CONSENSUS ANALYSIS AND DESIGN OF LINEAR INTERCONNECTED MULTI-AGENT SYSTEMS

We deal with the state consensus problem of a general Linear Interconnected Multi-Agent System(LIMAS) under a time-invariant and directed communication topology.Firstly,we propose a linear consensus protocol in a general form,which consists of state feedback of the agent itself and feedback form of the relative states between the agent and its neighbors.Secondly,a state-linear-transformation is applied to equivalently transform the state consensus problem into a partial stability problem.Based on the partial stability theory,we derive a sufficient and necessary criterion of consensus convergence,which is expressed via the Hurwitz stability of a real matrix constructed from the parameters of the agent models and the protocols,and present an analytical formula of the consensus function.Lastly,we propose a design procedure of the gain matrices in the protocol by solving a bilinear matrix inequality.     

具有部分状态信息的二阶多智能体系统的一致性

研究二阶连续多智能体系统的一致性问题,其中每个智能体只能在一系列离散时刻上获得位置信息.为了关于完全状态,即位置和速度,都达到一致,设计一类协议,并建立在该协议下,一致性成立的充要条件.该条件揭示了交流拓扑、控制器增益、采样周期和保持器的更新周期之间的关系.仿真例子表明理论结果是有效的.     

一阶多智能体系统的一致性分析

研究一阶连续多智能体系统的一致性问题,其中每个智能体只能在一系列离散时刻上获得其相对邻居的状态信息,并且每个智能体的保持器的周期和采样器的周期是不同的.通过分析多智能体系统的稳定性,获得了一致性成立的充要条件,该条件揭示了交流拓扑、控制器增益、采样器的周期和保持器的周期的关系.最后,提供一个仿真例子以说明理论结果的有效性.     

Dynamic output feedback consensus of continuous‐time networked multiagent systems

This article addresses the dynamic output feedback consensus problem of continuous‐time networked multiagent systems. Both a fixed topology and Markovian switching topologies are considered. The consensus algorithms are on the base of the output information of each agent's itself and its neighbors. Some sufficient conditions for consensus of multiagent systems are obtained in forms of bilinear matrix inequalities. The algorithm based on the homotopy continuation method is given to compute the feasible controller gains. Numerical simulations are given to show the effectiveness of the proposed results. © 2014 Wiley Periodicals, Inc. Complexity 20: 35–42, 2015     

Convergence rate for consensus with delays

We study the problem of reaching a consensus in the values of a distributed system of agents with time-varying connectivity in the presence of delays. We consider a widely studied consensus algorithm, in which at each time step, every agent forms a weighted average of its own value with values received from the neighboring agents. We study an asynchronous operation of this algorithm using delayed agent values. Our focus is on establishing convergence rate results for this algorithm. In particular, we first show convergence to consensus under a bounded delay condition and some connectivity and intercommunication conditions imposed on the multi-agent system. We then provide a bound on the time required to reach the consensus. Our bound is given as an explicit function of the system parameters including the delay bound and the bound on agents’ intercommunication intervals.     

Necessary and sufficient conditions for consensus of third-order discrete-time multi-agent systems in directed networks

This paper studies consensus of third-order discrete-time multi-agent systems in directed networks. When each agent can only receive its neighbor’s position information, necessary and sufficient conditions for consensus of the system are established. Compared with the preceding work, we not only answer what consensus value the system eventually achieves, but also clearly show the equivalent relationship between consensus, scaling parameters and nonzero eigenvalues of the involved Laplacian matrix. Illustrative examples are also given to demonstrate the effectiveness of the obtained theoretical results.     

Leader-following finite-time consensus for multi-agent systems with jointly-reachable leader

Finite-time consensus problems of the leader-following multi-agent systems with jointly-reachable leader and switching jointly-reachable leader are studied in this paper. Based on the graph theory, LaSalle’s invariance principle and Lyapunov stability theory, the finite-time consensus protocols are presented for the first-order and second-order leader-following systems. Some examples and simulation results are given to illustrate the effectiveness of the obtained theoretical results.     

