Anytime computation algorithms for stochastically parametric approach-evasion differential games

We consider an approach-evasion differential game where the inputs of one of the players are upper bounded by a random variable. The game enjoys the order preserving property where a larger relaxation of the random variable induces a smaller value function. Two numerical computation algorithms are proposed to asymptotically recover the expected value function. The performance of the proposed algorithms is compared via a stochastically parametric homicidal chauffeur game. The algorithms are also applied to the scenario of merging lanes in urban transportation.National Science Foundation (U.S.) (Grant 1239182)United States. Air Force Office of Scientific Research (Grant FA8650-07-2-3744