We address the problem of distributed state estimation of a linear dynamical process in an attack-prone environment. Recent attempts to solve this problem impose stringent redundancy requirements on the measurement and communication resources of the network. In this paper, we take a step towards alleviating such strict requirements by exploring two complementary directions: (i) making a small subset of the nodes immune to attacks, or "trusted", and (ii) incorporating diversity into the network. We define graph-theoretic constructs that formally capture the notions of redundancy, diversity, and trust. Based on these constructs, we develop a resilient estimation algorithm and demonstrate that even relatively sparse networks that either exhibit node-diversity, or contain a small subset of trusted nodes, can be just as resilient to adversarial attacks as more dense networks. Finally, given a finite budget for network design, we focus on characterizing the complexity of (i) selecting a set of trusted nodes, and (ii) allocating diversity, so as to achieve a desired level of robustness. We establish that, unfortunately, each of these problems is NP-complete.
Detection of Sensor Attack and Resilient State Estimation for Uniformly Observable Nonlinear Systems having Redundant Sensors
ASRI, Department of Electrical and Computer Engineering, Seoul National University（首尔大学电气与计算机工程系自动系统研究室）；Department of Information & Communication Engineering, DGIST（韩国电子通信研究院信息与通信工程系）
On Redundant Observability: From Security Index to Attack Detection and Resilient State Estimation
Hyundai Motor Company（现代汽车公司）；ASRI, Department of Electrical and Computer Engineering, Seoul National University（首尔大学电气与计算机工程自主机器人研究中心）；Department of Information & Communication Engineering, DGIST（韩国科学技术院信息通信工程系）
Distributed Nonlinear Control of Networked Two-Wheeled Robots under Adversarial Interactions
Institut Teknologi Sepuluh Nopember (ITS)（十月中旬理工学院）；Universitas Gadjah Mada (UGM)（加查马达大学）；Institut Teknologi Bandung (ITB)（万隆理工学院）；University of Groningen（格罗宁根大学）
Characterizing Trust and Resilience in Distributed Consensus for Cyberphysical Systems
Department of Electrical and Computer Engineering, Princeton University（普林斯顿大学电气工程与计算机科学系）；School of Electrical, Computer and Energy Engineering, Arizona State University（亚利桑那州立大学电气、计算机与能源工程学院）；Computer Science Department at the School of Engineering and Applied Sciences, Harvard University（哈佛大学工程与应用科学学院计算机科学系）
Fast Distributed Optimization over Directed Graphs under Malicious Attacks using Trust
School of Engineering and Applied Sciences, Harvard University（哈佛大学工程与应用科学学院）；Faculty of Engineering, Bar-Ilan University（巴伊兰大学工程学院）；School of Electrical, Computer and Energy Engineering, Arizona State University（亚利桑那州立大学电气、计算机与能源工程学院）
