An event-triggered control technique for consensus of multi-agent systems with general linear dynamics is presented. This paper extends previous work to consider agents that are connected using directed graphs. Additionally, the approach shown here provides asymptotic consensus with guaranteed positive inter-event time intervals. This event-triggered control method is also used in the case where communication delays are present. For the communication delay case we also show that the agents achieve consensus asymptotically and that, for every agent, the time intervals between consecutive transmissions is lower-bounded by a positive constant.
In this paper, we propose an integral based event-triggering controller for bipartite consensus of the multi-agent systems whose dynamics are described by general linear system. We prove that the system achieves the bipartite consensus in asymptotic regime and there is a positive minimum inter-event time (MIET) between two consecutive triggering times of each agent. The proof of the asymptotive stability involves a novel argument used to bound the norm of the difference between the true state and its estimated state (for each time) by an integration of its square. Numerical results are provide…
This paper presents the formulation and analysis of a fully distributed dynamic event-triggered communication based robust dynamic average consensus algorithm. Dynamic average consensus problem involves a networked set of agents estimating the time-varying average of dynamic reference signals locally available to individual agents. We propose an asymptotically stable solution to the dynamic average consensus problem that is robust to network disruptions. Since this robust algorithm requires continuous communication among agents, we introduce a novel dynamic event-triggered communication scheme…
We consider the distributed leader-follower consensus problem with event-triggered communications. The system under consideration is a non-linear input-affine multi agent system. The agents are assumed to have identical dynamics structure with uncertain parameters and satisfying an incremental stabilisability condition. A distributed control law is proposed which achieves consensus based on two novel Communication Triggering Conditions (CTCs): the first one to achieve an asymptotic consensus but without any guarantees on Zeno behaviour and the second one to exclude Zeno behaviour but with prac…
We consider the global consensus problem for multi-agent systems with input saturation over digraphs. Under a mild connectivity condition that the underlying digraph has a directed spanning tree, we use Lyapunov methods to show that the widely used distributed consensus protocol, which solves the consensus problem for the case without input saturation constraints, also solves the global consensus problem for the case with input saturation constraints. In order to reduce the overall need of communication and system updates, we then propose a distributed event-triggered control law. Global conse…
This technical note proposes the decentralized-partial-consensus optimization with inequality constraints, and a continuous-time algorithm based on multiple interconnected recurrent neural networks (RNNs) is derived to solve the obtained optimization problems. First, the partial-consensus matrix originating from Laplacian matrix is constructed to tackle the partial-consensus constraints. In addition, using the non-smooth analysis and Lyapunov-based technique, the convergence property about the designed algorithm is further guaranteed. Finally, the effectiveness of the obtained results is shown…
This article provides an introduction to event-triggered coordination for multi-agent average consensus. We provide a comprehensive account of the motivations behind the use of event-triggered strategies for consensus, the methods for algorithm synthesis, the technical challenges involved in establishing desirable properties of the resulting implementations, and their applications in distributed control. We pay special attention to the assumptions on the capabilities of the network agents and the resulting features of the algorithm execution, including the interconnection topology, the evaluat…
We analyze the convergence of decentralized consensus algorithm with delayed gradient information across the network. The nodes in the network privately hold parts of the objective function and collaboratively solve for the consensus optimal solution of the total objective while they can only communicate with their immediate neighbors. In real-world networks, it is often difficult and sometimes impossible to synchronize the nodes, and therefore they have to use stale gradient information during computations. We show that, as long as the random delays are bounded in expectation and a proper dim…
We consider decentralized optimization problems where one aims to minimize a sum of convex smooth objective functions distributed between nodes in the network. The links in the network can change from time to time. For the setting when the amount of changes is arbitrary, lower complexity bounds and corresponding optimal algorithms are known, and the consensus acceleration is not possible. However, in practice the magnitude of network changes may be limited. We derive lower communication complexity bounds for several regimes of velocity of networks changes. Moreover, we show how to obtain accel…
