On the Impact of Trusted Nodes in Resilient Distributed State Estimation of LTI Systems

Abstract

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. arXiv:2001.07056v1 [eess.SY]

Resilient Consensus Through Event-Based Communication

“…Theorem 2. Under the F -total malicious model, the normal agents with E-MSR using (23) and (5) reach resilient consensus if and only if the underlying graph is (F + 1, F + 1)robust. The safety interval is given by S = x(0),x(0) , and the consensus error level c is achieved if the parameter c 0 in the triggering function (3) satisfies…”

“…The initial values x i (0) of the nodes and the (constant) weights a ij (k) on the edges are indicated in the figure. Since the weights are all 1/2 (and thus γ = 1/2), for nodes having two neighbors, their own values are not used in the update rule (23). Moreover, for the node in the far left, a self-loop is shown to indicate that this node uses its own value.…”

“…In [31], a resilient version of distributed optimization is studied by employing MSR-like mechanisms to detect outliers in the neighbors' variables. Further, in [23], resilient distributed state estimation problem is studied, where another class of robust graphs relevant to the problem is introduced. In the robotics area, [6] applies MSR algorithms for cooperative robots and develops methods for the robots to find if and how the network for their interactions can be built with robust graph properties.…”

Finite-Time Guarantees for Byzantine-Resilient Distributed State Estimation With Noisy Measurements

“…However, this algorithm works under the assumption that an agent can fully observe the true state in the non-faulty condition [25, Section II.A], as opposed to our model which deals with both observability and noisy measurement issues. Mitra and Sundaram [26] consider the more general LTI systems and characterize the fundamental limits on adversary-resilient algorithms. However, unlike our work, [26] deals with noiseless observations and the focus is on asymptotic analysis.…”

Determining r- and (r,s)-robustness of digraphs using mixed integer linear programming

“…results that draw upon these papers include state estimation [18][19][20][21], rendezvous of mobile agents [22,23], output synchronization [11], simultaneous arrival of interceptors [17], distributed optimization [29,31], reliable broadcast [33,43], clock synchronization [8], randomized quantized consensus [5], self-triggered coordination [26], and multi-hop communication [30].…”