Consensus Protocol For Multi-agent Systems Research Articles

Almost Global Consensus on the <inline-formula> <tex-math notation="LaTeX">$n$</tex-math> </inline-formula> -Sphere

This paper establishes novel results regarding the global convergence properties of a large class of consensus protocols for multiagent systems that evolve in continuous time on the $n$ -dimensional unit sphere or $n$ -sphere. For any connected, undirected graph and all $n\in \mathbb{N} \backslash \lbrace 1\rbrace$ , each protocol in said class is shown to yield almost global consensus. The feedback laws are negative gradients of Lyapunov functions and one instance generates the canonical intrinsic gradient descent protocol. This convergence result sheds new light on the general problem of consensus on Riemannian manifolds; the $n$ -sphere for $n\in \mathbb{N}\backslash \lbrace 1\rbrace$ differs from the circle and $\mathsf {SO}(3)$ , where the corresponding protocols fail to generate almost global consensus. Moreover, we derive a novel consensus protocol on $\mathsf {SO}(3)$ by combining two almost globally convergent protocols on the $n$ -sphere for $n\in \lbrace 1,2\rbrace$ . Theoretical and simulation results suggest that the combined protocol yields almost global consensus on $\mathsf {SO}(3)$ .

A new class of fixed-time bipartite consensus protocols for multi-agent systems with antagonistic interactions

In this paper, we study the fixed-time consensus problem for multi-agent systems with structurally balanced signed graph. A new class of fixed-time nonlinear consensus protocols is designed by employing the neighbor’s information. By using Lyapunov stability method, states of all agents can be guaranteed to reach agreement in a fixed time under our presented protocols, and the consensus values are the same in modulus but different in sign. Moreover, it is shown that the settling time is not dependent on the initial conditions, and it makes a good convenience to estimate the convergence time by just knowing the graph topology and the information flow of the multi-agent systems. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed consensus protocols.

Sampling Effect on Secondary Control of Microgrids via Consensus Protocol of Multi-Agent Systems

This paper addresses the sampling effect problem in the microgrids consisted of multiple agents; easy example is the distributed generator. We would like to pay attention to the secondary control problem of the microgrids. Inhere, the sampling effect will be analyzed as the main constraint among multiple distributed generators in the microgrids. To do this, the proposed secondary control scheme for the microgrids is modeled by employing a directed graph structure because the microgrids were based on the network communicated through one-way links. By constructing suitable Lyapunov–Krasovskii functional and using some mathematical theory, a sufficient control condition, which is formulated to the consensus protocol form, for the target problem will be derived in terms of LMI. Finally, the simulation example is illustrated to bring the necessity of the analysis of the sampling effect out in operation of the microgrids.

Designing a novel consensus protocol for multiagent systems with general dynamics under directed networks

The consensus problem for general linear multi-agent systems (MASs) under directed topology is investigated. First, a novel consensus protocol based on proportional-integral-derivative (PID) control is proposed. Second, the consensus problem is converted into an asymptotic stability problem through transformations. Third, through a state projection method the consensus condition is proved and the explicit expression of the consensus function is given. Then, a Lyapunov function is constructed and the gain matrices of the protocol are given based on the linear matrix inequality. Finally, two experiments are conducted to explain the advantages of the method. Simulation results show the effectiveness of the proposed algorithm.

Weighted Consensus Protocols Design Based on Network Centrality for Multi-Agent Systems With Sampled-Data

This technical note aims at constructing and analyzing an efficient framework for the leader-following consensus protocol in multi-agent systems (MASs). We propose two novel consensus protocols weighted by calculating the betweenness and eigenvector centralities for agent and link which are determined by the interconnection structure of MASs. The concepts of centrality were introduced in the field of social science. Ultimately, the use of the proposed protocols can be described with regard to not only the number of each agent's neighbors, which was utilized in the existing works, but also more information about agents through considering two such centralities. By utilizing the Lyapunov method and some mathematical techniques, the leader-following guaranteed cost consensus conditions for MASs with the proposed protocols and sampled-data will be established in terms of linear matrix inequalities (LMIs). Based on the result of consensus criteria, two new protocol design methods which utilize the betweenness and eigenvector centralities will be proposed. Finally, some simulation results are given to illustrate the advantages of the proposed protocols in point of the robustness on sampling interval and the transient consensus performance.

