Consensus Problem In Networks Research Articles

Finite-Time Consensus with a Time-Varying Reference State and Switching Topology

The finite-time consensus problem in the networks of multiple mobile agents is comprehensively investigated. In order to resolve this problem, a novel nonlinear information exchange protocol is proposed. The proposed protocol ensures that the states of the agents are converged to a weighted-average consensus in finite time if the communication topology is a weighted directed graph with a spanning tree and each strongly connected component is detail-balanced. Furthermore, the proposed protocol is also able to solve the finite-time consensus problem of networks with a switching topology. Finally, computer simulations are presented to demonstrate and validate the effectiveness of the theoretical analysis under the proposed protocol.

Task space consensus in networks of heterogeneous and uncertain robotic systems with variable time‐delays

SummaryThis work deals with the leader‐follower and the leaderless consensus problems in networks of multiple robot manipulators. The robots are non‐identical, kinematically different (heterogeneous), and their physical parameters are uncertain. The main contribution of this work is a novel controller that solves the two consensus problems, in the task space, with the following features: it estimates the kinematic and the dynamic physical parameters; it is robust to interconnecting variable‐time delays; it employs the singularity‐free unit‐quaternions to represent the orientation; and, using energy‐like functions, the controller synthesis follows a constructive procedure. Simulations using a network with four heterogeneous manipulators illustrate the performance of the proposed controller. Copyright © 2016 John Wiley & Sons, Ltd.

Adaptive Group Consensus of Multi-Agent Networks via Pinning Control

This paper studies the group consensus problem in networks of multi-agent systems, in which the nonlinear dynamics of all agents are unknown and nonidentical. We assume that the unknown dynamics are linearly parameterized. Adaptive control method is adopted in the algorithm design. A novel algorithm is proposed for the multi-agent systems to reach group consensus via pinning control strategies, which only rely on the relative position information between neighboring agents. The stability and parameter convergence analysis are done based on Lyapunov theory, Barbalat's lemma, adaptive control theory and algebraic graph theory. Finally, a simulation example is given to validate our theoretical results.

Signed consensus problems on networks of agents with fixed and switching topologies

ABSTRACTThis paper deals with signed consensus problems for networks of agents in the presence of both fixed and switching topologies. By specifying signs for the agents, they are divided into two groups and are enabled to reach agreement on a consensus value which is the same in modulus for both groups but not in sign. Using nearest-neighbour interaction rules, we propose the distributed protocols and address their exponential convergence problem. It is shown that the quasi-strong connectivity of fixed networks or joint quasi-strong connectivity of switching networks can provide a necessary and sufficient guarantee for all agents to achieve signed consensus exponentially fast. In particular, the signed consensus results can include as special cases those of bipartite consensus in signed networks with fixed and switching topologies. Numerical simulations are also provided to illustrate the exponential convergence performance of the proposed signed consensus protocols.

Consensus networks with switching topology and time-delays over finite fields

The consensus problem in networks with both switching topology and time-delays over finite fields is investigated in this paper. The finite field, which is a kind of finite alphabet, is considered due to the fact that networks often possess limited computation, memory, and capabilities of communication. First, by graph-theoretic method, one necessary and sufficient condition is derived for finite-field consensus of switching networks without time-delays. Subsequently, another necessary and sufficient condition on finite-field consensus without time-delays is provided based on FFC property of matrices associated with switching networks. Moreover, by means of the results on delay-free networks, some necessary and sufficient conditions for finite-field consensus of networks with both switching topology and time-delays are obtained. Additionally, it can be shown that switching networks with time-delays present in each self-transmission cannot achieve consensus.

Distributed event-triggered coordination for average consensus on weight-balanced digraphs

This paper proposes a novel distributed event-triggered algorithmic solution to the multi-agent average consensus problem for networks whose communication topology is described by weight-balanced, strongly connected digraphs. The proposed event-triggered communication and control strategy does not rely on individual agents having continuous or periodic access to information about the state of their neighbors. In addition, it does not require the agents to have a priori knowledge of any global parameter to execute the algorithm. We show that, under the proposed law, events cannot be triggered an infinite number of times in any finite period (i.e., no Zeno behavior), and that the resulting network executions provably converge to the average of the initial agents’ states exponentially fast. We also provide weaker conditions on connectivity under which convergence is guaranteed when the communication topology is switching. Finally, we also propose and analyze a periodic implementation of our algorithm where the relevant triggering functions do not need to be evaluated continuously. Simulations illustrate our results and provide comparisons with other existing algorithms.

Multiplex PI control for consensus in networks of heterogeneous linear agents

In this paper, we propose a multiplex proportional–integral approach, for solving consensus problems in networks of heterogeneous nodes dynamics affected by constant disturbances. The proportional and integral actions are deployed on two different layers across the network, each with its own topology. Sufficient conditions for convergence are derived that depend upon the structure of the network, the parameters and topologies characterizing the control layers and the node dynamics. The effectiveness of the theoretical results is illustrated numerically on a set of representative examples including a power network model.

