摘要翻译:
我们给出了带期望约束的随机最优控制问题的动态规划原理。使用测试函数和约束的概率松弛的弱公式,避免了与可测选择有关的限制,但仍然隐含粘性意义下的Hamilton-Jacobi-Bellman方程。我们把开状态约束作为期望约束的特例,证明了一个比较定理,得到了闭状态约束的方程。
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英文标题:
《Weak Dynamic Programming for Generalized State Constraints》
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作者:
Bruno Bouchard, Marcel Nutz
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最新提交年份:
2012
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分类信息:
一级分类:Mathematics 数学
二级分类:Optimization and Control 优化与控制
分类描述:Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学,线性规划,控制论,系统论,最优控制,博弈论
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一级分类:Computer Science 计算机科学
二级分类:Systems and Control 系统与控制
分类描述:cs.SY is an alias for eess.SY. This section includes theoretical and experimental research covering all facets of automatic control systems. The section is focused on methods of control system analysis and design using tools of modeling, simulation and optimization. Specific areas of research include nonlinear, distributed, adaptive, stochastic and robust control in addition to hybrid and discrete event systems. Application areas include automotive and aerospace control systems, network control, biological systems, multiagent and cooperative control, robotics, reinforcement learning, sensor networks, control of cyber-physical and energy-related systems, and control of computing systems.
cs.sy是eess.sy的别名。本部分包括理论和实验研究,涵盖了自动控制系统的各个方面。本节主要介绍利用建模、仿真和优化工具进行控制系统分析和设计的方法。具体研究领域包括非线性、分布式、自适应、随机和鲁棒控制,以及混合和离散事件系统。应用领域包括汽车和航空航天控制系统、网络控制、生物系统、多智能体和协作控制、机器人学、强化学习、传感器网络、信息物理和能源相关系统的控制以及计算系统的控制。
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一级分类:Mathematics 数学
二级分类:Analysis of PDEs 偏微分方程分析
分类描述:Existence and uniqueness, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDE's, conservation laws, qualitative dynamics
存在唯一性,边界条件,线性和非线性算子,稳定性,孤子理论,可积偏微分方程,守恒律,定性动力学
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一级分类:Mathematics 数学
二级分类:Probability 概率
分类描述:Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用:例如中心极限定理,大偏差,随机微分方程,统计力学模型,排队论
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一级分类:Quantitative Finance 数量金融学
二级分类:Risk Management 风险管理
分类描述:Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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英文摘要:
We provide a dynamic programming principle for stochastic optimal control problems with expectation constraints. A weak formulation, using test functions and a probabilistic relaxation of the constraint, avoids restrictions related to a measurable selection but still implies the Hamilton-Jacobi-Bellman equation in the viscosity sense. We treat open state constraints as a special case of expectation constraints and prove a comparison theorem to obtain the equation for closed state constraints.
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PDF链接:
https://arxiv.org/pdf/1105.0745