Considering individual satisfaction levels enhances cooperation in a spatial prisoner’s dilemma game

Based on the observance in human society, the satisfaction level of an individual as a result of an obtained payoff depends on personal tendency to some extent; we establish a new model for spatial prisoner’s dilemma games. We describe individual satisfaction as a stochastically deviated value around each of the four payoffs stipulated by a payoff matrix, which is maintained throughout the life of a certain agent. When strategy updating, an agent who refers to his own satisfaction level cannot see neighbors’ satisfaction levels but can only observe neighbors’ accumulated payoffs. By varying the update rule and underlying topology, we perform numerical simulations that reveal cooperation is significantly enhanced by this change. We argue that this enhancement of cooperation is analogous to a stochastic resonance effect, like the payoff noise effects Perc (2006).     

Consensus seeking in multi-agent systems via hybrid protocols with impulse delays

This paper studies the consensus problem of multi-agent systems with both fixed and switching topologies. A hybrid consensus protocol is proposed to take into consideration of continuous-time communications among agents and delayed instant information exchanges on a sequence of discrete times. Based on the proposed algorithms, the multi-agent systems with the hybrid consensus protocols are described in the form of impulsive systems or impulsive switching systems. By employing results from matrix theory and algebraic graph theory, some sufficient conditions for the consensus of multi-agent systems with fixed and switching topologies are established, respectively. Our results show that, for small impulse delays, the hybrid consensus protocols can solve the consensus problem if the union of continuous-time and impulsive-time interaction digraphs contains a spanning tree frequently enough. Simulations are provided to demonstrate the effectiveness of the proposed consensus protocols.     

Distributed Stochastic Subgradient Projection Algorithms for Convex Optimization

We consider a distributed multi-agent network system where the goal is to minimize a sum of convex objective functions of the agents subject to a common convex constraint set. Each agent maintains an iterate sequence and communicates the iterates to its neighbors. Then, each agent combines weighted averages of the received iterates with its own iterate, and adjusts the iterate by using subgradient information (known with stochastic errors) of its own function and by projecting onto the constraint set.     

Messy broadcasting — Decentralized broadcast schemes with limited knowledge

We consider versions of broadcasting that proceed in the absence of information about the network. In particular, the vertices of the network do not know the structure of the network or the starting time, originator, or state of the broadcast. Furthermore, the protocols are not coordinated. This synchronous anonymous communication model has been called messy broadcasting. We perform a worst case analysis of three variants of messy broadcasting. These results also provide upper bounds on broadcasting where every vertex simply calls each of its neighbors once in random order. We prove exact bounds on the time required for broadcasting under two variants and give a conjectured value for the third.     

Leader-following consensus for networks with single- and double-integrator dynamics

In the paper, consensus protocols for networks of dynamic agents with single- and double-integrator dynamics are proposed. We provide necessary and sufficient conditions for leader-following consensus problem of the presented models. In order to examine the studied cases in a general way the time scale calculus is employed to get the results. The method used in the proofs is based on spectral characterization of stability for time invariant linear systems on time scales. All the results are enriched in illustrative examples and numerical simulations.     

Sampled-data distributed protocol for coordinated aggregation of multi-agent systems subject to communication delays

This paper studies the coordinated aggregation problem of a multi-agent system. Particularly, all the agents reach a consensus within a pre-specified target region. However, only a subset of agents have access to this target region, and each agent merely interacts with its neighbors by communication. Moreover, there exist unknown heterogeneous delays in communication channels. The underlying communication topology is characterized by a digraph. To accommodate the practical digital disposal, a sampled-data distributed protocol is proposed, where the sampling is asynchronous in the sense that the sampling periods of distinct agents are heterogeneous. The resulting closed-loop system from the proposed sampled-data distributed protocol is in a hybrid fashion that the continuous system is fed-back by using discrete states at sampling instants. The convergence performance of this hybrid closed-loop system is analyzed based on the contraction theory. More specifically, it is first shown that all the states are coordinated to aggregate within the target region, i.e., coordinated aggregation. With this result, it is next shown that all the states are coordinated towards a consensus, i.e., state agreement. These together guarantee the fulfillment of the concerned coordinated aggregation objective. Finally, a simulation example is given to validate the theoretical results.     