We consider a resource allocation problem over an undirected network of agents, where edges of the network define communication links. The goal is to minimize the sum of agent-specific convex objective functions, while the agents' decisions are coupled via a convex conic constraint. We derive two methods by applying the alternating direction method of multipliers (ADMM) for decentralized consensus optimization to the dual of our resource allocation problem. Both methods are fully parallelizable and decentralized in the sense that each agent exchanges information only with its neighbors in the …
In this paper, an event-triggered Reinforcement Learning (RL) method is proposed for the optimal attitude consensus of multiple rigid body networks with unknown dynamics. Firstly, the consensus error is constructed through the attitude dynamics. According to the Bellman optimality principle, the implicit form of the optimal controller and the corresponding Hamilton-Jacobi-Bellman (HJB) equations are obtained. Because of the augmented system, the optimal controller can be obtained directly without relying on the system dynamics. Secondly, the self-triggered mechanism is applied to reduce the co…
In this chapter we look at one of the canonical driving examples for multi-agent systems: average consensus. In this scenario, a group of agents seek to agree on the average of their initial states. Depending on the particular application, such states might correspond to sensor measurements, estimates about the position of a target, or some other data that needs to be fused. Due to its numerous applications in networked systems, many algorithmic solutions exist to the multi-agent average consensus problem; however, a majority of them rely on agents having continuous or periodic availability of…
This paper focuses on the decentralized optimization problem, where agents in a network cooperate to minimize the sum of their local objective functions by information exchange and local computation. Based on the alternating direction method of multipliers (ADMM), we propose CC-DQM, a communication-efficient decentralized second-order optimization algorithm that combines compressed communication with event-triggered communication. Specifically, agents are allowed to transmit the compressed message only when the current primal variables have changed greatly compared to its last estimate. Moreov…
This work addresses the decentralized optimization problem where a group of agents with coupled private objective functions work together to exactly optimize the summation of local interests. Upon modeling the decentralized problem as an equality-constrained centralized one, we leverage the linearized augmented Lagrangian method (LALM) to design an event-triggered decentralized algorithm that only requires light local computation at generic time instants and peer-to-peer communication at sporadic triggering time instants. The triggering time instants for each agent are locally determined by co…
In this work, we introduce ADAPD, $\textbf{A}$ $\textbf{D}$ecentr$\textbf{A}$lized $\textbf{P}$rimal-$\textbf{D}$ual algorithmic framework for solving non-convex and smooth consensus optimization problems over a network of distributed agents. The proposed framework relies on a novel problem formulation that elicits ADMM-type updates, where each agent first inexactly solves a local strongly convex subproblem with any method of its choice and then performs a neighbor communication to update a set of dual variables. We present two variants that allow for a single gradient step for the primal upda…
Decentralized Inexact Cubic Newton Method with Consensus Procedure
Mohamed bin Zayed University of Artificial Intelligence (MBZUAI)（穆罕默德·本·扎耶德人工智能大学）；Moscow Independent Research Institute of Artificial Intelligence（莫斯科独立人工智能研究院）；Trusted AI Research Center, RAS（俄罗斯科学院可信人工智能研究中心）；Innopolis University（因诺波利斯大学）
The effective resistance between a pair of nodes in a weighted undirected graph is defined as the potential difference induced between them when a unit current is injected at the first node and extracted at the second node, treating edge weights as the conductance values of edges. The effective resistance is a key quantity of interest in many applications and fields including solving linear systems, Markov Chains and continuous-time averaging networks. We develop an efficient linearly convergent distributed algorithm for computing effective resistances and demonstrate its performance through n…
Decentralized Linearized Consensus ADMM with Efficient Quantized Communication
The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））；The Hong Kong University of Science and Technology（香港科技大学）；KTH Royal Institute of Technology（瑞典皇家理工学院）
In this paper, we consider minimizing a sum of local convex objective functions in a distributed setting, where the cost of communication and/or computation can be expensive. We extend and generalize the analysis for a class of nested gradient-based distributed algorithms (NEAR-DGD; Berahas, Bollapragada, Keskar and Wei, 2018) to account for multiple gradient steps at every iteration. We show the effect of performing multiple gradient steps on the rate of convergence and on the size of the neighborhood of convergence, and prove R-Linear convergence to the exact solution with a fixed number of …