Reset strategy for consensus in networks of clusters

This paper addresses the problem of consensus in networks structured in several clusters. The clusters are represented by fixed, directed and strongly connected graphs. They are composed by a number of agents which are able to interact only with other agents belonging to the same cluster. To every agent we associate a scalar real value representing its state. The states continuously evolve following a linear consensus protocol and approach local agreements specific to each cluster. In order to enforce a global agreement over the whole network, we consider that each cluster contains an agent that can be exogenously controlled. The state of this agent, called leader, will be quasi-periodically reseted by a local master controller that receives information from some neighboring leaders. In order to control the consensus value we have to firstly characterize it. Precisely we show that it depends only on the initial condition and the interaction topologies. Secondly, we provide sufficient Linear Matrix Inequality (LMI) conditions for the global uniform exponential stability of the consensus in presence of a quasi-periodic reset rule. The study of the network behavior is completed by a decay rate analysis. Finally we design the interaction network of the leaders which allows to reach a prescribed consensus value. Numerical implementation strategy is provided before illustrating the results by some simulations.

Consensus networks with time-delays over finite fields

ABSTRACTIn this paper, we investigate the consensus problem in networks with time-delays over finite fields. The delays are categorised into three cases: single constant delay, multiple constant delays, and time-varying bounded delays. For all cases, some sufficient and necessary conditions for consensus are derived. Furthermore, assuming that the communication graph is strongly connected, some of the obtained necessary conditions reveal that the conditions for consensus with time-delays over finite fields depend not only on the diagonal entries but also on the off-diagonal entries, something that is intrinsically distinct from the case over real numbers (where having at least one nonzero diagonal entry is a sufficient and necessary condition to guarantee consensus). In addition, it is shown that delayed networks cannot achieve consensus when the interaction graph is a tree if the corresponding delay-free networks cannot reach consensus, which is consistent with the result over real numbers. As for average consensus, we show that it can never be achieved for delayed networks over finite fields, although it indeed can be reached under several conditions for delay-free networks over finite fields. Finally, networks with time-varying delays are discussed and one sufficient condition for consensus is presented by graph-theoretic method.

Consensus analysis of networks with time-varying topology and event-triggered diffusions

This paper studies the consensus problem of networks with time-varying topology. Event-triggered rules are employed in diffusion coupling terms to reduce the updating load of the coupled system. Two strategies are considered: event-triggered strategy, that each node observes the state information in an instantaneous way, to determine the next triggering event time, and self-triggered strategy, that each node only needs to observe the state information at the event time to predict the next triggering event time. In each strategy, two kinds of algorithms are considered: the pull-based algorithm, that the diffusion coupling term of every node is updated at the latest observations of the neighborhood at its triggered time, and push-based algorithm, the diffusion coupling term of every node uses the state information of its neighborhood at their latest triggered time. It is proved that if the coupling matrix across time intervals with length less than some given constant has spanning trees, then the proposed algorithms can realize consensus. Examples with numerical simulation are provided to show the effectiveness of the theoretical results.

Nonsingular fixed-time consensus tracking for second-order multi-agent networks

This paper investigates the fixed-time consensus tracking problem for second-order multi-agent systems in networks with directed topology. Global well-defined nonlinear consensus protocols are constructed with the aid of a newly-designed sliding surface for each double-integrator agent dynamics. In particular, the proposed framework eliminates the singularity and the settling time is assignable for any initial conditions. This makes it possible for network consensus problems to design and estimate the convergence time off-line. Finally, simulation is included to demonstrate the performance of the new protocols.

Consensus of Second-Order Multiagent Systems with Fixed Topology and Time-Delay

We are concerned with the consensus problems for networks of second-order agents, where each agent can only access the relative position information from its neighbours. We aim to find the largest tolerable input delay such that the system consensus can be reached. We introduce a protocol with time-delay and fixed topology. A sufficient and necessary condition is given to guarantee the consensus. By using eigenvector-eigenvalue method and frequency domain method, it is proved that the largest tolerable time-delay is only related to the eigenvalues of the graph Laplacian. And simulation results are also provided to demonstrate the effectiveness of our theoretical results.

Delayed Consensus Problem for Single and Double Integrator Systems

This work deals with the analysis of the consensus problem for networks of agents constituted by single and double integrator systems. It is assumed that the communication among agents is affected by a constant time-delay. Previous and numerous analysis of the problem shows that the maximum communication time-delay that can be introduced to the network without affecting the consensus of the group of the agents depends on the considered topology. In this work, a control scheme that is based on the estimation of future states of the agents and that allows increasing the magnitude of a possible time-delay affecting the communication channels is proposed. How the proposed delay compensation strategy is independent of the network topology in the sense that the maximum allowable time-delay that could be supported by the network depends on a design parameter and not on the maximum eigenvalue of the corresponding Laplacian matrix is shown. It is formally proven that, under the proposed prediction scheme, the consensus of the group can be achieved by improving the maximum time-delay bounds previously reported in the literature. Numerical simulations show the effectiveness of the proposed solution.

