BELLMAN EQUATIONS
    CORTEYDUMONT, P
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 1987, 9 (02) : 198 - 209
  • [30] AN ASYMPTOTIC FORMULA FOR SOLUTIONS OF HAMILTON-JACOBI-BELLMAN EQUATIONS
    KOIKE, S
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1987, 11 (03) : 429 - 436
12345