We are concerned with finding Nash Equilibria in agent-based multi-cluster games, where agents are separated into distinct clusters. While the agents inside each cluster collaborate to achieve a common goal, the clusters are considered to be virtual players that compete against each other in a non-cooperative game with respect to a coupled cost function. In such scenarios, the inner-cluster problem and the game between the clusters need to be solved simultaneously. Therefore, the resulting inter-cluster Nash Equilibrium should also be a minimizer of the social welfare problem inside the clusters. In this work, this setup is cast as a distributed optimization problem with sparse state information. Hence, critical information, such as the agent's cost functions, remain private. We present a distributed algorithm that converges with a linear rate to the optimal solution. Furthermore, we apply our algorithm to an extended cournot game to verify our theoretical results.
In this paper, we study the leaderless consensus problem for multiple Lagrangian systems in the presence of parametric uncertainties and external disturbances under directed graphs. For achieving asymptotic behavior, a robust continuous term with adaptive varying gains is added to alleviate the effects of the external disturbances with unknown bounds. In the case of a fixed directed graph, by introducing an integrate term in the auxiliary variable design, the final consensus equilibrium can be explicitly derived. We show that the agents achieve weighted average consensus, where the final equil…
Guaranteed Cost Tracking for Uncertain Coupled Multi-agent Systems Using Consensus over a Directed Graph
The University of New South Wales at the Australian Defence Force Academy（澳大利亚国防军学院新南威尔士大学）；Australian National University（澳大利亚国立大学）；Southeast University（东南大学）
This paper studies cooperative tracking problem of heterogeneous Euler-Lagrange systems with an uncertain leader. Different from most existing works, system dynamic knowledge of the leader node is unaccessible to any follower node in our paper. Distributed adaptive observers are designed for all follower nodes, simultaneously estimate the state and parameters of the leader node. The observer design does not rely on the frequency knowledge of the leader node, and the estimation errors are shown to converge to zero exponentially. Moreover, the results are applied to general directed graphs, wher…
We consider the problem of decentralized optimization over time-varying directed networks. The network nodes can access only their local objectives, and aim to collaboratively minimize a global function by exchanging messages with their neighbors. Leveraging sparsification, gradient tracking and variance-reduction, we propose a novel communication-efficient decentralized optimization scheme that is suitable for resource-constrained time-varying directed networks. We prove that in the case of smooth and strongly-convex objective functions, the proposed scheme achieves an accelerated linear conv…
This paper addresses a formation tracking problem for nonlinear multi-agent systems with time-varying actuator faults, in which only a subset of agents has access to the leader's information over the directed leader-follower network with a spanning tree. Both the amplitudes and signs of control coefficients induced by actuator faults are unknown and time-varying. The aforementioned setting improves the practical relevance of the problem to be investigated, and meanwhile, it poses technical challenges to distributed controller design and asymptotic stability analysis. By introducing a distribut…
Optimal tracking of continuous time nonlinear systems has been extensively studied in literature. However, in several applications, absence of knowledge about system dynamics poses a severe challenge to solving the optimal tracking problem. This has found growing attention among researchers recently, and integral reinforcement learning (IRL)-based method augmented with actor neural network (NN) have been deployed to this end. However, very few studies have been directed to model-free $H_{\infty}$ optimal tracking control that helps in attenuating the effect of disturbances on the system perfor…
A unified framework of fully distributed adaptive output time-varying formation control for linear multi-agent systems: an observer viewpoint
Ecole Centrale de Lille（里尔中央理工学院）；Beihang University（北京航空航天大学）；Beijing Engineering Center for Clean Energy & High Efficient Power, Beihang University（北京航空航天大学清洁能源与高效动力工程中心）；Department of Mathematics, Beijing Jiaotong University（北京交通大学数学系）；CRIStAL, UMR CNRS 9189, Ecole Centrale de Lille（里尔中央理工学院 CRIStAL 实验室）
Fast Distributed Optimization over Directed Graphs under Malicious Attacks using Trust
School of Engineering and Applied Sciences, Harvard University（哈佛大学工程与应用科学学院）；Faculty of Engineering, Bar-Ilan University（巴伊兰大学工程学院）；School of Electrical, Computer and Energy Engineering, Arizona State University（亚利桑那州立大学电气、计算机与能源工程学院）
