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

当前科学和工程中的许多挑战都与复杂网络有关，而多智能体网络系统是当前许多新应用的焦点。这些应用与日益流行的在线社交网络有关：大规模网络数据集的分析；政治、经济和生物系统中各主体之间的相互作用所产生的问题；以及电力和无线网络在我们日常生活中的扩展。尽管传统的方法用于分析多智能体网络系统，但现有的结果在处理通信网络结构与智能体行为/决策之间存在强烈相互依赖的现实情况时存在不足。这项工作承诺将几种工程和数学工具（如控制、优化和博弈论）结合在一起，采用系统的方法来分析在复杂动态网络上相互作用的代理的行为。拟议的工作将提供关键技术，以实现大规模、安全和高效的多代理网络系统的部署和分析。待开发的技术有望提供对多智能体网络系统中异质性影响的前所未有的理解，例如社会网络中的意见形成和机器人会合。要进行的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优的安全决策。这项研究的结果将推动几个领域的知识状态，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。该项目将重点研究具有状态依赖切换拓扑的多智能体网络决策系统的基于二元性的稳定性和收敛性分析。一旦考虑到潜在的代理网络动态的不对称或异质性，这些系统就会变得更加复杂，这类问题在控制、社会科学和许多其他相关领域都带来了长期的挑战。这项变革性的研究将提供必要的数学基础，将多智能体系统的现有结果从静态同构设置扩展到高度动态的异构环境。研究结果将用于分析几个主要应用程序，如设计有效的资源分配算法和在高动态网络上开发安全策略。本研究的具体目标包括i)对多智能体网络系统进行非常规分析，例如构建新的Lyapunov函数；Ii)利用新颖的博弈论技术分析异构网络代理的策略行为；iii)开发计算平衡点并进行收敛速度分析的有效算法。该奖项反映了美国国家科学基金会的法定使命，并通过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，被认为值得支持。

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.