TY - JOUR

T1 - Sustainable Optimal Control for Switched Pollution-Control Problem with Random Duration

AU - Ву, Ийлунь

AU - Тур, Анна Викторовна

AU - Wang, Hongbo

PY - 2023/10/8

Y1 - 2023/10/8

N2 - Considering the uncertainty of game duration and periodic seasonal fluctuation, an n-player switched pollution-control differential game is modeled to investigate a sustainable and adaptive strategy for players. Based on the randomness of game duration, two scenarios are considered in this study. In the first case, the game duration is a random variable, Tf, described by the shifted exponential distribution. In the second case, we assumed that players' equipment is heterogeneous, and the i-th player's equipment failure time, Tfi, is described according to the shifted exponential distribution. The game continues until a player's equipment breaks down. Thus, the game duration is defined as Tf=min{Tf1,…,Tfn}. To achieve the goal of sustainable development, an environmentally sustainable strategy and its corresponding condition are defined. By using Pontryagin's maximum principle, a unique control solution is obtained in the form of a hybrid limit cycle, the state variable converges to a stable hybrid limit cycle, and the total payoff of all players increases and then converges. The results indicate that the environmentally sustainable strategy in the n-player pollution-control cooperative differential game with switches and random duration is a unique strategy that not only ensures profit growth but also considers environmental protection.

AB - Considering the uncertainty of game duration and periodic seasonal fluctuation, an n-player switched pollution-control differential game is modeled to investigate a sustainable and adaptive strategy for players. Based on the randomness of game duration, two scenarios are considered in this study. In the first case, the game duration is a random variable, Tf, described by the shifted exponential distribution. In the second case, we assumed that players' equipment is heterogeneous, and the i-th player's equipment failure time, Tfi, is described according to the shifted exponential distribution. The game continues until a player's equipment breaks down. Thus, the game duration is defined as Tf=min{Tf1,…,Tfn}. To achieve the goal of sustainable development, an environmentally sustainable strategy and its corresponding condition are defined. By using Pontryagin's maximum principle, a unique control solution is obtained in the form of a hybrid limit cycle, the state variable converges to a stable hybrid limit cycle, and the total payoff of all players increases and then converges. The results indicate that the environmentally sustainable strategy in the n-player pollution-control cooperative differential game with switches and random duration is a unique strategy that not only ensures profit growth but also considers environmental protection.

KW - cooperative game

KW - differential game

KW - random duration

KW - sustainability

KW - switched system

UR - https://www.mendeley.com/catalogue/23812829-8be7-3644-80b6-06d2fbcf0c4f/

U2 - 10.3390/e25101426

DO - 10.3390/e25101426

M3 - Article

C2 - 37895547

VL - 25

JO - Entropy

JF - Entropy

SN - 1099-4300

IS - 10

M1 - 1426

ER -