Time-optimal pursuit of two evaders in given succession

Igor I. Shevchenko

Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 3 (2011) no. 2, pp. 102-117

Résumé

The paper studies two games, $\Gamma_{1,2}$ and $\Gamma_{2,1}$, of a faster pursuer $P$ and two slower evaders $E_1$ and $E_2$ controlled by a player $E$. $P$, $E_1$ and $E_2$ move in the plane with simple motions. In $\Gamma_{l,3-l}$, $P$ strives to approach $E_l$, and then capture $E_{3-l}$ in minimum total time, $l\in\{1,2\}$. $\Gamma_{l,3-l}$ models tactic operations where $E$ sets a decoy to seduce $P$ to follow it, and $P$ is to construct a pursuit strategy and evaluate a guaranteed total time needed to reclassify the decoy ($E_l$) and to seize the real target ($E_{3-l}$). $\Gamma_{l,3-l}$ is divided into two stages. The second stage is a simple pursuit game $\Gamma^{II}_{l,3-l}$ with a known solution. At the first stage $\Gamma^I_{l,3-l}$, the payoff is equal to the sum of the duration and the value of $\Gamma^{II}_{l,3-l}$ at the terminal state. We analyze $\Gamma^I_{1,2}$ in detail using the classic characteristics for Isaacs–Bellman equation.

Détail

Keywords: Isaacs' approach, discriminating feedback strategies, singular surfaces, directionally differentiable value function
Mots-clés : decoy.