A novel finite-time average consensus protocol for multi-agent systems with switching topology

Multi-agent consensus has been widely applied in engineering. A novel protocol that can achieve an average state consensus for multi-agent systems in finite time is presented in this paper. The proposed protocol contains a non-linear and a linear term. The state consensus is achieved in finite time by the non-linear term and convergence performance is improved by the linear term to some degree. The protocol can be applied to systems with a switching topology as long as the communication graph is always undirected and connected. The upper bound of convergence time is obtained. The relationship between convergence time and protocol parameter, communication topology and initial state is analysed. Lastly, simulations are conducted to verify the effectiveness of the results.

Distributed edge event-triggered consensus protocol of multi-agent systems with communication buffer

Summary This paper proposes a distributed edge event-triggered (DEET) scheme of multi-agent systems via a communication buffer to reduce unnecessary update of controllers induced by fast information transmission. This edge scheme avoids a synchronous phenomenon in node event-triggered mechanism, in which the triggering of one agent activates information transmission of all edges linked with this agent. Hence, the node event-triggered scheme leads to unnecessary update of control protocols while the DEET provides a new approach without constrains on synchronous phenomenon of edge information exchange. That is, the communication on each edge is independent with other edges. In addition, we investigate another case where edge information transmission is subject to quantization and a quantized edge event-triggered control protocol is proposed. Note that such a quantized protocol guarantees asymptotical consensus instead of bounded consensus in most of the existing literature. Meanwhile, both DEET and quantized edge event-triggered schemes have nontrivial properties of excluding Zeno behavior. Furthermore, an algorithm is provided to avoid continuous event detection; hence, the communication traffic of the whole network is reduced significantly. Copyright © 2016 John Wiley & Sons, Ltd.

Fixed-time consensus protocols for multi-agent systems with linear and nonlinear state measurements

This paper deals with fixed-time consensus problem for multi-agent systems under detail-balanced directed graph, where both protocols with linear and nonlinear state measurements are proposed. For the case where linear state measurements are available, protocols are presented with uniformly bounded setting time for any initial condition. By introducing a class of admissible nonlinear functions, consensus protocols with linear measurements are extended to protocols with nonlinear measurements. It also can be proven that under nonlinear measurement protocols, the states of the agents can also converge to a common value with a uniformly bounded setting time. Numerical simulations are presented to demonstrate the efficiency of our proposed protocols.

Nonlinear finite-time bipartite consensus protocol for multi-agent systems associated with signed graphs

In this paper, finite-time multi-agent consensus problems are considered under networks associated with signed graphs whose edge weights can be not only positive but also negative. A nonlinear consensus protocol is proposed to guarantee the states of all agents to converge in a finite time. If the signed graph is structurally balanced, then the final consensus states of all agents are the same in modulus but not in sign. Otherwise, if the signed graph is structurally unbalanced, then the states of all agents converge to zero. Moreover, the final consensus states of agents can be provided uniformly regarding a signed-average quantity that depends on both the initial states of agents and the topology structure of the whole multi-agent network. Numerical simulations illustrate that the protocol is effective in achieving the finite-time consensus of agents under signed graphs and can particularly solve the finite-time average consensus problem of agents when their associated graph has all positive edge weights.

Distributed consensus protocol design for general linear multi‐agent systems: a consensus region approach

This study presents a consensus region approach to designing distributed consensus protocols for multi-agent systems with general continuous-time linear node dynamics. The consensus region approach has a favourable decoupling feature, which decouples the design of the feedback gain matrices of the consensus protocols from the communication graph. Multi-step algorithms are presented to construct the fixed-gain consensus protocols, which requires the smallest non-zero eigenvalue of the Laplacian matrix. To remove this limitation, distributed adaptive protocols with time-varying coupling weights are designed for the cases with undirected and directed graphs, which can be implemented in a fully distributed fashion. The robustness issue of the adaptive protocols in the presence of external disturbances is also discussed. For the case where there exists a leader of bounded unknown control input, distributed discontinuous and continuous controllers are designed to solve the distributed tracking problem.

Fault-Tolerant Consensus of Multi-Agent System With Distributed Adaptive Protocol.

In this paper, fault-tolerant consensus in multi-agent system using distributed adaptive protocol is investigated. Firstly, distributed adaptive online updating strategies for some parameters are proposed based on local information of the network structure. Then, under the online updating parameters, a distributed adaptive protocol is developed to compensate the fault effects and the uncertainty effects in the leaderless multi-agent system. Based on the local state information of neighboring agents, a distributed updating protocol gain is developed which leads to a fully distributed continuous adaptive fault-tolerant consensus protocol design for the leaderless multi-agent system. Furthermore, a distributed fault-tolerant leader-follower consensus protocol for multi-agent system is constructed by the proposed adaptive method. Finally, a simulation example is given to illustrate the effectiveness of the theoretical analysis.

