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1. Distributed Detection of Adversarial Attacks for Resilient Cooperation of Multi-Robot Systems with Intermittent Communication

   Bahrami, Rayan; Jafarnejadsani, Hamidreza (October 2024, IEEE transactions on control of network systems)

   This paper concerns the consensus and formation of a network of mobile autonomous agents in adversarial settings where a group of malicious (compromised) agents are subject to deception attacks. In addition, the communication network is arbitrarily time-varying and subject to intermittent connections, possibly imposed by denial-of-service (DoS) attacks. We provide explicit bounds for network connectivity in an integral sense, enabling the characterization of the system’s resilience to specific classes of adversarial attacks. We also show that under the condition of connectivity in an integral sense uniformly in time, the system is finite-gain L stable and uniformly exponentially fast consensus and formation are achievable, provided malicious agents are detected and isolated from the network. We present a distributed and reconfigurable framework with theoretical guarantees for detecting malicious agents, allowing for the resilient cooperation of the remaining cooperative agents. Simulation studies are provided to illustrate the theoretical findings. 

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2. Distributed Optimization Over Time-Varying Graphs With Imperfect Sharing of Information

   https://doi.org/10.1109/TAC.2022.3207866  

   Reisizadeh, Hadi; Touri, Behrouz; Mohajer, Soheil (July 2023, IEEE Transactions on Automatic Control)

   We study strongly convex distributed optimization problems where a set of agents are interested in solving a separable optimization problem collaboratively. In this article, we propose and study a two-time-scale decentralized gradient descent algorithm for a broad class of lossy sharing of information over time-varying graphs. One time-scale fades out the (lossy) incoming information from neighboring agents, and one time-scale regulates the local loss functions' gradients. We show that assuming a proper choice of step-size sequences, certain connectivity conditions, and bounded gradients along the trajectory of the dynamics, the agents' estimates converge to the optimal solution with the rate of O(T^{−1/2}) . We also provide novel tools to study distributed optimization with diminishing averaging weights over time-varying graphs. 

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3. Multi-Agent Maximization of a Monotone Submodular Function via Maximum Consensus

   https://doi.org/10.1109/CDC45484.2021.9682818  

   Rezazadeh, Navid; Kia, Solmaz S. (December 2021, IEEE Conference on Decision and Control)

   This paper studies distributed submodular optimization subject to partition matroid. We work in the value oracle model where the only access of the agents to the utility function is through a black box that returns the utility function value. The agents are communicating over a connected undirected graph and have access only to their own strategy set. As known in the literature, submodular maximization subject to matroid constraints is NP-hard. Hence, our objective is to propose a polynomial-time distributed algorithm to obtain a suboptimal solution with guarantees on the optimality bound. Our proposed algorithm is based on a distributed stochastic gradient ascent scheme built on the multilinear-extension of the submodular set function. We use a maximum consensus protocol to minimize the inconsistency of the shared information over the network caused by delay in the flow of information while solving for the fractional solution of the multilinear extension model. Furthermore, we propose a distributed framework of finding a set solution using the fractional solution. We show that our distributed algorithm results in a strategy set that when the team objective function is evaluated at worst case the objective function value is in 1−1/e−O(1/T) of the optimal solution in the value oracle model where T is the number of communication instances of the agents. An example demonstrates our results. 

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4. Distributed Multi-Agent Bayesian Optimization for Unknown Design Space Exploration

   https://doi.org/10.1115/DETC2024-143377  

   Chen, Siyu; Bayrak, Alparslan Emrah; Sha, Zhenghui (August 2024, American Society of Mechanical Engineers)

   In multi-agent Bayesian optimization for Design Space Exploration (DSE), identifying a communication network among agents to share useful design information for enhanced cooperation and performance, considering the trade-off between connectivity and cost, poses significant challenges. To address this challenge, we develop a distributed multi-agent Bayesian optimization (DMABO) framework and study how communication network structures/connectivity and the resulting cost would impact the performance of a team of agents when finding the global optimum. Specifically, we utilize Lloyd’s algorithm to partition the design space to assign distinct regions to individual agents for exploration in the distributed multi-agent system (MAS). Based on this partitioning, we generate communication networks among agents using two models: 1) a range-limited model of communication constrained by neighborhood information; and 2) a range-free model without neighborhood constraints. We introduce network density as a metric to quantify communication costs. Then, we generate communication networks by gradually increasing the network density to assess the impact of communication costs on the performance of MAS in DSE. The experimental results show that the communication network based on the range-limited model can significantly improve performance without incurring high communication costs. This indicates that increasing the density of a communication network does not necessarily improve MAS performance in DSE. Furthermore, the results indicate that communication is only beneficial for team performance if it occurs between specific agents whose search regions are critically relevant to the location of the global optimum. The proposed DMABO framework and the insights obtained can help identify the best trade-off between communication structure and cost for MAS in unknown design space exploration. 

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5. Scale fragilities in localized consensus dynamics

   https://doi.org/10.1016/j.automatica.2023.111046  

   Tegling, Emma; Bamieh, Bassam; Sandberg, Henrik (July 2023, Automatica)

   We consider distributed consensus in networks where the agents have integrator dynamics of order two or higher (n>=2). We assume all feedback to be localized in the sense that each agent has a bounded number of neighbors and consider a scaling of the network through the addition of agents in a modular manner, i.e., without re-tuning controller gains upon addition. We show that standard consensus algorithms, which rely on relative state feedback, are subject to what we term scale fragilities, meaning that stability is lost as the network scales. For high-order agents (n>=3), we prove that no consensus algorithm with fixed gains can achieve consensus in networks of any size. That is, while a given algorithm may allow a small network to converge, it causes instability if the network grows beyond a certain finite size. This holds in families of network graphs whose algebraic connectivity, that is, the smallest non-zero Laplacian eigenvalue, is decreasing towards zero in network size (e.g. all planar graphs). For second-order consensus (n=2) we prove that the same scale fragility applies to directed graphs that have a complex Laplacian eigenvalue approaching the origin (e.g. directed ring graphs). The proofs for both results rely on Routh–Hurwitz criteria for complex-valued polynomials and hold true for general directed network graphs. We survey classes of graphs subject to these scale fragilities, discuss their scaling constants, and finally prove that a sub-linear scaling of nodal neighborhoods can suffice to overcome the issue. 

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