CAREER: Towards Secure Large-Scale Networked Systems: Resilient Distributed Algorithms for Coordination in Networks under Cyber Attacks

大型网络系统（如电网、互联网、多机器人系统和智慧城市）由大量相互连接的组件组成。为了使整个系统有效地运行，这些组件必须相互通信并使用交换的信息，以便估计整个系统的状态并采取最佳操作。然而，这种大规模的网络系统也越来越多地受到复杂的网络攻击的威胁，这些攻击可以破坏某些组件，导致它们的行为不稳定或向网络注入恶意信息。现有的大规模网络分布式协调算法极易受到此类攻击。该项目将通过创建新的算法来解决这一关键问题，使大规模网络中的组件能够协同采取最佳行动，并在大量组件受到攻击的情况下评估系统状态。这些算法将提供可证明的安全性和性能保证，并识别易受攻击的网络和算法的特征。该项目将确定设计网络的新方法，以提供所需的攻击恢复能力。从研究中产生的算法将使设计更安全的网络和关键基础设施能够在攻击下保持功能，对社会有实质性的好处。除了技术和科学贡献外，该项目还将培训学生设计安全的网络系统，并将通过互动式展览和当地博物馆的讲习班，使印第安纳州中部的当地社区参与学习网络知识。本提案提出了一个集成的研究和教育计划，重点是建立分布式优化、学习和估计算法的基础，这些算法对攻击具有弹性。研究议程主要集中在三个方面：(i)为静态目标函数的分布式优化设计弹性算法；（ii）为优化目标随时间变化的设置设计弹性学习算法；（iii）为大规模动态系统设计弹性分布式状态估计器。这三个研究重点都带来了新的理论贡献。首先，提出的研究将建立衡量分布式优化算法弹性的新指标，并将建立在通常研究的优化方法（这些方法在现有形式下极易受到对手的攻击）的基础上，以派生弹性分布式优化算法。其次，它将建立在对抗行为下分布式在线学习算法可以实现的遗憾的新基本下界，并通过设计新的学习算法来表征可实现的遗憾边界。第三，本研究将研究底层物理系统的动力学与分布式观测器之间的通信网络拓扑之间的相互作用，以设计具有弹性的分布式状态估计方案。提出的研究将导致对影响分布式优化、学习和估计动态弹性的基本因素的更好理解，并建立系统程序来设计能够在攻击下以接近最佳方式运行的大规模网络系统。鉴于缺乏关于该主题的现有工作，该研究将为大规模网络中分布式决策和协调的弹性算法的大量进一步探索奠定基础。

Large-scale networked systems (such as the power grid, the internet, multi-robot systems, and smart cities) consist of a large number of interconnected components. To allow the entire system to function efficiently, these components must communicate with each other and use the exchanged information in order to estimate the state of the entire system and take optimal actions. However, such large-scale networked systems are also increasingly under threat from sophisticated cyber-attacks that can compromise some of the components and cause them to behave erratically or inject malicious information into the network. Existing algorithms for distributed coordination in large-scale networks are highly vulnerable to such attacks. This project will address this critical problem by creating new algorithms to enable components in large-scale networks to cooperatively take optimal actions and estimate the state of the system despite attacks on a large number of the components. The algorithms will provide provable security and performance guarantees, and identify characteristics of networks and algorithms that are vulnerable to attacks. The project will identify new ways to design networks that provide a desired level of resilience to attacks. The algorithms that arise from the research will enable the design of more secure networks and critical infrastructure that remain functional under attacks, with substantial benefits to society. In addition to the technical and scientific contributions, the project will also train students in the design of secure networked systems, and will engage the local community in central Indiana in learning about networks via interactive exhibits and workshops at the local museum.This proposal presents an integrated research and education program focused on establishing the foundations of distributed optimization, learning, and estimation algorithms that are resilient to attacks. The research agenda is focused along three thrusts: (i) designing resilient algorithms for distributed optimization of static objective functions, (ii) designing resilient learning algorithms for settings where optimization objectives change over time, and (iii) designing resilient distributed state estimators for large scale dynamical systems. The three research thrusts each lead to new theoretical contributions. First, the proposed research will establish new metrics for measuring resilience in distributed optimization algorithms, and will build upon commonly studied optimization approaches (which are highly vulnerable to adversaries in their existing forms) to derive resilient distributed optimization algorithms. Second, it will establish new fundamental lower bounds on the regret that can be achieved with distributed online learning algorithms under adversarial behavior, and characterize achievable regret bounds via the design of new learning algorithms. Third, the proposed research will investigate the interplay between the dynamics of underlying physical systems and the communication network topology between distributed observers in order to design resilient distributed state estimation schemes. The proposed research will lead to a greater understanding of the fundamental factors that affect the resilience of distributed optimization, learning, and estimation dynamics, and establish systematic procedures to design large-scale networked systems that are capable of operating in a near-optimal manner under attacks. Given the lack of existing work on this topic, the research will lay the groundwork for substantial further explorations of resilient algorithms for distributed decision-making and coordination in large-scale networks.