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.

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.

Mean square average-consensus for multi-agent systems with measurement noise and time delay

Mean square average consensus for multi-agent systems with measurement noise and time delay under fixed digraph is studied in this article. The time-varying consensus-gain is introduced to attenuate the measurement noise. By combining the tools of algebraic graph theory, matrix theory and stochastic analysis, consensus protocols for multi-agent systems with measurement noise and time delay are elaborately analysed. The example and simulation results are given to illustrate the effectiveness of the obtained theoretical results. Moreover, the simulations demonstrate that, the proper consensus-gain function in the consensus protocol is the necessary and sufficient condition for the convergence of the multi-agent systems.

A Nonlinear Consensus Protocol of Multiagent Systems Considering Measuring Errors

In order to avoid a potential waste of energy during consensus controls in the case where there exist measurement uncertainties, a nonlinear protocol is proposed for multiagent systems under a fixed connected undirected communication topology and extended to both the cases with full and partial access a reference. Distributed estimators are utilized to help all agents agree on the understandings of the reference, even though there may be some agents which cannot access to the reference directly. An additional condition is also considered, where self-known configuration offsets are desired. Theoretical analyses of stability are given. Finally, simulations are performed, and results show that the proposed protocols can lead agents to achieve loose consensus and work effectively with less energy cost to keep the formation, which have illustrated the theoretical results.

On the general second-order consensus protocol in multi-agent systems with input delays

In this paper we study a general consensus protocol for directed networks of double integrators with input delays. A necessary and sufficient condition is provided, under which not only the consensus is guaranteed but also the agents’ states are not exponentially diverging. Based on this condition, the delay robustness of the general protocol is analyzed. The maximal allowable upper bound of the input delay is obtained; the analysis is constructively given and different consensus modes can be regarded as special cases with different parameters. Simulation results are presented to illustrate the effectiveness of the theoretical results.

Iterative learning approaches to design finite-time consensus protocols for multi-agent systems

In this paper, the finite-time output consensus problem of multi-agent systems is considered by using the iterative learning control (ILC) approach. Two classes of distributed protocols are constructed from the two-dimensional system point of view (with time step and iteration number as independent variables), and are termed as iterative learning protocols. If learning gains are chosen appropriately, then all agents in a directed graph can be enabled to achieve finite-time consensus with the iterative learning protocols. Moreover, all agents in a directed graph can be guaranteed to reach finite-time consensus at any desired terminal output if the iterative learning protocols are improved by introducing the desired terminal output to some (not necessarily all) of the agents. Simulation results are finally presented to illustrate the performance and effectiveness of our iterative learning protocols.

Finite-time consensus for stochastic multi-agent systems

In this article, we study the finite-time consensus in probability for stochastic multi-agent systems. First, we give the nonlinear consensus protocol for multi-agent systems with Gaussian white noise, and define the concept of finite-time consensus in probability. Second, we prove that multi-agent systems can achieve the finite-time consensus in probability under five different kinds of communication topologies by using graph theory, stochastic Lyapunov theory and probability theory. Finally, some simulation examples are provided to illustrate the effectiveness of the theoretical results.

Emergence of cooperation through coevolving time scale in spatial prisoner’s dilemma

We study evolutionary prisoner's dilemma game by considering adaptive strategy-selection time scale among individuals according to a "win-slower, lose-faster" rule: if an individual successfully resists the invasion of an opponent, she is prone to hold her strategy for longer time through decreasing her strategy-selection time scale; otherwise, she increases the time scale because of losing. We find that the greater the losers increase their strategy-selection time scales, the better for cooperation. Interestingly, optimal cooperation can be induced by proper adaptive rate in the strategy-selection time scale. Our results may have potential implications in the design of consensus protocol in multiagent systems.

Distributed average consensus control in networks of agents using outdated states

Time delays are commonly considered as a negative factor in the literature on consensus problems of multi-agent systems. This, however, is not always the fact. Here, the authors propose some consensus protocols for multi-agent systems with a fixed undirected communication topology. Different from the common consensus protocols for multi-agent systems, which uses the current states only, the protocols proposed here use both current states and outdated states. It is shown that the use of the outdated information can accelerate the consensus if the consensus protocols are chosen properly. Simulation examples are given to illustrate the effectiveness of the proposed algorithms.