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

现代控制系统越来越分散化、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无人机环境监测。对于这样的系统，需要设计分散控制算法，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。** 本提案是关于发展和继续一个关于随机控制及其分散化、鲁棒性和学习以及信息约束下的控制的各个方面的连贯研究计划。(i)分散随机控制：这涉及多个决策者，他们为共同的目标而奋斗，但只能访问本地信息。很少有结果是已知的系统方法，以达到最佳的解决方案，为经典的随机控制的工具不适用于分散系统。我的团队已经在最优策略及其结构、存在性、近似和分散学习方面获得了非常普遍的结果。我们将继续发展一个完整的和系统的理论，用于最优政策的结构和近似，以及在分散约束下的学习，并研究拥有大量决策者的影响。(ii)鲁棒性和数据驱动控制：工程师通常会得到一个不完整的系统模型，或者一个需要随着时间的推移学习各种参数的模型。这些设置导致随机控制理论的重要方面：鲁棒性和经验学习。对于具有大的状态空间和动作空间的随机控制问题，特别是部分可观测的随机控制问题，也存在大量的计算挑战。这些问题将通过扰动和近似分析来研究。** (iii)网络控制系统：这种系统是指分散式系统，其中组件通过通信信道连接，并且需要在给定网络所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，我们的团队已经取得了基础性的成果。然而，仍然有许多关键的非线性系统的随机理论缺乏开放的问题。另一个方向是联合优化编码和控制策略的设计。** 研究和培训的6名博士，4名硕士，1名博士后和2名USRA人员将有助于产生技术，这些技术将保持加拿大在创新前沿的地位，并将使机器学习，能源，汽车，航空航天和信息技术部门受益。

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.