Stochastic control: Decentralization, robustness and learning, and information constraints

随机控制：去中心化、鲁棒性和学习以及信息约束

• 批准号: RGPIN-2018-06060
• 负责人: Yuksel, Serdar
• 金额: $ 9.32万
• 依托单位: Queen's University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=759185
• 关键词: Stochastic; control; Decentralization; robustness; learning

Modern control systems are increasingly decentralized, networked, reconfigurable, and adaptive. Applications include adaptive energy management systems in the Smart Grid, the Internet of Things applications, and unmanned aerial environmental monitoring of Canada's North through remote control. For such systems, one needs to design decentralized control algorithms, develop a system model learned through empirical data, and jointly analyze communication and control aspects. Stochastic control theory provides the mathematical foundation for the design and study of such systems. This proposal is on the development and continuation of a coherent research program on stochastic control and various aspects of it on decentralization, robustness and learning, and control under information constraints.(i) Decentralized Stochastic Control: This involves multiple decision makers who strive for a common goal but who have access only to local information. Few results are known regarding systematic methods to arrive at optimal solutions as the tools available for classical stochastic control are not applicable to decentralized systems. My group has already obtained very general results on optimal policies, and their structure, existence, approximations, and decentralized learning. We will continue to develop a complete and systematic theory for the structure and approximations of optimal policies, and for learning under decentralization constraints, and study the effects of having a large number of decision makers.(ii) Robustness and Data-Driven Control: Often an engineer is given a system with an incomplete model or a model with various parameters to be learned over time. These setups lead to important aspects in stochastic control theory: robustness and empirical learning. There are also substantial computational challenges for stochastic control problems with large state and action spaces, especially for partially observed stochastic control problems. These problems will be studied through a perturbation and approximation analysis.(iii) Networked Control Systems: Such systems refer to decentralized systems in which the components are connected through communication channels and one needs to design such systems given the information transfer constraints imposed by the network. Over the past few years, our group has developed foundational results. However, there remain many crucial open problems on non-linear systems for which a stochastic theory is lacking. Another direction is on the design of jointly optimal coding and control policies. The research and the trained 6 PhD, 4 MSc, 1 Postdoc and 2 USRA personnel will help produce technologies which will maintain Canada's position in the frontiers of innovation and will benefit the machine learning, energy, automotive, aerospace, and information technology sectors.

现代控制系统越来越分散、网络化、可重构和自适应。应用包括智能电网中的自适应能源管理系统、物联网应用以及通过远程控制对加拿大北部进行的无人机环境监测。对于此类系统，需要设计分散的控制算法，开发通过经验数据学习的系统模型，并联合分析通信和控制方面。随机控制理论为此类系统的设计和研究提供了数学基础。该提案是关于随机控制及其分散性、鲁棒性和学习以及信息约束下控制的各个方面的连贯研究计划的发展和延续。（i）分散随机控制：这涉及多个决策者，他们努力实现共同的目标，但只能访问本地信息。由于可用于经典随机控制的工具不适用于分散系统，因此关于获得最佳解决方案的系统方法知之甚少。我的小组已经在最优策略及其结构、存在、近似和去中心化学习方面获得了非常普遍的结果。我们将继续为最优政策的结构和近似以及去中心化约束下的学习开发完整且系统的理论，并研究拥有大量决策者的影响。（ii）鲁棒性和数据驱动控制：通常给工程师一个模型不完整的系统，或者一个具有需要随着时间的推移学习的各种参数的模型。这些设置引出了随机控制理论的重要方面：鲁棒性和经验学习。对于具有大状态和动作空间的随机控制问题，尤其是部分观察到的随机控制问题，也存在巨大的计算挑战。这些问题将通过扰动和近似分析进行研究。（iii）网络控制系统：此类系统是指分散的系统，其中组件通过通信通道连接，并且需要考虑到网络施加的信息传输约束来设计此类系统。几年来，我们课题组取得了基础性成果。然而，非线性系统仍然存在许多缺乏随机理论的关键开放问题。另一个方向是联合最优编码和控制策略的设计。这项研究和训练有素的 6 名博士、4 名硕士、1 名博士后和 2 名 USRA 人员将有助于开发技术，保持加拿大在创新前沿的地位，并使机器学习、能源、汽车、航空航天和信息技术领域受益。