Control-Theoretic Approaches to Communication-Efficient, Distributed Convex Optimization over Wireless Networks

该研究奖的目标是开发高效、健壮和可扩展的分布式算法，使移动自组网或传感器网络中的代理能够在网络上协作和异步地解决凸和可分离的约束优化问题。该方法融合了控制论、最优化理论和无线网络的工具和思想，结合了反馈迭代控制、Lyapunov稳定性概念、网络动态系统、拉格朗日乘子方法和协议设计技术。所要解决的问题包括一般的凸规划及其两个重要的特例，线性规划和二次规划。要研究的模型包括具有静态和动态问题数据的模型、代理成员关系和网络拓扑。研究成果包括分布式算法的集合、对其行为的理论分析、对其性能的计算机模拟、研究成果的文档记录以及研究与高中、本科和研究生教育的整合。如果成功，该研究的结果将增强移动自组织和无线传感器网络的能力和功能，使代理能够协作地完成需要信息融合、分散决策和行动协调的复杂任务。这些反过来又将扩大此类网络的科学和工程应用。研究结果还将对控制理论做出贡献，为多智能体系统的控制创造了一种新的范式，即基于Lyapunov的何时通信和计算的反馈控制，从而使智能体能够通过最小的局部交互来快速实现最优的全局行为。研究与教育的结合将通过外展活动和机器人竞赛指导使高中生受益，通过课堂教学和NSF本科生研究经验补助金使本科生受益，通过研究指导和提供新的研究生课程使研究生受益。

The objective of this research award is to develop efficient, robust, and scalable distributed algorithms, which allow agents in a mobile ad hoc or sensor network to collaboratively and asynchronously solve convex and separable constrained optimization problems over the network. The approach is based on a blend of tools and ideas from control theory, optimization theory, and wireless networking, bringing together notions of feedback iteration control, Lyapunov stability concepts, networked dynamical systems, Lagrange multiplier methods, and protocol design techniques. The problems to be addressed include general convex program and its two important special cases, linear and quadratic programs. The models to be studied include models with static and dynamic problem data, agent memberships, and network topologies. The deliverables include a collection of distributed algorithms, theoretical analysis of their behaviors, computer simulation of their performances, documentation of the research outcomes, and integration of the research with high school, undergraduate, and graduate education.If successful, the results of this research will enhance the capability and functionality of mobile ad hoc and wireless sensor networks, enabling agents to cooperatively accomplish sophisticated tasks that require fusion of information, decentralized decision making, and coordination of actions. These will, in turn, broaden the scientific and engineering applications of such networks. The results will also make contributions to control theory by creating a new paradigm in control of multi-agent systems, namely, Lyapunov-based feedback control of when to communicate and compute, so that agents can achieve optimized global behavior quickly through minimal local interactions. Integration of the research with education will benefit high school students via outreach activities and robotics competition mentorship, undergraduate students via classroom instruction and an NSF Research Experiences for Undergraduates grant, and graduate students via research supervision and offering of a new graduate course.