Standard

The Hamilton–Jacobi–Bellman Equation for Differential Games with Composite Distribution of Random Time Horizon. / Balas, Tatyana ; Tur, Anna .

In: Mathematics, Vol. 11, No. 2, 462, 15.01.2023.

Research output: Contribution to journal › Article › peer-review

Harvard

Balas, T & Tur, A 2023, 'The Hamilton–Jacobi–Bellman Equation for Differential Games with Composite Distribution of Random Time Horizon', Mathematics, vol. 11, no. 2, 462. https://doi.org/10.3390/math11020462

APA

Balas, T., & Tur, A. (2023). The Hamilton–Jacobi–Bellman Equation for Differential Games with Composite Distribution of Random Time Horizon. Mathematics, 11(2), [462]. https://doi.org/10.3390/math11020462

Vancouver

Balas T, Tur A. The Hamilton–Jacobi–Bellman Equation for Differential Games with Composite Distribution of Random Time Horizon. Mathematics. 2023 Jan 15;11(2). 462. https://doi.org/10.3390/math11020462

Author

Balas, Tatyana ; Tur, Anna . / The Hamilton–Jacobi–Bellman Equation for Differential Games with Composite Distribution of Random Time Horizon. In: Mathematics. 2023 ; Vol. 11, No. 2.

BibTeX

@article{0d5f50c8caf0430984c472fcdcd61747,
title = "The Hamilton–Jacobi–Bellman Equation for Differential Games with Composite Distribution of Random Time Horizon",
abstract = "A differential game with random duration is considered. The terminal time of the game is a random variable settled using a composite distribution function. Such a scenario occurs when the operating mode of the system changes over time at the appropriate switching points. On each interval between switchings, the distribution of the terminal time is characterized by its own distribution function. A method for solving such games using dynamic programming is proposed. An example of a non-renewable resource extraction model is given, where a solution of the problem of maximizing the total payoff in closed-loop strategies is found. An analytical view of the optimal control of each player and the optimal trajectory depending on the parameters of the described model is obtained.",
keywords = "differential game, random time horizon, composite distribution function, non-renewable resource extraction",
author = "Tatyana Balas and Anna Tur",
note = "Balas, T.; Tur, A. The Hamilton–Jacobi–Bellman Equation for Differential Games with Composite Distribution of Random Time Horizon. Mathematics 2023, 11, 462. https://doi.org/10.3390/math11020462",
year = "2023",
month = jan,
day = "15",
doi = "https://doi.org/10.3390/math11020462",
language = "English",
volume = "11",
journal = "Mathematics",
issn = "2227-7390",
publisher = "MDPI AG",
number = "2",

}

RIS

TY - JOUR

T1 - The Hamilton–Jacobi–Bellman Equation for Differential Games with Composite Distribution of Random Time Horizon

AU - Balas, Tatyana

AU - Tur, Anna

N1 - Balas, T.; Tur, A. The Hamilton–Jacobi–Bellman Equation for Differential Games with Composite Distribution of Random Time Horizon. Mathematics 2023, 11, 462. https://doi.org/10.3390/math11020462

PY - 2023/1/15

Y1 - 2023/1/15

N2 - A differential game with random duration is considered. The terminal time of the game is a random variable settled using a composite distribution function. Such a scenario occurs when the operating mode of the system changes over time at the appropriate switching points. On each interval between switchings, the distribution of the terminal time is characterized by its own distribution function. A method for solving such games using dynamic programming is proposed. An example of a non-renewable resource extraction model is given, where a solution of the problem of maximizing the total payoff in closed-loop strategies is found. An analytical view of the optimal control of each player and the optimal trajectory depending on the parameters of the described model is obtained.

AB - A differential game with random duration is considered. The terminal time of the game is a random variable settled using a composite distribution function. Such a scenario occurs when the operating mode of the system changes over time at the appropriate switching points. On each interval between switchings, the distribution of the terminal time is characterized by its own distribution function. A method for solving such games using dynamic programming is proposed. An example of a non-renewable resource extraction model is given, where a solution of the problem of maximizing the total payoff in closed-loop strategies is found. An analytical view of the optimal control of each player and the optimal trajectory depending on the parameters of the described model is obtained.

KW - differential game

KW - random time horizon

KW - composite distribution function

KW - non-renewable resource extraction

UR - https://www.mendeley.com/catalogue/329568bc-d073-37fa-bdad-f29085c4d892/

U2 - https://doi.org/10.3390/math11020462

DO - https://doi.org/10.3390/math11020462

M3 - Article

VL - 11

JO - Mathematics

JF - Mathematics

SN - 2227-7390

IS - 2

M1 - 462

ER -

ID: 102416649