A consensus system is a linear multi-agent system in which agents communicate to reach a so-called consensus state, defined as the average of the initial states of the agents. Consider a more generalized situation in which each agent is given a positive weight and the consensus state is defined as the weighted average of the initial conditions. We characterize in this paper the weighted averages that can be evaluated in a decentralized way by agents communicating over a directed graph. Specifically, we introduce a linear function, called the objective map, that defines the desired final state as a function of the initial states of the agents. We then provide a complete answer to the question of whether there is a decentralized consensus dynamics over a given digraph which converges to the final state specified by an objective map. In particular, we characterize not only the set of objective maps that are feasible for a given digraph, but also the consensus dynamics that implements the objective map. In addition, we present a decentralized algorithm to design the consensus dynamics.
Restricting Voltage Deviation of DC Microgrids with Critical and Ordinary Nodes: A Generalized Consensus Approach
School of Electrical Engineering, Yellow River Conservancy Technical Institute（黄河水利职业技术学院电气工程学院）；School of Intelligence Science and Engineering, Harbin Institute of Technology, Shenzhen（哈尔滨工业大学（深圳）智能科学与工程学院）
We propose a distributed nonparametric algorithm for solving measure-valued optimization problems with additive objectives. Such problems arise in several contexts in stochastic learning and control including Langevin sampling from an unnormalized prior, mean field neural network learning and Wasserstein gradient flows. The proposed algorithm comprises a two-layer alternating direction method of multipliers (ADMM). The outer-layer ADMM generalizes the Euclidean consensus ADMM to the Wasserstein consensus ADMM, and to its entropy-regularized version Sinkhorn consensus ADMM. The inner-layer ADMM…
Several algorithms in prior literature have been proposed which guarantee consensus of normally behaving agents in a network that may contain adversarially behaving agents. These algorithms guarantee that the consensus value lies within the convex hull of initial normal agents' states, with the exact consensus value possibly being unknown. In leader-follower consensus problems however, the objective is for normally behaving agents to track a reference state that may take on values outside of this convex hull. In this paper we present methods for agents in time-varying graphs with discrete-time…
The problem of consensus in the presence of adversarially behaving agents has been studied extensively in the literature. The proposed algorithms typically guarantee that the consensus value lies within the convex hull of initial normal agents' states. In leader-follower consensus problems however, the objective for normally behaving agents is to track a time-varying reference state that may take on values outside of this convex hull. In this paper we present a method for agents with discrete-time dynamics to resiliently track a set of leaders' common time-varying reference state despite a bou…
Constrained submodular set function maximization problems often appear in multi-agent decision-making problems with a discrete feasible set. A prominent example is the problem of multi-agent mobile sensor placement over a discrete domain. However, submodular set function optimization problems are known to be NP-hard. In this paper, we consider a class of submodular optimization problems that consists of maximization of a monotone and submodular set function subject to a uniform matroid constraint over a group of networked agents that communicate over a connected undirected graph. Our objective…
Recently, many cooperative distributed multi-agent reinforcement learning (MARL) algorithms have been proposed in the literature. In this work, we study the effect of adversarial attacks on a network that employs a consensus-based MARL algorithm. We show that an adversarial agent can persuade all the other agents in the network to implement policies that optimize an objective that it desires. In this sense, the standard consensus-based MARL algorithms are fragile to attacks.
Distributed estimation in the context of sensor networks is considered, where distributed agents are given a set of sensor measurements, and are tasked with estimating a target variable. A subset of sensors are assumed to be faulty. The objective is to minimize i) the mean square estimation error at each node (accuracy objective), and ii) the mean square distance between the estimates at each pair of nodes (consensus objective). It is shown that there is an inherent tradeoff between the former and latter objectives. Assuming a general stochastic model, the sensor fusion algorithm optimizing th…
This paper proposes a continuous-time dynamic active weighted average consensus algorithm in which the agents can alternate between active and passive modes depending on their ability to access to their reference input. The objective is to enable all the agents, both active and passive, to track the weighted average of the reference inputs of the active agents. The algorithm is modeled as a switched linear system whose convergence properties are carefully studied considering the agents' piece-wise constant access to the reference signals and possible piece-wise constant weights of the agents. …
In this paper, we study the relationship between resilience and accuracy in the resilient distributed multi-dimensional consensus problem. We consider a network of agents, each of which has a state in $\mathbb{R}^d$. Some agents in the network are adversarial and can change their states arbitrarily. The normal (non-adversarial) agents interact locally and update their states to achieve consensus at some point in the convex hull $\calC$ of their initial states. This objective is achievable if the number of adversaries in the neighborhood of normal agents is less than a specific value, which is …
AFRL’s Control Science Center of Excellence（美国空军研究实验室控制科学卓越中心）；Infoscitex Corp.（Infoscitex公司）；Department of Electrical Engineering, UC Santa Cruz（加州大学圣克鲁兹分校电气工程系）
University of Notre Dame（圣母大学）；Stony Brook University（石溪大学）
Adversarial attacks during training can strongly influence the performance of multi-agent reinforcement learning algorithms. It is, thus, highly desirable to augment existing algorithms such that the impact of adversarial attacks on cooperative networks is eliminated, or at least bounded. In this work, we consider a fully decentralized network, where each agent receives a local reward and observes the global state and action. We propose a resilient consensus-based actor-critic algorithm, whereby each agent estimates the team-average reward and value function, and communicates the associated pa…
Distributed Optimization via Energy Conservation Laws in Dilated Coordinates
Data & Decision Sciences division of Tata Consultancy Services Research（塔塔咨询公司数据与决策科学部门）；Faculty of Systems & Control group, Indian Institute of Technology Bombay（印度理工学院孟买分校系统与控制学院）
