A resilient convex combination for consensus-based distributed algorithms

Wang, Xuan; Mou, Shaoshuai; Sundaram, Shreyas

doi:10.3934/naco.2019018

Cited by 26 publications

(16 citation statements)

References 36 publications

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“…Numerical examples have been worked out to confirm our theoretical findings and demonstrate the flexibility of the multiplex consensus framework. An interesting future direction is to consider vector states [39], [40], which offer an opportunity to generate the current multiplex network framework from two layers to more layers.…”

Section: Discussionmentioning

confidence: 99%

Resilient Consensus for Robust Multiplex Networks with Asymmetric Confidence Intervals

Shang

2021

IEEE Trans. Netw. Sci. Eng.

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The consensus problem with asymmetric confidence intervals considered in this paper is characterized by the fact that each agent can have optimistic and/or pessimistic interactions with its neighbors. To deal with the asymmetric confidence scenarios, we introduce a novel multiplex network presentation for directed graphs and its associated connectivity concepts including the pseudo-strongly connectivity and graph robustness, which provide a resilience characterization in the presence of malicious nodes. We develop distributed resilient consensus strategies for a group of dynamical agents with locally bounded Byzantine agents in both continuous-time and discrete-time multi-agent systems. Drawing on our multiplex network framework, much milder connectivity conditions compared to existing works are proposed to ensure resilient consensus. The results are further extended to cope with resilient scaled consensus problems which allow both cooperative and antagonistic agreements among agents. Numerical examples are also exhibited to confirm the theoretical results and reveal the factors that affect the speed of convergence in our multiplex network framework.

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Section: Discussionmentioning

confidence: 99%

Resilient Consensus for Robust Multiplex Networks with Asymmetric Confidence Intervals

Shang

2021

IEEE Trans. Netw. Sci. Eng.

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“…The resilient consensus problem is more challenging when the state vector is in R d where d ≥ 2. Although variants of the W-MSR algorithm has been applied to mobile multi-robot systems for formation control [20] and flocking [21] applications, such methods cannot guarantee the resilient vector consensus in fact as we discuss in Section V. To achieve resilient vector consensus, Tverberg partition [22]- [25] and centerpoint-based [26] approaches have been proposed. The approximate Tverberg point-based approach has also been successfully applied to the resilient multi-robots rendezvous problem [13].…”

Section: Related Workmentioning

confidence: 99%

Resilient Distributed Diffusion for Multi-Robot Systems Using Centerpoint

Abbas

Shabbir

et al. 2020

Robotics: Science and Systems XVI

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In this paper, we study the resilient diffusion problem in a network of robots aiming to perform a task by optimizing a global cost function in a cooperative manner. In distributed diffusion, robots combine the information collected from their local neighbors and incorporate this aggregated information to update their states. If some robots are adversarial, this cooperation can disrupt the convergence of robots to the desired state. We propose a resilient aggregation rule based on the notion of centerpoint, which is a generalization of the median in the higher dimensional Euclidean space. Robots exchange their ddimensional state vectors with neighbors. We show that if a normal robot implements the centerpoint-based aggregation rule and has n neighbors, of which at most n d+1 − 1 are adversarial, then the aggregated state always lies in the convex hull of the states of the normal neighbors of the robot. Consequently, all normal robots implementing the distributed diffusion algorithm converge resiliently to the true target state. We also show that commonly used aggregation rules based on the coordinate-wise median and geometric median are, in fact, not resilient to certain attacks. We numerically evaluate our results on mobile multirobot networks and demonstrate the cases where diffusion with the weighted average, coordinate-wise median, and geometric median-based aggregation rules fail to converge to the true target state, whereas diffusion with the centerpoint-based rule is resilient in the same scenario.Index Terms-Resilient distributed learning and optimization, resilient aggregation, centerpoint n d+1 − 1. Here, n is the size of the neighborhood, and d is the dimension of the state vector of the robots.• We analyze the resilience and performance in terms of steadystate mean-square-deviation (MSD) of the centerpoint-based distributed diffusion. We also discuss the time complexity of computing a centerpoint.

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“…Algorithm 1 adopts a similar idea to that in most resilient protocols. At every step, the normal agent i obtains the states 2 A method to calculate this set with low complexity can be found in [23].…”

Section: B Relationship With the Existing Algorithms In Scalar Systemsmentioning

confidence: 99%

Resilient Multi-Dimensional Consensus in Adversarial Environment

Yan¹,

Li²,

Mo³

et al. 2020

Preprint

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This paper considers the multi-dimensional consensus and optimization in networked systems, where some of the agents might be misbehaving (or faulty). Despite the influence of these misbehaviors, the healthy agents aim to reach an agreement within the convex hull of their initial states in the consensus setting. To this end, we develop a "safe kernel" updating scheme, where each healthy agent computes a "safe kernel" based on the information from its neighbors, and modifies its state towards this kernel at every step. Assuming that the number of malicious agents is upper bounded, sufficient conditions on the network topology are presented to guarantee the achievement of resilient consensus. Given that the consensus serves as a fundamental objective of many distributed coordination problems, we next investigate the application of the proposed algorithm in distributed optimization. A resilient subgradient descent algorithm is subsequently developed, which combines the aforementioned safe kernel approach with the standard subgradient method. We show that, with appropriate stepsizes, the states of benign agents converge to a subset of the convex hull formed by their local minimizers. Some numerical examples are finally provided to verify the theoretical results.

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A resilient convex combination for consensus-based distributed algorithms

Cited by 26 publications

References 36 publications

Resilient Consensus for Robust Multiplex Networks with Asymmetric Confidence Intervals

Resilient Consensus for Robust Multiplex Networks with Asymmetric Confidence Intervals

Resilient Distributed Diffusion for Multi-Robot Systems Using Centerpoint

Resilient Multi-Dimensional Consensus in Adversarial Environment

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