Open AccessA geometric approach to reach‐avoid games with time limits
Author(s) -
Chen Xi,
Yu Jianqiao,
Yang Di,
Niu Kang
Publication year - 2023
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/cth2.12374
Subject(s) - differential game , computer science , limit (mathematics) , construct (python library) , scope (computer science) , mathematical optimization , time limit , state (computer science) , sequential game , game theory , repeated game , work (physics) , simultaneous game , state space , mathematical economics , mathematics , algorithm , engineering , mechanical engineering , mathematical analysis , statistics , systems engineering , programming language
The differential games have been widely used to analyze the conflicts between intelligent agents. Motivated by the fact that the agents always have finite energy or time requirements, a novel reach‐avoid game with time limits is investigated in this work. The attacker aims to reach the target region without being captured or reaching its time limit, while the defender strives to intercept the attacker or delay it. This game is beyond the scope of the classical Hamilton‐Jacobi‐Isaacs (HJI) approach. To make the problem possible to solve, we introduce the concept of reaching region and provide the optimal strategies of the players based on it. Using these strategies, we construct a hypersurface, called the barrier, in the game state space which partitions it into two parts that lead to different outcomes of the game. In this work, the complete analytical expressions of the barrier in all possible situations are provided. The game results can be obtained by substituting the initial states into the related expression and there is barely any computational burden. Compare to the existing works, the game with time limits is more practical. Also, this work provides the foundation for analyzing general multiple‐attacker‐multiple‐defender games.