Decentralized design of consensus protocols with minimal communication links based on directed spanning tree
College of Artificial Intelligence and Automation, Beijing University of Technology（北京工业大学人工智能与自动化学院）；Engineering Research Center of Digital Community, Ministry of Education（教育部数字社区工程研究中心）
We propose decentralized primal-dual methods for cooperative multi-agent consensus optimization problems over both static and time-varying communication networks, where only local communications are allowed. The objective is to minimize the sum of agent-specific convex functions over conic constraint sets defined by agent-specific nonlinear functions; hence, the optimal consensus decision should lie in the intersection of these private sets. Under the strong convexity assumption, we provide convergence rates for sub-optimality, infeasibility, and consensus violation in terms of the number of c…
This paper considers consensus optimization problems where each node of a network has access to a different summand of an aggregate cost function. Nodes try to minimize the aggregate cost function, while they exchange information only with their neighbors. We modify the dual decomposition method to incorporate a curvature correction inspired by the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton method. The resulting dual D-BFGS method is a fully decentralized algorithm in which nodes approximate curvature information of themselves and their neighbors through the satisfaction of a secant …
This paper considers the decentralized consensus optimization problem defined over a network where each node holds a second-order differentiable local objective function. Our goal is to minimize the summation of local objective functions and find the exact optimal solution using only local computation and neighboring communication. We propose a novel Newton tracking algorithm, where each node updates its local variable along a local Newton direction modified with neighboring and historical information. We investigate the connections between the proposed Newton tracking algorithm and several ex…
We study the decentralized consensus and stochastic optimization problems with compressed communications over static directed graphs. We propose an iterative gradient-based algorithm that compresses messages according to a desired compression ratio. The proposed method provably reduces the communication overhead on the network at every communication round. Contrary to existing literature, we allow for arbitrary compression ratios in the communicated messages. We show a linear convergence rate for the proposed method on the consensus problem. Moreover, we provide explicit convergence rates for …
Federal University of Alagoas（阿拉戈斯联邦大学）；Federal University of Minas Gerais（米纳斯吉拉斯联邦大学）；Massachusetts Institute of Technology（麻省理工学院）
This paper presents a solution based on dual quaternion algebra to the general problem of pose (i.e., position and orientation) consensus for systems composed of multiple rigid-bodies. The dual quaternion algebra is used to model the agents' poses and also in the distributed control laws, making the proposed technique easily applicable to time-varying formation control of general robotic systems. The proposed pose consensus protocol has guaranteed convergence when the interaction among the agents is represented by directed graphs with directed spanning trees, which is a more general result whe…
This paper proposes decentralized resource-aware coordination schemes for solving network optimization problems defined by objective functions which combine locally evaluable costs with network-wide coupling components. These methods are well suited for a group of supervised agents trying to solve an optimization problem under mild coordination requirements. Each agent has information on its local cost and coordinates with the network supervisor for information about the coupling term of the cost. The proposed approach is feedback-based and asynchronous by design, guarantees anytime feasibilit…
Distributed and Decentralized Optimization Algorithms via Consensus ALADIN
The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））；The Hong Kong University of Science and Technology（香港科技大学）；University of Pittsburgh（匹兹堡大学）；KTH Royal Institute of Technology（皇家理工学院）；Digital Futures（数字未来）
The alternating direction method of multipliers (ADMM) has recently been recognized as a promising approach for large-scale machine learning models. However, very few results study ADMM from the aspect of communication costs, especially jointly with running time. In this letter, we investigate the communication efficiency and running time of ADMM in solving the consensus optimization problem over decentralized networks. We first review the effort of random walk ADMM (W-ADMM), which reduces communication costs at the expense of running time. To accelerate the convergence speed of W-ADMM, we pro…
This paper considers decentralized consensus optimization problems where different summands of a global objective function are available at nodes of a network that can communicate with neighbors only. The proximal method of multipliers is considered as a powerful tool that relies on proximal primal descent and dual ascent updates on a suitably defined augmented Lagrangian. The structure of the augmented Lagrangian makes this problem non-decomposable, which precludes distributed implementations. This problem is regularly addressed by the use of the alternating direction method of multipliers. T…
