Designing Proportional-Integral Consensus Protocols for Second-Order Multi-Agent Systems Using Delayed and Memorized State Information

This paper is concerned with consensus of a secondorder linear time-invariant multi-agent system in the situation that there exists a communication delay among the agents in the network.A proportional-integral consensus protocol is designed by using delayed and memorized state information.Under the proportional-integral consensus protocol,the consensus problem of the multi-agent system is transformed into the problem of asymptotic stability of the corresponding linear time-invariant time-delay system.Note that the location of the eigenvalues of the corresponding characteristic function of the linear time-invariant time-delay system not only determines the stability of the system,but also plays a critical role in the dynamic performance of the system.In this paper,based on recent results on the distribution of roots of quasi-polynomials,several necessary conditions for Hurwitz stability for a class of quasi-polynomials are first derived.Then allowable regions of consensus protocol parameters are estimated.Some necessary and sufficient conditions for determining effective protocol parameters are provided.The designed protocol can achieve consensus and improve the dynamic performance of the second-order multi-agent system.Moreover,the effects of delays on consensus of systems of harmonic oscillators/double integrators under proportional-integral consensus protocols are investigated.Furthermore,some results on proportional-integral consensus are derived for a class of high-order linear time-invariant multi-agent systems.

Hyperbolic Tangent Function-Based Protocols for Global/Semi-Global Finite-Time Consensus of Multi-Agent Systems

This paper investigates the problem of global/semi-global finite-time consensus for integrator-type multi-agent sys-tems.New hyperbolic tangent function-based protocols are pro-posed to achieve global and semi-global finite-time consensus for both single-integrator and double-integrator multi-agent systems with leaderless undirected and leader-following directed commu-nication topologies.These new protocols not only provide an explicit upper-bound estimate for the settling time,but also have a user-prescribed bounded control level.In addition,compared to some existing results based on the saturation function,the pro-posed approach considerably simplifies the protocol design and the stability analysis.Illustrative examples and an application demonstrate the effectiveness of the proposed protocols.

Second-order consensus in networks of dynamic agents with communication time-delays

This paper proposes second-order consensus protocols with time-delays and gives the measure of the robustness of the protocols to the time-delay existing in the network of agents with second-order dynamics. By employing a frequency domain method, it is proven that the information states and their time derivatives of all the agents in the network achieve consensus asymptotically, respectively, for appropriate communication timedelay if the topology of weighted network is connected. Particularly, a tight upper bound on the communication time-delay that can be tolerated in the dynamic network is found. The consensus protocols are distributed in the sense that each agent only needs information from its neighboring agents, which reduces the complexity of connections between neighboring agents significantly. Numerical simulation results are provided to demonstrate the effectiveness and the sharpness of the theoretical results for second-order consensus in networks in the presence of communication time-delays.

Cluster consensus of second-order multi-agent systems via pinning control

This paper investigates the cluster consensus problem for second-order multi-agent systems by applying the pinning control method to a small collection of the agents. Consensus is attained independently for different agent clusters according to the community structure generated by the group partition of the underlying graph and sufficient conditions for both cluster and general consensus are obtained by using results from algebraic graph theory and the LaSalle Invariance Principle. Finally, some simple simulations are presented to illustrate the technique.

Nonlinear consensus protocols for multi-agent systems based on centre manifold reduction

Nonlinear consensus protocols for dynamic directed networks of multi-agent systems with fixed and switching topologies are investigated separately in this paper. Based on the centre manifold reduction technique, nonlinear consensus protocols are presented. We prove that a group of agents can reach a β-consensus, the value of which is the group decision value varying from the minimum and the maximum values of the initial states of the agents. Moreover, we derive the conditions to guarantee that all the agents reach a β-consensus on a desired group decision value. Finally, a simulation study concerning the vertical alignment manoeuvere of a team of unmanned air vehicles is performed. Simulation results show that the nonlinear consensus protocols proposed are more effective than the linear protocols for the formation control of the agents and they are an improvement over existing protocols.

Distributed event-triggered consensus tracking of second-order multi-agent systems with a virtual leader

This paper investigates the consensus tracking problems of second-order multi-agent systems with a virtual leader via event-triggered control. A novel distributed event-triggered transmission scheme is proposed, which is intermittently examined at constant sampling instants. Only partial neighbor information and local measurements are required for event detection. Then the corresponding event-triggered consensus tracking protocol is presented to guarantee second-order multi-agent systems to achieve consensus tracking. Numerical simulations are given to illustrate the effectiveness of the proposed strategy.

