Convergence Speed Of Consensus Research Articles

Consensus Convergence Speed in Social Network DeGroot Model: The Effects of the Agents With High Self-Confidence Levels

In group decision making (GDM), opinion dynamics is a useful tool to investigate consensus formation. Notably, consensus convergence speed is of key importance to manage the consensus formation in GDM with opinion dynamics. Recently, social network DeGroot (SNDG) model has been widely used in opinion dynamics. Based on this, this article dedicates to study how agents’ high self-confidence levels affect the consensus convergence speed in SNDG model. Interestingly, using theoretical analysis, we prove that: 1) the speed of consensus reaching is subject to the largest self-confidence level of opinion followers and 2) the speed of consensus reaching is also subject to the top two self-confidence levels of opinion leaders. Furthermore, through extensive simulation’, we find that the theoretical results are robust to the topological structure and the size of social networks.

Leader–follower consensus of nonlinear time-delay multiagent systems: A time-varying gain approach

In this paper, the leader–follower consensus problem is investigated for feedforward nonlinear time-delay multiagent systems under a fixed directed topology. A novel static low-gain observer is first proposed for each follower by only utilizing the output information of the follower and its neighbor agents. Based on an appropriate state transformation, the distributed output feedback controller with a static gain is then designed for each follower such that the consensus of the multiagent system is achieved. It is however noted that under the static gain controllers, the consensus convergence speed is slow and transient performance leaves much to be desired. To improve performance of the consensus protocol, the distributed output feedback controllers with bounded time-varying gains are further designed. It is shown that the proposed time-varying gain approach plays a significant role in improving the convergence speed and transient performance of the distributed consensus protocol. Through a simulation example, the effectiveness of the proposed consensus protocol is illustrated, and the advantages of the proposed time-varying gain approach are also demonstrated.

Detecting Hierarchical and Overlapping Network Communities Based on Opinion Dynamics

It is common for communities in real-world networks to possess hierarchical and overlapping structures, which make community detection even more challenging. In this paper, by investigating consensus process of the classical DeGroot model in opinion dynamics, we propose a novel method based on the cumulative opinion distance (COD) to discover hierarchical and overlapping communities. It is shown that this method is different from those classical algorithms relying on static fitness metrics that depict the inhomogeneous connectivity across the network. The proposed method is validated from two aspects. First, by estimating the eigenvectors of adjacency matrices, we investigate the detectability limit of our algorithms on random networks, which together with the results concerning the convergence speed of consensus guarantees the performance of our method theoretically. Second, experiments on both \tcb{large scale} real-world networks and artificial benchmarks show that our method is very effective and competitive on hierarchical modular graphs. In particular, it outperforms the state-of-the-art algorithms on overlapping community detection.

Distributed accelerating of quantized second‐order consensus with bounded input

AbstractIn this paper, the convergence speed of consensus for a second‐order integrator with the fixed undirected graph is investigated. Additionally, the quantized information and bounded control input are applied to the system. To accelerate the convergence speed, a distributed variable adjacency matrix is proposed where the links' weight are functions defined based on the distance to the neighbors. The stability of the whole system for both of the quantized and non‐quantized consensus protocol considering a general weight function is shown using Lyapunov's direct approach. Furthermore, it is mentioned that the consensus value of the position depends on the structure of the quantizer.

Consensus reaching in social network DeGroot Model: The roles of the Self-confidence and node degree

In this paper, we investigate how the agent's self-confidence level and the node degree influence the consensus opinion formation and the consensus convergence speed in the social network DeGroot model. We find that (1) the higher self-confidence will increase the agent's importance degree to determine the consensus opinion, but will also slow down the convergence speed for all agents to be able to obtain consensus, and (2) it is conducive to accelerating the convergence speed to be able to reach a consensus where all agents can manage to balance self-confidence levels and node degrees in the social network.

Potential-Game Based Optimally Rigid Topology Control in Wireless Sensor Networks

In this paper, the optimally rigid topology control problem in wireless sensor networks is considered to improve the algebraic rigidity properties. This problem is first formulated as a constrained optimization problem which can be solved by two stages. A minimally rigid network is constructed in the first stage, then the optimally rigid topology in the second stage. A potential game approach is proposed for solving the optimization problem by choosing a different performance metric as the potential function. It can be seen that the proposed algorithm can significantly improve the network performance, such as reducing communication complexity and transmit power, prolonging network lifetime, and so on. Finally, some simulations demonstrate the effectiveness of the proposed algorithms from multiple perspectives: topology complexity, average degree, consensus convergence speed, average radius, average link length, and network lifetime.

