New Mathematicals and Analysis for Stochastic Mean-Field Models, Stochastic Recursive Algorithms with Interactions, Hybrid Systems, and Distributed Controls and Games
Abstract
Modern systems are increasingly characterized by connections among their subsystems, interactions with environments, large and time-varying uncertainties, coordinated mission, and feedback and learning requirements. Motivated by a wide range of emerging applications, this project aims to develop novel mathematical models, frameworks, and approaches for stochastic mean-field models, stochastic recursive algorithms with interactions, hybrid control systems, and distributed optimization and controls and games. Several fundamental problems will be studied. (1) New models and analysis methods of large-scale stochastic systems with mean-field influence will be developed. Limit behavior of stochastic processes with mean-field interactions will be studied. Maximum principles for switching diffusions will be established and mean-field games of switching diffusions will be investigated. Our effort will lead to new mathematical models and analysis methodologies based on careful handling of measure-valued random processes, martingales, and conditional means of certain processes. The expected results will be fundamental for a multi-front of applications in mathematics, and applications in control, optimization, differential games, and systems analysis. (2) Social networks are characterized by interactions among many elements with dynamic changes in their connections, exemplified by social groups, research collaborations, large gathering for events, and organization structures. A new framework for stochastic approximation and optimization with social interactions will be developed. The research will contribute to stochastic approximation and optimization of systems involving a large number of participating ``players with mean-field type of interactions. New analysis methods will be introduced. The expected results will have potential impacts on many applications. (3) Many systems naturally encounter topology switching among components or players, caused by either system uncertainties such as random communication channel interruptions and packet loss, or active control of system configurations such as adding or removing subsystems. Integrating switching uncertainty and control strategies, the proposed work will derive fundamental testing conditions and active control techniques to enhance the interconnected system s ability for estimation, optimization, control, and system coordination. A new paradigm of hybrid control methods along with stochastic hybrid controllability and observability will be introduced. The findings will accommodate control and communication in a holistic framework with broad application potential in areas of autonomous systems, smart grids, smart buildings, etc. (4) Distributed strategies are essential for reducing communication and computing complexity in interconnected systems. The theoretical foundation for multi-objective, stochastic, hybrid, distributed optimization, controls, and games will be pursued to advance technology capability in modern networked control systems. Impact of stochastic noise and switching topologies on optimality, convergence, stability, and performance of distributed strategies will be investigated. The proposed work will introduce new mathematics frameworks, develop new algorithms and methodologies for distributed hybrid optimization and games, and accelerate their potential usage in selected areas leading to substantial impact on a multitude of applications.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- May 13, 2019
- Source ID
- W911NF1910176
Entities
People
- Gang George Yin
Organizations
- Army Contracting Command
- United States Army
- Wayne State University