Resilient distributed state estimation with mobile agents: overcoming Byzantine adversaries, communication losses, and intermittent measurements

Mitra, Arindam; Richards, John A.; Bagchi, Saurabh; Sundaram, Shreyas

doi:10.1007/s10514-018-9813-7

Cited by 50 publications

(47 citation statements)

References 76 publications

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“…Proof. (Theorem 2) Let us begin by noting that given any desired convergence rate ρ ∈ (0, 1), each node i ∈ S ∩ R can choose its observer gain l i to guarantee |e i [k]| ≤ αρ k , ∀k ∈ N, based on the observer (15…”

Section: Appendix B Proof Of Propositionmentioning

confidence: 99%

“…Next, in line 16, node i considers the set M i [k]∪{J i [k]\M i [k]}, and appends/retains only those 2f +1 nodes that have the lowest freshness-indices. 10 The rationale behind breaking up the "appending" operation into two steps (lines [15][16] is to avoid the possibility of having multiple appearances of a single node in M i [k]. Note that for both Case 1 and Case 2, the values of M i , v i and φ i at the beginning of time-step k + 1 are initialized with their values at the end of time-step k (lines 14 and 18); their values at the end of time-step k + 1 will naturally depend on the new information available to node i at time k+1.…”

mentioning

confidence: 99%

“…2 requires each node i to maintain a freshness-index τ i [k] ∈ N ∪ {ω}. Each source node i ∈ S maintains τ i [k] = 0 for all time, and updateŝ x i [k] based on a standard Luenberger observer (see Eq (15)…”

mentioning

confidence: 99%

See 2 more Smart Citations

Finite-Time Distributed State Estimation over Time-Varying Graphs: Exploiting the Age-of-Information

Mitra¹,

Richards

Bagchi³

et al. 2019

2019 American Control Conference (ACC)

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We study the problem of designing a distributed observer for an LTI system over a time-varying communication graph. The limited existing work on this topic imposes various restrictions either on the observation model or on the sequence of communication graphs. In contrast, we propose a single-timescale distributed observer that works under mild assumptions. Specifically, our communication model only requires strongconnectivity to be preserved over non-overlapping, contiguous intervals that are even allowed to grow unbounded over time. We show that under suitable conditions that bound the growth of such intervals, joint observability is sufficient to track the state of any discrete-time LTI system exponentially fast, at any desired rate. In fact, we also establish finite-time convergence based on our approach. Finally, we develop a variant of our algorithm that is provably robust to worst-case adversarial attacks, provided the sequence of graphs is sufficiently connected over time. The key to our approach is the notion of a "freshness-index" that keeps track of the age-of-information being diffused across the network. Such indices enable nodes to reject stale estimates of the state, and, in turn, contribute to stability of the error dynamics.1 Such approaches, referred to as two-time-scale approaches, incur high communication cost, and might hence be prohibitive for real-time applications. arXiv:2001.07006v1 [eess.SY]

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Section: Appendix B Proof Of Propositionmentioning

confidence: 99%

mentioning

confidence: 99%

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Finite-Time Distributed State Estimation over Time-Varying Graphs: Exploiting the Age-of-Information

Mitra¹,

Richards

Bagchi³

et al. 2019

2019 American Control Conference (ACC)

Self Cite

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“…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].…”

Section: Introductionmentioning

confidence: 99%

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

Usevitch

Panagou

2020

Automatica

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There has been an increase in the use of resilient control algorithms based on the graph theoretic properties of r-and (r, s)robustness. These algorithms guarantee consensus of normally behaving agents in the presence of a bounded number of arbitrarily misbehaving agents if the values of the integers r and s are sufficiently large. However, determining an arbitrary graph's robustness is a highly nontrivial problem. This paper introduces a novel method for determining the r-and (r, s)robustness of digraphs using mixed integer linear programming; to the best of the authors' knowledge it is the first time that mixed integer programming methods have been applied to the robustness determination problem. The approach only requires knowledge of the graph Laplacian matrix, and can be formulated with binary integer variables. Mixed integer programming algorithms such as branch-and-bound are used to iteratively tighten the lower and upper bounds on r and s. Simulations are presented which compare the performance of this approach to prior robustness determination algorithms.

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“…However, allowing for sophisticated attack models comes at the expense of rather stringent requirements on the communication network topology. Specifically, the guarantees provided in [14], [15] hold only when the network exhibits a sufficient amount of redundancy in both its measurement and communication resources. We are thus motivated to ask: Can one relax the redundancy requirements on the network, and yet, tolerate a worst-case attack model?…”

Section: Introductionmentioning

confidence: 99%

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

Mitra

Abbas

Sundaram

2018

2018 IEEE Conference on Decision and Control (CDC)

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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]

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Resilient distributed state estimation with mobile agents: overcoming Byzantine adversaries, communication losses, and intermittent measurements

Cited by 50 publications

References 76 publications

Finite-Time Distributed State Estimation over Time-Varying Graphs: Exploiting the Age-of-Information

Finite-Time Distributed State Estimation over Time-Varying Graphs: Exploiting the Age-of-Information

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

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

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