摘要翻译：
本文首次针对一类无穷维随机系统，即时滞跳扩散系统，提出了一种自动的、逐构造校正的控制器综合方案。首先，我们构造了有限个近似双线性的非概率滞后系统的抽象，这些抽象对应于具有某种稳定性的原始系统，即增量输入到状态稳定性。然后，我们给出了在概率条件下，所得到的有限抽象的输出轨迹与原时滞跳扩散系统的输出轨迹之间距离的量化结果。利用所提出的结果，可以将有限抽象综合的控制策略细化到原系统，同时保证满足高层需求的概率。此外，我们根据线性系统的增量Lyapunov函数的存在性，给出了增量稳定性概念的充分条件，这些增量Lyapunov函数可归结为一些矩阵不等式。最后，以一个十室建筑模型为时滞跳扩散系统的温度控制器为例，说明了所提结果的有效性。
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英文标题：
《Symbolic Models for Retarded Jump-Diffusion Systems》
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作者：
Pushpak Jagtap and Majid Zamani
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最新提交年份：
2019
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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：Electrical Engineering and Systems Science        电气工程与系统科学
二级分类：Systems and Control        系统与控制
分类描述：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.
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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英文摘要：
  In this paper, we provide for the first time an automated, correct-by-construction, controller synthesis scheme for a class of infinite dimensional stochastic systems, namely, retarded jump-diffusion systems. First, we construct finite abstractions approximately bisimilar to non-probabilistic retarded systems corresponding to the original systems having some stability property, namely, incremental input-to-state stability. Then, we provide a result on quantifying the distance between output trajectory of the obtained finite abstraction and that of the original retarded jump-diffusion system in a probabilistic setting. Using the proposed result, one can refine the control policy synthesized using finite abstractions to the original systems while providing guarantee on the probability of satisfaction of high-level requirements. Moreover, we provide sufficient conditions for the proposed notion of incremental stability in terms of the existence of incremental Lyapunov functions which reduce to some matrix inequalities for the linear systems. Finally, the effectiveness of the proposed results is illustrated by synthesizing a controller regulating the temperatures in a ten-room building modelled as a delayed jump-diffusion system.
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PDF链接：
https://arxiv.org/pdf/1704.0369