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1. Byzantine-Resilient Multi-Agent Optimization

   https://doi.org/10.1109/TAC.2020.3008139  

   Su, L; Vaidya, N.H. (January 2021, IEEE transactions on automatic control)

   null (Ed.)

   We consider the problem of multiagent optimization wherein an unknown subset of agents suffer Byzantine faults and thus behave adversarially. We assume that each agent i has a local cost function fi , and the overarching goal of the good agents is to collaboratively minimize a global objective that properly aggregates these local cost functions. To the best of our knowledge, we are among the first to study Byzantine-resilient optimization where no central coordinating agent exists, and we are the first to characterize the structures of the convex coefficients of the achievable global objectives. Dealing with Byzantine faults is very challenging. For example, in contrast to fault-free networks, reaching Byzantine-resilient agreement even in the simplest setting is far from trivial. We take a step toward solving the proposed Byzantine-resilient multiagent optimization problem by focusing on scalar local cost functions. Our results might provide useful insights for the general local cost functions. 

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2. A Study of Privacy Preservation in Average Consensus Algorithm via Deterministic Obfuscation Signals

   https://doi.org/10.1109/TCNS.2023.3290114  

   Rezazadeh, Navid; Kia, Solmaz S. (March 2024, IEEE Transactions on Control of Network Systems)

   This article is a study on the use of additive obfuscation signals to keep the reference values of the agents in the continuous-time Laplacian average consensus algorithm private from eavesdroppers. Obfuscation signals are perturbations that agents add to their local dynamics and their transmitted-out messages to conceal their private reference values. An eavesdropper is an agent inside or outside the network that has access to some subset of the interagent communication messages, and its knowledge set also includes the network topology. Rather than focusing on using a zero-sum and vanishing additive signal, our work determines the necessary and sufficient conditions that define the set of admissible obfuscation signals that do not perturb the convergence point of the algorithm from the average of the reference values of the agents. Of theoretical interest, our results show that this class includes nonvanishing signals as well. Given this broader class of admissible obfuscation signals, we define a deterministic notion of privacy preservation. In this definition, privacy preservation for an agent means that neither the private reference value nor a finite set of values to which the private reference value of the agent belongs to can be obtained. Then, we evaluate the agents’ privacy against eavesdroppers with different knowledge sets. 

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3. Ensemble inference of unobserved infections in networks using partial observations

   https://doi.org/10.1371/journal.pcbi.1011355  

   Zhang, Renquan; Tai, Jilei; Pei, Sen (August 2023, PLOS Computational Biology)

   Fu, Feng (Ed.)

   Undetected infections fuel the dissemination of many infectious agents. However, identification of unobserved infectious individuals remains challenging due to limited observations of infections and imperfect knowledge of key transmission parameters. Here, we use an ensemble Bayesian inference method to infer unobserved infections using partial observations. The ensemble inference method can represent uncertainty in model parameters and update model states using all ensemble members collectively. We perform extensive experiments in both model-generated and real-world networks in which individuals have differential but unknown transmission rates. The ensemble method outperforms several alternative approaches for a variety of network structures and observation rates, despite that the model is mis-specified. Additionally, the computational complexity of this algorithm scales almost linearly with the number of nodes in the network and the number of observations, respectively, exhibiting the potential to apply to large-scale networks. The inference method may support decision-making under uncertainty and be adapted for use for other dynamical models in networks. 

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4. Balancing Agility and Communication: Denser Networks Require Faster Agents

   https://doi.org/10.1109/OJCSYS.2023.3324274  

   Huang, Yu-Mei; de_Oliveira, Arthur_C B; Murugan, Dinesh; Siami, Milad (January 2023, IEEE Open Journal of Control Systems)

   This article delves into the challenges of ensuring stability (in some sense) and robustness in large-scale second-order consensus networks (SOCNs) and autonomous vehicle platoons in the discrete-time domain. We propose a graph-theoretic methodology for designing a state feedback law for these systems in a discrete-time framework. By analyzing the behavior of the solutions of the networks based on the algebraic properties of the Laplacian matrices of the underlying graphs and on the value of the update cycle (also known as the time step) of each vehicle, we provide a necessary and sufficient condition for the stability of a linear second-order consensus network in the discrete-time domain. We then perform an $$\mathcal {H}_{2}$$ -based robustness analysis to demonstrate the relationship between the $$\mathcal {H}_{2}$$ -norm of the system, network size, connectivity, and update cycles, providing insights into how these factors impact the convergence and robustness of the system. A key contribution of this work is the development of a formal framework for understanding the link between an $$\mathcal {H}_{2}$$ -based performance measure and the restrictions on the update cycle of the vehicles. Specifically, we show that denser networks (i.e., networks with more communication links) might require faster agents (i.e., smaller update cycles) to outperform or achieve the same level of robustness as sparse networks (i.e., networks with fewer communication links) - see Fig. 1. These findings have important implications for the design and implementation of large-scale consensus networks and autonomous vehicle platoons, highlighting the need for a balance between network density and update cycle speed for optimal performance. We finish the article with results from simulations and experiments that illustrate the effectiveness of the proposed framework in predicting the behavior of vehicle platoons, even for more complex agents with nonlinear dynamics, using Quanser's Qlabs and Qcars. 

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5. Exact Byzantine Consensus on Undirected Graphs under Local Broadcast Model

   https://doi.org/10.1145/3293611.3331619  

   Khan, Muhammad Samir; Naqvi, Syed Shalan; Vaidya, Nitin H. (July 2019, ACM Symposium on Principles in Distributed Computing)

   This paper considers the Byzantine consensus problem for nodes with binary inputs. The nodes are interconnected by a network represented as an undirected graph, and the system is assumed to be synchronous. Under the classical point-to-point communication model, it is well-known that the following two conditions are both necessary and sufficient to achieve Byzantine consensus among n nodes in the presence of up to ƒ Byzantine faulty nodes: n & 3 #8805; 3 ≥ ƒ+ 1 and vertex connectivity at least 2 ƒ + 1. In the classical point-to-point communication model, it is possible for a faulty node to equivocate, i.e., transmit conflicting information to different neighbors. Such equivocation is possible because messages sent by a node to one of its neighbors are not overheard by other neighbors. This paper considers the local broadcast model. In contrast to the point-to-point communication model, in the local broadcast model, messages sent by a node are received identically by all of its neighbors. Thus, under the local broadcast model, attempts by a node to send conflicting information can be detected by its neighbors. Under this model, we show that the following two conditions are both necessary and sufficient for Byzantine consensus: vertex connectivity at least ⌋ 3 fƒ / 2 ⌊ + 1 and minimum node degree at least 2 ƒ. Observe that the local broadcast model results in a lower requirement for connectivity and the number of nodes n, as compared to the point-to-point communication model. We extend the above results to a hybrid model that allows some of the Byzantine faulty nodes to equivocate. The hybrid model bridges the gap between the point-to-point and local broadcast models, and helps to precisely characterize the trade-off between equivocation and network requirements. 

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