On consensus speed of multi-agent systems with double-integrator dynamics

The performance of multi-agent systems is an important issue. In this paper, it is focused on consensus speed for multi-agent systems with double-integrator dynamics and fixed undirected graphes under a kind of consensus protocols. It is revealed that, under some conditions, the maximum consensus speed is determined by the largest and the smallest nonzero eigenvalues of the Laplacian matrix of the undirected connected graph. Based on the mentioned results, arbitrary desired consensus speed can be achieved by choosing suitable feedback gains. Numerical simulations are given to illustrate the main results.     

A fully distributed ADMM-based dispatch approach for virtual power plant problems

In this paper, a fully distributed approach is proposed for a class of virtual power plant (VPP) problems. By characterizing two specific VPP problems, we first give a comprehensive VPP formulation that maximizes the economic benefit subjected to the power balance constraint, line transmission limits and local constraints of all distributed energy resources (DERs). Then, utilizing the alternating direction method of multipliers and consensus optimization, a distributed VPP dispatch algorithm is developed for the general VPP problem. In particular, Theorem 1 is derived to show the convergence of the algorithm. The proposed algorithm is completely distributed without requiring a centralized controller, and each DER is regarded as an agent by implementing local computation and only communicates information with its neighbors to cooperatively find the globally optimal solution. The algorithm brings some advantages, such as the privacy protection and more scalability than centralized control methods. Furthermore, a new variant of the algorithm is presented for improving the convergence rate. Finally, several case studies are used to illustrate the efficiency and effectiveness of the proposed algorithms.     

Discrete leader‐following consensus

In this paper, a leader‐following consensus of discrete‐time multi‐agent systems with nonlinear intrinsic dynamics is investigated. We propose and prove conditions ensuring a leader‐following consensus. Numerical examples are given to illustrate our results.     

Analysis and stability of consensus in networked control systems

In this paper, the consensus problem in networks of integrators is investigated. After recalling the classical diffusive protocol, we present in a unified framework some results on the rate of convergence previously presented in the literature. Then, we introduce two switching communication protocols, one based on a switching coupling law between neighboring nodes, the other on the conditional activation of links in the network. We show that the former protocol induces the monotonicity of each system in the network, enhancing the speed of convergence to consensus. Moreover, adopting this novel protocol, we are able to control the network, steering the nodes’ dynamics to a desired consensus value. The aim of the latter protocol is instead to select adaptively the activation of the edges of the network, in accordance with the dynamics of the network. After showing the effectiveness of both approaches through numerical simulations, the stability properties of these protocols are discussed.     

Further improvement of finite-time consensus protocols for detail-balanced networks

This paper presents a new class of protocols to solve finite-time consensus for multi-agent systems. The protocols are induced from the classical finite-time consensus algorithm by using the so-called protocol function. Sufficient conditions are established for networked agents to experience finite-time consensus under time-varying undirected and fixed directed topologies. Numerical simulations show that the proposed protocols can provide more flexibility to improve convergence rate.     

House exchange and residential segregation in networks

This paper considers a Schelling model in an arbitrary fixed network where there are no vacant houses. Agents have preferences either for segregation or for mixed neighborhoods. Utility is non-transferable. Two agents exchange houses when the trade is mutually beneficial. We find that an allocation is stable when for two agents of opposite-color each black (white) agent has a higher proportion of neighbors who are black (white). This result holds irrespective of agents’ preferences. When all members of both groups prefer mixed neighborhoods, an allocation is also stable provided that if an agent belongs to the minority (majority), then any neighbor of opposite-color is in a smaller minority (larger majority).     

Incorporating the information from direct and indirect neighbors into fitness evaluation enhances the cooperation in the social dilemmas

We propose an improved fitness evaluation method to investigate the evolution of cooperation in the spatial social dilemmas. In our model, a focal player’s fitness is calculated as the linear combination of his own payoff, the average payoffs of direct and indirect neighbors in which two independent selection parameters (α and β) are used to control the proportion of various payoff contribution to the current fitness. Then, the fitness-based strategy update rule is still Fermi-like, and asynchronous update is adopted here. A large plethora of numerical simulations are performed to validate the behaviors of the current model, and the results unambiguously demonstrate that the cooperation level is greatly enhanced by introducing the payoffs from the surrounding players. In particular, the influence of direct neighbors become more evident when compared with indirect neighbors since the correlation between focal players and their direct neighbors is much closer. Current outcomes are significant for us to further illustrate the origin and emergence of cooperation within a wide variety of natural and man-made systems.