具有时变障碍的半马尔可夫决策过程的到达-避障问题
Reach-avoid semi-Markov decision processes with time-varying obstacles
AI总结：
本文针对具有时变障碍的半马尔可夫决策过程，通过构造等价的二维模型并设计改进值型算法，求解有限时域内最大到达-避障概率及其ε-最优策略。
摘要：
我们考虑在有限时域内，具有时变障碍的半马尔可夫决策过程到达目标的最大到达-避障概率。由于障碍集合的时变性，模型 \eqref{Model} 是非齐次的。为克服这一困难，我们构造了一个相关的二维模型 \eqref{newModel}，并证明了原模型的到达-避障概率与该相关二维模型的到达-避障概率之间的等价性。对于相关的二维模型，我们分析了等价到达-避障概率的一些特殊性质。在此基础上，我们提供了一种特殊的改进值型算法，以获得等价的最大到达-避障概率及其 $ε$-最优策略。然后，在算法的最后一步，利用这两个模型之间的等价性，我们得到了原模型的最大到达-避障概率及其 $ε$-最优策略。
英文摘要：
We consider the maximal reach-avoid probability to a target in finite horizon for semi-Markov decision processes with time-varying obstacles. Since the variance of the obstacle set, the model \eqref{Model} is non-homogeneous. To overcome such difficulty, we construct a related two-dimensional model \eqref{newModel}, and then prove the equivalence between such reach-avoid probability of the original model and that of the related two-dimensional one. For the related two-dimensional model, we analyze some special characteristics of the equivalent reach-avoid probability. On this basis, we provide a special improved value-type algorithm to obtain the equivalent maximal reach-avoid probability and its $ε$-optimal policy. Then, at the last step of the algorithm, by the equivalence between these two models, we obtain the original maximal reach-avoid probability and its $ε$-optimal policy for the original model.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
