CAREER: Duality and Stability in Complex State-Dependent Networked Dynamics

当前科学和工程领域的许多挑战都与复杂网络有关，多智能体网络系统是当前许多新应用的焦点。这些应用与在线社交网络的日益普及有关：大规模网络数据集的分析;政治，经济和生物系统中代理之间的相互作用引起的问题;以及我们日常生活中电力和无线网络的扩展。尽管传统的方法用于分析多智能体网络系统，现有的结果有缺点，以解决现实的情况下，有一个很强的相互依赖性之间的通信网络结构和代理的行为/决策。这项工作有望汇集几个工程和数学工具，如控制，优化和博弈论，进行系统的方法来分析在复杂的动态网络中交互的代理的行为。拟议的工作将提供关键技术，使大规模，安全和高效的多智能体网络系统的部署和分析。待开发的技术，预计将提供一个前所未有的理解的异质性的影响，在多智能体网络系统，如意见形成社交网络和机器人会合。研究将导致新的经济和工程设计政策，如有效的资源分配和最佳的安全决策。研究成果将推动多个领域的知识发展，包括分布式控制和优化、社会经济网络和网络安全。该项目将有助于提高我们理解动态网络中战略关系演变的能力，并通过保护网络免受恶意对抗性干预来确保网络物理安全，从而有利于美国的长期国防利益。 本计画的研究重点为具有状态相依切换拓扑结构之多智能体网路决策系统之对偶稳定性与收敛性分析。这些系统变得更加复杂，一旦一个帐户的不对称性或异质性的基本代理网络动力学，这类问题带来了长期的挑战，在控制，社会科学和许多其他相关领域。这一变革性的研究将提供必要的数学基础，以扩展现有的多智能体系统的结果从静态同质设置高度动态异构的环境。研究结果将被用来分析几个主要的应用，如设计高效的资源分配算法和开发高度动态网络的安全策略。本研究的具体目标包括：i）多智能体网络系统的非常规分析，如构造新的李雅普诺夫函数; ii）通过新的博弈论技术分析异构网络智能体的策略行为;以及iii）该奖项反映了NSF的法定使命，并被认为是值得支持的，使用基金会的知识价值和更广泛的影响审查标准进行评估。

Many of the current challenges in science and engineering are related to complex networks, and multiagent network systems are currently the focal point of many new applications. Such applications relate to the growing popularity of online social networks: the analysis of large-scale network data sets; problems that arise from interactions among agents in political, economic, and biological systems; and the expansion of power and wireless networks in our daily lives. Despite conventional methods for the analysis of multiagent network systems, the existing results have shortcomings to address realistic situations where there is a strong interdependence between the communication network structure and the agents’ behavior/decisions. This work promises to bring together several engineering and mathematical tools such as control, optimization, and game theory, to undertake a systematic approach to the analysis of the behavior of agents interacting over complex dynamic networks. The proposed work will provide key technologies to enable the deployment and analysis of large-scale, secure and efficient multiagent networked systems. The techniques to be developed are expected to provide an unprecedented understanding of the influence of heterogeneity in multiagent networked systems, such as opinion formation in social networks and robotic rendezvous. Research to be undertaken will lead to new economic and engineering design policies such as efficient resource allocation and optimal security decisions. The outcome of the research will advance the state of knowledge in several areas, including distributed control and optimization, socio-economic networks, and network security. This project will contribute toward enhancing our ability to understand the evolution of strategic relationships in dynamic networks and to ensure cyber-physical security by safeguarding networks against malicious adversarial interventions, thus benefiting long-term US defense interests. This project will be focused on duality-based stability and convergence analysis of multiagent networked decision systems with state-dependent switching topologies. These systems become further complicated once one accounts for asymmetry or heterogeneity of the underlying agent-network dynamics, and this class of problems have entailed longstanding challenges in control, social sciences, and many other related fields. This transformative research will provide the necessary mathematical foundations to extend the existing results on multiagent systems from the static homogeneous setting to highly dynamic heterogeneous environments. The results will be leveraged to analyze several major applications such as devising efficient resource allocation algorithms and developing security strategies over highly dynamic networks. Specific goals of this research include i) unconventional analysis of multiagent networked systems, such as construction of novel Lyapunov functions; ii) analysis of the strategic behavior of heterogeneous networked agents via novel game-theoretic techniques; and iii) development of efficient algorithms for computing equilibrium points and conducting convergence rate analysis.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.