Distributed Time Synchronization in Wireless Sensor Networks via Second-Order Consensus Algorithms

This paper proposes a distributed second-order consensus time synchronization, which incorporates the second-order consensus algorithm into wireless sensor networks. Since local clocks may have different skews and offsets, the algorithm is designed to include offset compensation and skew compensation. The local clocks are not directly modified, thus the virtual clocks are built according to the local clocks via the compensation parameters. Each node achieves a virtual consensus clock by periodically updated compensation parameters. Finally, the effectiveness of the proposed algorithm is verified through a number of simulations in a mesh network. It is proved that the proposed algorithm has the advantage of being distributed, asymptotic convergence, and robust to new node joining.

CONSENSUS OF THE SECOND-ORDER MULTI-AGENT SYSTEMS WITH AN ACTIVE LEADER AND COUPLING TIME DELAY

This article investigates the consensus problem of the second-order multi-agent systems with an active leader and coupling time delay in direct graph. One decentralized state control rule is constructed for each agent to track the active leader and it is proved that the proposed control scheme enables the consensus to be obtained when the adjacency topology is fixed/switched. Simulation results show effectiveness of the proposed theoretical analysis.

Consensus of Second-order Multi-agent Systems with Nonsymmetric Interconnection and Heterogeneous Delays

In this paper, a consensus algorithm of multi-agent second-order dynamical systems with nonsymmetric interconnection and heterogeneous delays is studied. With the hypothesis of directed weighted topology graph with a globally reachable node, decentralized consensus condition is obtained by applying generalized Nyquist criterion. For the systems with both communication and input delays, it is shown that the consensus condition is dependent on input delays but independent of communication delays.

Reference model based consensus control of second-order multi-agent systems

This paper deals with the consensus problem of multi-agent systems with second-order dynamics. The objective is to design algorithms such that all agents will have same positions and velocities. First, a reference model based consensus algorithm is proposed. It is proved that the consensus can be achieved if the communication graph has a spanning tree. Different from most of the consensus algorithms proposed in the literature, the parameters of the control laws are different among agents. Therefore, each agent can design its control law independently. Secondly, it gives a consensus algorithm for the case that the velocities of the agents are not available. Thirdly, the effectiveness of the input delay and the communication delay is considered. It shows that consensus can be achieved if the input delay of every agent is smaller than a bound related to parameters in its control law. Finally, some numerical examples are given to illustrate the proposed results.

H_∞ consensus control of a class of second-order multi-agent systems without relative velocity measurement

This paper studies consensus control problems for a class of second-order multi-agent systems without relative velocity measurement. Some dynamic neighbour-based rules are adopted for the agents in the presence of external disturbances. A sufficient condition is derived to make all agents achieve consensus while satisfying desired H∞ performance. Finally, numerical simulations are provided to show the effectiveness of our theoretical results.

Bounded consensus tracking of second-order multi-agent systems with sampling delay under directed networks

The bounded consensus tracking problems of second-order multi-agent systems under directed networks with sam- pling delay are addressed in this paper. When the sampling delay is more than a sampling period, new protocols based on sampled-data control are proposed so that each agent can track the time-varying reference state of the virtual leader. By using the delay decomposition approach, the augmented matrix method, and the frequency domain analysis, necessary and sufficient conditions are obtained, which guarantee that the bounded consensus tracking is realized. Furthermore, some numerical simulations are presented to demonstrate the effectiveness of the theoretical results.

Multi-agent consensus algorithm for second-order systems with a time-varying reference state

Two second-order consensus algorithms with a time-vary reference state without relative velocity measurements are proposed in a directed topology. Necessary and sufficient conditions are presented to ensure second-order consensus. It is shown that all the coupling strengths and the ei- genvalues of the Laplacian matrix play important roles in reaching consensus. Specially when all non- zero eigenvalues of the Laplacian matrix are real, consensus can be achieved if and only if the cou- pling strengths are positive and the directed topology has a spanning tree for the first algorithm, and for the second one, consensus can be achieved if and only if the coupling strengths are positive. Fi- nally, simulation examples are presented to verify the theoretical analysis.

