Approximation schemes for solving disturbed control problems with non-terminal time and state constraints
Approximation schemes for solving disturbed control problems with non-terminal time and state constraints
复制标题
求解非终结时间和状态约束的扰动控制问题的近似方案
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
V. Turova
中科院分区：
文献类型：
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作者：
N. Botkin;K. Hoffmann;Natalie Mayer;V. Turova
摘要 提出了一种用于寻找 Hamilton-Jacobi 方程具体问题的粘度解的有限差分格式。此类问题的解满足粘度解定义中涉及的两个微分不等式。具体来说，不等式必须仅在解小于给定函数或大于另一个给定函数的区域中成立。从最优控制理论和微分博弈论的角度来看，这些结果可以应用于寻找非终结支付函数和状态约束问题中的价值函数。
Abstract A finite difference scheme for finding viscosity solutions of specifically stated problems for Hamilton–Jacobi equations is proposed. Solutions of such problems satisfy two differential inequalities involved into the definition of viscosity solutions. The specifics is that the inequalities must hold only in the region where solutions are less than a given function or greater than another given function. From the point of view of optimal control theory and the theory of differential games, these results can be applied to finding value functions in problems with nonterminal payoff functionals and state constraints.