This paper investigates the distributed optimal output consensus problem of second-order uncertain nonlinear multi-agent systems over weight-unbalanced directed networks. Under the standard assumption that local cost functions are strongly convex with globally Lipschitz gradients, a novel distributed dynamic state feedback controller is developed such that the outputs of all the agents reach the optimal solution to minimize the global cost function which is the sum of all the local cost functions. The controller design is based on a two-layer strategy, where a distributed optimal coordinator a…
In this paper, we propose Push-SAGA, a decentralized stochastic first-order method for finite-sum minimization over a directed network of nodes. Push-SAGA combines node-level variance reduction to remove the uncertainty caused by stochastic gradients, network-level gradient tracking to address the distributed nature of the data, and push-sum consensus to tackle the challenge of directed communication links. We show that Push-SAGA achieves linear convergence to the exact solution for smooth and strongly convex problems and is thus the first linearly-convergent stochastic algorithm over arbitrar…
In this contribution, the properties of sub-stochastic matrix and super-stochastic matrix are applied to analyze the bipartite tracking issues of multi-agent systems (MASs) over signed networks, in which the edges with positive weight and negative weight are used to describe the cooperation and competition among the agents, respectively. For the sake of integrity of the study, the overall content is divided into two parts. In the first part, we examine the dynamics of bipartite tracking for first-order MASs, second-order MASs and general linear MASs in the presence of asynchronous interactions…
In this note, a novel observer-based output feedback control approach is proposed to address the distributed optimal output consensus problem of uncertain nonlinear multi-agent systems in the normal form over unbalanced directed graphs. The main challenges of the concerned problem lie in unbalanced directed graphs and nonlinearities of multi-agent systems with their agent states not available for feedback control. Based on a two-layer controller structure, a distributed optimal coordinator is first designed to convert the considered problem into a reference-tracking problem. Then a decentraliz…
In this paper, we study the problem of consensus-based distributed optimization where a network of agents, abstracted as a directed graph, aims to minimize the sum of all agents' cost functions collaboratively. In existing distributed optimization approaches (Push-Pull/AB) for directed graphs, all agents exchange their states with neighbors to achieve the optimal solution with a constant stepsize, which may lead to the disclosure of sensitive and private information. For privacy preservation, we propose a novel state-decomposition based gradient tracking approach (SD-Push-Pull) for distributed…
In this report, we study decentralized stochastic optimization to minimize a sum of smooth and strongly convex cost functions when the functions are distributed over a directed network of nodes. In contrast to the existing work, we use gradient tracking to improve certain aspects of the resulting algorithm. In particular, we propose the~\textbf{\texttt{S-ADDOPT}} algorithm that assumes a stochastic first-order oracle at each node and show that for a constant step-size~$α$, each node converges linearly inside an error ball around the optimal solution, the size of which is controlled by~$α$. For…
Online Leader Selection for Improved Collective Tracking and Formation Maintenance
CNRS, LAAS（法国国家科学研究中心，系统分析与研究实验室）；Univ de Toulouse, LAAS（图卢兹大学，系统分析与研究实验室）；CNRS at Irisa and Inria Rennes Bretagne Atlantique（法国国家科学研究中心与布列塔尼大西洋雷恩国家信息与自动化研究所，Irisa）
Distributed optimization enables networked agents to cooperatively solve a global optimization problem even with each participating agent only having access to a local partial view of the objective function. Despite making significant inroads, most existing results on distributed optimization rely on noise-free information sharing among the agents, which is problematic when communication channels are noisy, messages are coarsely quantized, or shared information are obscured by additive noise for the purpose of achieving differential privacy. The problem of information-sharing noise is particul…
Provably Accelerated Decentralized Gradient Method Over Unbalanced Directed Graphs
Shanghai Center for Mathematical Sciences, Fudan University（复旦大学上海数学中心）；School of Mathematical Sciences, Fudan University（复旦大学数学科学学院）；Shanghai Key Laboratory for Contemporary Applied Mathematics（上海现代应用数学重点实验室）；Shanghai Artificial Intelligence Laboratory（上海人工智能实验室）；School of Data Science, The Chinese University of Hong Kong, Shenzhen (CUHK-Shenzhen)（香港中文大学（深圳）数据科学学院）；Shenzhen Research Institute of Big Data（深圳大数据研究院）
In this paper, a new yet indirect performance guaranteed framework is established to address the distributed tracking control problem for networked uncertain nonlinear strict-feedback systems with unknown time-varying gains under a directed interaction topology. The proposed framework involves two steps: In the first one, a fully distributed robust filter is constructed to estimate the desired trajectory for each agent with guaranteed observation performance that allows the directions among the agents to be non-identical. In the second one, by establishing a novel lemma regarding Nussbaum func…
