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Reflected dynamics: Viscosity analysis for L∞ cost, relaxation and abstract dynamic programming
Journal of Differential Equations ( IF 2.4 ) Pub Date : 2021-04-30 , DOI: 10.1016/j.jde.2021.04.024
Dan Goreac , Hadjer Hechaichi , Oana-Silvia Serea

We study an optimal control problem consisting in minimizing the L norm of a Borel measurable cost function, in finite time, and over all trajectories associated with a controlled dynamics which is reflected in a compact prox-regular set. The first part of the paper provides the viscosity characterization of the value function for uniformly continuous costs. The second part is concerned with linear programming formulations of the problem and the ensued by-products as e.g. dynamic programming principle for merely measurable costs.



中文翻译:

反映的动力学:粘度分析 大号 成本,松弛和抽象动态规划

我们研究了一个最优控制问题,该问题包括最大程度地减少 大号有限时间内在与可控动力学相关的所有轨迹上的Borel可测量成本函数的范数,这反映在紧凑的正则常规集中。本文的第一部分提供了用于均匀连续成本的价值函数的粘度表征。第二部分涉及问题的线性规划公式以及随后的副产品,例如动态规划原理,仅用于可衡量的成本。

更新日期:2021-05-02
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