Surveillance-Evasion games under uncertainty
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Surveillance-Evasion games are continuous path planning problems in which an evader chooses his trajectory to hinder the surveillance by an enemy observer. In the classical setting, both players are assumed to have full information about each other's actions, and seek an optimal response in real time. In contrast to that classical case, we discuss a game where both players have to plan under uncertainty as they are unable to observe each other's strategy. We consider two types of evader behavior: in the first one, a completely risk-averse evader seeks a trajectory minimizing his worst-case observability, and in the second one, the evader is concerned with the average-case observability. The latter version is naturally interpreted as a semi-infinite strategic game, and we provide an algorithm to compute an approximation to the resulting Nash equilibrium. The proposed approach draws on methods from game theory, convex optimization, optimal control, and multiobjective dynamic programming. We illustrate our algorithm using numerical examples and discuss the computational complexity, including for the generalized version with multiple evaders.
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