Circular Target Defense Differential Games
成果类型：
Article
署名作者：
Von Moll, Alexander; Pachter, Meir; Shishika, Daigo; Fuchs, Zachariah
署名单位：
United States Department of Defense; United States Air Force; University System of Ohio; University of Cincinnati; United States Department of Defense; United States Air Force; Air Force Institute of Technology (AFIT); George Mason University; University System of Ohio; University of Cincinnati
刊物名称：
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
ISSN/ISSBN：
0018-9286
DOI：
10.1109/TAC.2022.3203357
发表日期：
2023
页码：
4065-4078
关键词：
Differential equations
differential games
optimal control
摘要：
In this article, the problem of guarding a circular target wherein the Defender(s) is constrained to move along its perimeter is posed and solved using a differential game theoretic approach. Both the one-Defender and two Defender scenarios are analyzed and solved. The mobile Attacker seeks to reach the perimeter of the circular target, whereas the Defender(s) seeks to align itself with the Attacker, thereby ending the game. In the former case, the Attacker-wins, and the Attacker and Defender play a zero sum differential game where the payoff/cost is the terminal angular separation. In the latter case, the Defender(s) wins, and the Attacker and Defender play a zero-sum differential game where the cost/payoff is the Attacker's terminal distance to the target. This formulation is representative of a scenario in which the Attacker inflicts damage on the target as a function of its terminal distance. The state-feedback equilibrium strategies and Value functions for the Attacker win and Defender(s)-win scenarios are derived for both the one-and two-Defender cases, thus providing a solution to the Game of Degree. Analytic expressions for the separating surfaces between the various terminal scenarios are derived, thus providing a solution to the Game of Kind. An alternative game is formulated and solved in the case of Attacker-win wherein the Attacker seeks to minimize time to reach the target.