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Stochastic near-optimal control: additive, multiplicative, non-Markovian and applications
The European Physical Journal Special Topics ( IF 2.8 ) Pub Date : 2021-06-06 , DOI: 10.1140/epjs/s11734-021-00185-y Lourival Lima , Paulo Ruffino , Francys Souza
中文翻译:
随机近最优控制:加法、乘法、非马尔可夫和应用
更新日期:2021-06-07
The European Physical Journal Special Topics ( IF 2.8 ) Pub Date : 2021-06-06 , DOI: 10.1140/epjs/s11734-021-00185-y Lourival Lima , Paulo Ruffino , Francys Souza
In this survey we present the near-optimal stochastic control problem according to some recent tools in the literature. In particular, we focus on the approach of a discretization of the noise values instead of the canonical time-discretization. This is the so called skeleton structure. This allows to obtain an \(\epsilon \)-optimal control in non-Markovian systems (the main Theorem). A simple example illustrates the technique. The importance of the approach is emphasised in a final section on open problems related to more geometrical framework and discontinuous noise.
中文翻译:
随机近最优控制:加法、乘法、非马尔可夫和应用
在本次调查中,我们根据文献中的一些最新工具提出了接近最优的随机控制问题。特别是,我们专注于噪声值的离散化而不是规范时间离散化的方法。这就是所谓的骨架结构。这允许在非马尔可夫系统(主要定理)中获得\(\epsilon \) -最优控制。一个简单的例子说明了该技术。在与更多几何框架和不连续噪声相关的开放问题的最后一节中强调了该方法的重要性。