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- W4292059072 abstract "<p>This paper addresses a target-guarding differential game involving a single attacker, a group of faster defenders, and a convex target set. The goal of the defenders is to guard the target set, which is assumed to be a convex subset of R^n, from the attacker who attempts to reach the same set. In contrast to standard geometric formulations of this type of problems in the literature, we propose a new solution approach based on parametric optimization. In the proposed approach, the high- dimensional game is reduced into a parametric convex program, whose parameter corresponds to the state of the game and its objective is to find the capture point that determines the optimal policies of the players. The solution of this program is proven to be the unique fixed point of the composite projection operator associated with the feasible set of the program and the target set. An algorithm to find the latter solution is presented. We further show that, under certain conditions, the value function of the program is continuously differentiable and satisfies the Hamilton- Jacobi-Isaacs equation, thereby verifying its equivalence with the Value function of the game. Lastly, we highlight the effectiveness of our approach by means of numerical simulations.</p>" @default.
- W4292059072 created "2022-08-17" @default.
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- W4292059072 date "2022-08-16" @default.
- W4292059072 modified "2023-09-28" @default.
- W4292059072 title "Solutions for Games of Guarding an Arbitrary Convex Target Set with Multiple Defenders in R^n" @default.
- W4292059072 doi "https://doi.org/10.36227/techrxiv.20468970.v1" @default.
- W4292059072 hasPublicationYear "2022" @default.
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