In smart grids, distributed energy resources (DERs) have penetrated residential zones to provide a new form of electricity supply, mainly from renewable energy. Residential households and commercial buildings with DERs have become prosumers in the local grids, since they can sell surplus power to others. Researches have been initiated to integrate and utilize DERs through better control and communication strategies. With the advances in the Internet of Things (IoT) technology, unprecedented coordination among DERs can be achieved to facilitate energy trading and transactive energy management. …
This paper investigates the distributed event-based consensus problem of switching networks satisfying the jointly connected condition. Both the state consensus of homogeneous linear networks and output consensus of heterogeneous networks are studied. Two kinds of event-based protocols based on local sampled information are designed, without the need to solve any matrix equation or inequality. Theoretical analysis indicates that the proposed event-based protocols guarantee the achievement of consensus and the exclusion of Zeno behaviors for jointly connected undirected switching graphs. These …
In this paper, we consider the problem of privacy preservation in the average consensus problem when communication among nodes is quantized. More specifically, we consider a setting where some nodes in the network are curious but not malicious and they try to identify the initial states of other nodes based on the data they receive during their operation (without interfering in the computation in any other way), while some nodes in the network want to ensure that their initial states cannot be inferred exactly by the curious nodes. We propose two privacy-preserving event-triggered quantized av…
Optimal transport has been used extensively in resource matching to promote the efficiency of resources usages by matching sources to targets. However, it requires a significant amount of computations and storage spaces for large-scale problems. In this paper, we take a consensus-based approach to decentralize discrete optimal transport problems and develop fully distributed algorithms with alternating direction method of multipliers. We show that our algorithms guarantee certain levels of efficiency and privacy besides the distributed nature. We further derive primal and dual algorithms by ex…
University of California, Los Angeles（加利福尼亚大学洛杉矶分校）；US Army Research Lab（美国陆军研究实验室）
In this paper, we propose and analyze SPARQ-SGD, which is an event-triggered and compressed algorithm for decentralized training of large-scale machine learning models. Each node can locally compute a condition (event) which triggers a communication where quantized and sparsified local model parameters are sent. In SPARQ-SGD each node takes at least a fixed number ($H$) of local gradient steps and then checks if the model parameters have significantly changed compared to its last update; it communicates further compressed model parameters only when there is a significant change, as specified b…
Motivated by decentralized sensing and policy evaluation problems, we consider a particular type of distributed stochastic optimization problem over a network, called the online stochastic distributed averaging problem. We design a dual-based method for this distributed consensus problem with Polyak--Ruppert averaging and analyze its behavior. We show that the proposed algorithm attains an accelerated deterministic error depending optimally on the condition number of the network, and also that it has an order-optimal stochastic error. This improves on the guarantees of state-of-the-art distrib…
The alternating direction method of multipliers (ADMM) has been recently recognized as a promising optimizer for large-scale machine learning models. However, there are very few results studying ADMM from the aspect of communication costs, especially jointly with privacy preservation, which are critical for distributed learning. We investigate the communication efficiency and privacy-preservation of ADMM by solving the consensus optimization problem over decentralized networks. Since walk algorithms can reduce communication load, we first propose incremental ADMM (I-ADMM) based on the walk alg…
Peking University（北京大学）；Shanghai Artificial Intelligence Laboratory（上海人工智能实验室）；The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；Michigan State University（密歇根州立大学）；Fudan University（复旦大学）；Alibaba DAMO Academy（阿里巴巴达摩院）；Princeton University（普林斯顿大学）
Decentralized optimization is an emerging paradigm in distributed learning in which agents achieve network-wide solutions by peer-to-peer communication without the central server. Since communication tends to be slower than computation, when each agent communicates with only a few neighboring agents per iteration, they can complete iterations faster than with more agents or a central server. However, the total number of iterations to reach a network-wide solution is affected by the speed at which the agents' information is ``mixed'' by communication. We found that popular communication topolog…
