Formal solutions for a class of stochastic pursuit-evasion games
Formal solutions for a class of stochastic pursuit-evasion games
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一类随机追逃博弈的形式化解
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发表时间：
1968
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通讯作者：
W. Willman
中科院分区：
文献类型：
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作者：
W. Willman
研究了一类微分追逃博弈，其中动力学是线性的，受加性高斯白噪声的干扰，性能指标是二次的，两个参与者都接受受加性高斯白噪声独立干扰的测量。线性极大极小解是用一组隐式积分微分方程来表示的。这种类型的博弈还具有“确定性-巧合”属性，即在所有噪声值为零的情况下，其极小-极大行为与相应的确定性博弈一致。该特性用于将极大极小策略分解为确定性等效项和误差项的和。
A class of differential pursuit-evasion games is examined in which the dynamics are linear and perturbed by additive white Gaussian noise, the performance index is quadratic, and both players receive measurements perturbed independently by additive white Gaussian noise. Linear minimax solutions are characterized in terms of a set of implicit integro-differential equations. A game of this type also possesses a "certainty-coincidence" property, meaning that its minimax behavior coincides with that of the corresponding deterministic game in the event that all noise values are zero. This property is used to decompose the minimax strategies into sums of a certainty-equivalent term and error terms.