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

大规模网络系统（如电网、互联网、多机器人系统和智能城市）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，以估计整个系统的状态并采取最佳行动。 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，这些网络攻击可能会损害一些组件并导致它们行为不稳定或将恶意信息注入网络。 现有的算法在大规模网络中的分布式协调是非常容易受到这种攻击。 该项目将通过创建新的算法来解决这个关键问题，使大规模网络中的组件能够合作采取最佳行动，并估计系统的状态，尽管大量组件受到攻击。 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能够设计出更安全的网络和关键基础设施，这些网络和基础设施在受到攻击时仍能正常工作，并为社会带来实质性的好处。 除了技术和科学贡献，该项目还将培训学生设计安全的网络系统，并将通过当地博物馆的互动展览和研讨会，让印第安纳州中部的当地社区了解网络。该提案提出了一个综合的研究和教育计划，重点是建立分布式优化，学习，以及对攻击有弹性的估计算法。 研究议程集中在沿着三个推力：（i）设计弹性算法的静态目标函数的分布式优化，（ii）设计弹性学习算法的优化目标随时间变化的设置，和（iii）设计弹性分布式状态估计器的大规模动态系统。 这三个研究方向各自带来了新的理论贡献。 首先，拟议的研究将建立新的度量标准来衡量分布式优化算法的弹性，并将建立在通常研究的优化方法（在其现有形式下极易受到对手的攻击）的基础上，以获得弹性分布式优化算法。 其次，它将建立新的基本下限的遗憾，可以实现与分布式在线学习算法下的对抗行为，并通过新的学习算法的设计，可实现的遗憾界的特征。 第三，拟议的研究将调查底层物理系统的动态和分布式观测器之间的通信网络拓扑结构之间的相互作用，以设计弹性分布式状态估计方案。拟议的研究将导致更好地了解影响分布式优化，学习和估计动态弹性的基本因素，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型网络系统。 鉴于缺乏现有的工作在这个问题上，研究将奠定基础，大量的进一步探索弹性算法的分布式决策和协调在大规模网络。

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.