Design, Analysis, and Experimental Validation of a Distributed Protocol for Platooning in the Presence of Time-Varying Heterogeneous Delays

This paper presents a novel control design framework for vehicle platooning together with its experimental validation. The problem of controlling the vehicles within a platoon, so that they converge to their desired velocities and intervehicle distances, is formulated as a high-order network consensus problem. By means of Lyapunov–Razumikhin functions, convergence is proven of the platoon to the desired consensus speed and intervehicle spacing under both fixed and switching communication network topologies, thus confirming the capability of the proposed approach to cope with maneuvers where vehicles join or leave the platoon and communication failures. Tuning criteria for the control gains are provided to guarantee string stability under the proposed control law. Finally, results of numerical simulations and in-vehicle experiments demonstrate the effectiveness of the proposed approach in a three-vehicle platoon.

Weighted average consensus problem in networks of agents with diverse time-delays

This paper studies the weighted average consensus problem for networks of agents with fixed directed asymmetric unbalance information exchange topology. We suppose that the classical distributed consensus protocol is destroyed by diverse time-delays which include communication time-delay and self time-delay. Based on the generalized Nyquist stability criterion and the Gerschgorin disk theorem, some sufficient conditions for the consensus of multi-agent systems are obtained. And we give the expression of the weighted average consensus value for our consensus protocol. Finally, numerical examples are presented to illustrate the theoretical results.

Distributed robust finite-time nonlinear consensus protocols for multi-agent systems

This paper investigates the robust finite-time consensus problem of multi-agent systems in networks with undirected topology. Global nonlinear consensus protocols augmented with a variable structure are constructed with the aid of Lyapunov functions for each single-integrator agent dynamics in the presence of external disturbances. In particular, it is shown that the finite settling time of the proposed general framework for robust consensus design is upper bounded for any initial condition. This makes it possible for network consensus problems to design and estimate the convergence time offline for a multi-agent team with a given undirected information flow. Finally, simulation results are presented to demonstrate the performance and effectiveness of our finite-time protocols.

Average Consensus Problems in Networks of Agents with Fixed and Switching Topology and Unknown Control Direction

This paper is devoted to the average consensus problems in directed networks of agents with unknown control direction. In this paper, by using Nussbaum function techniques and Laplacian matrix, novel average consensus protocols are designed for multiagent systems with unknown control direction in the cases of directed networks with fixed and switching topology. In the case of switching topology, the disagreement vector is utilized. Finally, simulation is provided to demonstrate the effectiveness of our results.

Leaderless Consensus in Networks of Flexible–Joint Manipulators

This work studies the leaderless consensus problem in networks composed of non-identical flexible-joint robot manipulators. Using standard functional analysis, i.e., Barbâlat's Lemma, it is established that a simple control law provides a solution to the leaderless consensus problem. The network is modeled as an undirected graph and the interconnection can exhibit variable time-delays. The proposed controller consists of two different terms, one that dynamically compensates the robot gravity and another which ensures the desired consensus objective. This last term is a simple Proportional plus damping scheme. Simulations, using a network with nine 2-degrees of freedom manipulators, are provided to support the theoretical contributions of this work.

The consensus problem in networks with transmission delays

We study discrete- and continuous-time consensus problems on networks in the presence of distributed time delays. We focus on information transmission delays, as opposed to information processing delays, so that each node of the network compares its current state with the past states of its neighbours. We consider directed and weighted networks where the connection structure is described by a normalized Laplacian matrix and show that consensus is achieved if and only if the underlying graph contains a directed spanning tree. This statement holds independently of the transmission delays, which is in contrast to the case of processing delays. Furthermore, we calculate the consensus value explicitly, and show that it is determined by the history of the system over an interval of time, unlike the case of processing delays where the consensus value depends only on the initial state of the system at time zero. This provides the consensus algorithm with improved robustness against noise.

A new class of finite-time nonlinear consensus protocols for multi-agent systems

This paper is devoted to investigating the finite-time consensus problem for a multi-agent system in networks with undirected topology. A new class of global continuous time-invariant consensus protocols is constructed for each single-integrator agent dynamics with the aid of Lyapunov functions. In particular, it is shown that the settling time of the proposed new class of finite-time consensus protocols is upper bounded for arbitrary initial conditions. This makes it possible for network consensus problems that the convergence time is designed and estimated offline for a given undirected information flow and a group volume of agents. Finally, a numerical simulation example is presented as a proof of concept.