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

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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.