Optimal convergence speed of consensus under constrained damping for multi-agent systems with discrete-time double-integrator dynamics

This paper considers the optimization of the convergence speed of consensus under given damping constraints for multi-agent systems with discrete-time double-integrator dynamics with fixed interconnection topology. This work summarizes and details existing results in the case of undirected topologies and extends them to directed ones. The interconnection topology is assumed to be connected or to contain a rooted-out branching, respectively. Depending on the minimum required damping, for undirected interconnection topologies in most cases analytic solutions are provided. The structure of these solutions is independent of the size of the network and only depends on the largest and second smallest eigenvalue of the corresponding Laplacian. For the remaining cases without analytic solutions provided, a combined bisection grid search is presented that solves the constrained optimization problem efficiently. This algorithm can also be applied to directed interconnection topologies and, as for the undirected case, converges to the single optimum. Simulation results are provided that demonstrate the effectiveness of the proposed approach.

Consensus rate regulation for general linear multi-agent systems under directed topology

Recently, optimization in distributed multi-agent coordination has been studied concerning convergence speed. The optimal convergence speed of consensus for multi-agent systems consisting of general linear node dynamics is still an open problem. This paper aims to design optimal distributed consensus protocols for general identical linear continuous time cooperative systems which not only minimize some local quadric performances, but also regulate the consensus rate (including convergence rate and damping rate) for the multi-agent systems. The graph topology is assumed to be fixed and directed. The inverse optimal design method is utilized and the resulting optimal distributed protocols place part of close-loop poles of the global disagreement systems at specified locations asymptotically, while the remains far from the imaginary axis enough. It turns out that for the identical linear continuous time multi-agent systems, the convergence speed has no upper bound. The main advantages of the developed method over the LQR design method are that the resulting multi-agent systems can achieve specified consensus rate asymptotically and the resulting protocols have the whole right half complex plane as its asymptotical consensus region. Numerical examples are given to illustrate the effectiveness of the proposed design procedures.

Improvement of consensus convergence speed for linear multi-agent systems based on state observer

A novel consensus protocol is presented for linear multi-agent systems(MASs) in which all the agents have the same continuous-time linear dynamics with high dimension. A fast convergence speed can be obtained by using this protocol for the MASs where each agent gets its own state through the full-order observer. Every agent can also obtain the states of its neighbors׳ and its instantaneous neighbors׳ to reach consensus. Necessary and sufficient conditions of consensus for the MASs are proposed to improve the convergence speed. Finally, the corresponding convergence speeds of different protocols are showed by numerical simulation, and extended to directed topology.

Fast Consensus of Networked Multiagent Systems with Two-Hop Network

This paper studies the consensus convergence speed of multiagent systems (MASs) from two aspects including communication topology and the state of agents. Two-hop network is considered in the communication topology. A novel consensus protocol that includes the information of the states motions and their integrals is introduced. And the protocol has much faster convergence speed by choosing some appropriate weight values. The protocol can be applied to distributed control and large-scale systems. A numerical example is presented to illustrate the effectiveness and superiority of the proposed method.

Delay-dependent coupling for a multi-agent LTI consensus system with inter-agent delays

Delay-dependent coupling (DDC) is considered in this paper in a broadly studied linear time-invariant multi-agent consensus system in which agents communicate with each other under homogeneous delays, while attempting to reach consensus. The coupling among the agents is designed here as an explicit parameter of this delay, allowing couplings to autonomously adapt based on the delay value, and in order to guarantee stability and a certain degree of robustness in the network despite the destabilizing effect of delay. Design procedures, analysis of convergence speed of consensus, comprehensive numerical studies for the case of time-varying delay, and limitations are presented.

THE CONSENSUS IN MULTI-AGENT SYSTEM WITH SPEED-OPTIMIZED NETWORK

In this paper, we mainly investigate the character of consensus convergence speed of Multi-Agent Systems (MAS) with small-world communication network and the method of devising a speed-optimized small-world communication network in consensus problem based on genetic-algorithm (GA). It is found that, for a small-world communication network, the time to reach a consensus changes rapidly with the change of the number of long-range communication links and the agents which the long-range links connect. The convergence speed of consensus of MAS increases rapidly with the number of long-range links increasing. As we construct a small-world communication network for MAS with a smaller network size and fixed long-range links, we can optimize the long-range link configuration using GA methodology to obtain a small-world communication network with faster consensus speed for MAS.