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

现代控制系统的分散化、网络化、可重构化和自适应程度越来越高。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的无人驾驶航空环境进行监测。对于这类系统，需要设计分散控制算法，建立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。*这项建议是关于发展和继续一项关于随机控制及其关于权力下放、稳健性和学习的各个方面的连贯研究方案，以及信息约束下的控制。*(I)分散随机控制：这涉及为共同目标而奋斗的多个决策者，但他们只能获得当地信息。由于用于经典随机控制的工具不适用于分散系统，因此关于获得最优解的系统方法的结果很少。我的小组已经在最优策略及其结构、存在性、近似性和分散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在权力下放限制下的学习发展完整和系统的理论，并研究拥有大量决策者的影响。*(Ii)稳健性和数据驱动控制：经常给工程师提供一个模型不完整的系统或一个需要随着时间学习的各种参数的模型。这些设置导致了随机控制理论的重要方面：稳健性和经验学习。对于具有大状态空间和大动作空间的随机控制问题，特别是对于部分观测随机控制问题，也存在着巨大的计算挑战。这些问题将通过摄动和近似分析来研究。*(Iii)网络控制系统：这种系统是指分散的系统，其中的部件通过通信通道连接，并且需要在给定网络施加的信息传输约束的情况下设计这种系统。在过去的几年里，我们的团队取得了基础性的成果。然而，在缺乏随机理论的情况下，仍然有许多关于非线性系统的关键公开问题。另一个方向是设计联合最优的编码和控制策略。*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人员将帮助产生将保持加拿大在创新前沿的地位的技术，并将使机器学习、能源、汽车、航空航天和信息技术行业受益。

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.