A Review of Consensus Protocols in Permissioned Blockchains

Consensus protocols are used for the distributed management of large databases in an environment without trust among participants.The choice of a specific protocol depends on the purpose and characteristics of the system itself.The subjects of the paper are consensus protocols in permissioned blockchains.The objective of this paper is to identify functional advantages and disadvantages of observed protocol.The analysis covers a total of six consensus protocols for permissioned blockchains.The following characteristics were compared:security,trust among participants,throughput and scalability.The results show that no protocol shows absolute dominance in all aspects of the comparison.Paxos and Raft are intended for systems in which there is no suspicion of unreliable users,but only the problem of a temporary shutdown.Practical Byzantine Fault Tolerance is intended for systems with a small number of nodes.Federated Byzantine Fault Tolerance shows better scalability and is more suitable for large systems,but can withstand a smaller number of malicious nodes.Proof-of-authority can withstand the largest number of malicious nodes without interfering with the functioning of the system.When choosing a consensus protocol for a blockchain application,one should take into account priority characteristics.

Consensus tracking protocol and formation control of multi-agent systems with switching topology

Consensus tracking control problems for single-integrator dynamics of multi-agent systems with switching topology are investigated. In order to design effective consensus tracking protocols for a more general class of networks, which are aimed at ensuring that the concerned states of agents converge to a constant or time-varying reference state, new consensus tracking protocols with a constant and time-varying reference state are proposed, respectively. Particularly, by contrast with spanning tree, an improved condition of switching interaction topology is presented. And then, convergence analysis of two consensus tracking protocols is provided by Lyapunov stability theory. Moreover, consensus tracking protocol with a time-varying reference state is extended to achieve the fbrmation control. By introducing formation structure set, each agent can gain its individual desired trajectory. Finally, several simulations are worked out to illustrate the effectiveness of theoretical results. The test results show that the states of agents can converge to a desired constant or time-varying reference state. In addition, by selecting appropriate structure set, agents can maintain the expected formation under random switching interaction topologies.

Consensus protocol for multi-agent continuous systems

Based on the algebraic graph theory, the networked multi-agent continuous systems are investigated. Firstly, the digraph （directed graph） represents the topology of a networked system, and then a consensus convergence criterion of system is proposed. Secondly, the issue of stability of multi-agent systems and the consensus convergence problem of information states are all analysed. Furthermore, the consensus equilibrium point of system is proved to be global and asymptotically reach the convex combination of initial states. Finally, two examples are taken to show the effectiveness of the results obtained in this paper.

Consensus protocol for heterogeneous multi-agent systems: A Markov chain approach

This paper deals with the consensus problem for heterogeneous multi-agent systems. Different from most existing consensus protocols, we consider the consensus seeking of two types of agents, namely, active agents and passive agents. The objective is to directly control the active agents such that the states of all the agents would achieve consensus. In order to obtain a computational approach, we subtly introduce an appropriate Markov chain to cast the heterogeneous systems into a unified framework. Such a framework is helpful for tackling the constraints from passive agents. Furthermore, a sufficient and necessary condition is established to guarantee the consensus in heterogeneous multi-agent systems. Finally, simulation results are provided to verify the theoretical analysis and the effectiveness of the proposed protocol.

Ripple+:An Improved Scheme of Ripple Consensus Protocol in Deployability,Liveness and Timing Assumption

Ripple acts as a real-time settlement and payment system to connect banks and payment providers.As the consensus support of the Ripple network to ensure network consistency,Ripple consensus protocol has been widely concerned in recent years.Compared with those Byzantine fault tolerant protocols,Ripple has a significant difference that the system can reach an agreement under decentralized trust model.However,Ripple has many problems both in theory and practice,which arementioned in the previous researches.This paper presents Ripple+,an improved scheme of Ripple consensus protocol,which improves Ripple fromthree aspects:(1)Ripple+employs a specific trustmodel and a corresponding guideline for Unique Node List selection,which makes it easy to deploy in practice to meet the safety and liveness condition;(2)the primary and viewchangemechanismare joined to solve the problem discussed by the previous research that Ripple may lose liveness in some extreme scenarios;(3)we remove the strong synchrony clock and timeout during consensus periods to make it suitable for weak synchrony assumption.We implemented a prototype of Ripple+and conducted experiments to show that Ripple+can achieve the throughput of tens of thousands of transactions per second with no more than half a minute latency,and the view change mechanism hardly incurs additional cost.

Consensus problems on networks with free protocol

In the real world,rule makers can only restrict,not completely control the behavior of the governed,while the governed can only choose their behavior patterns under these restrictions.In this paper,we design a new control protocol called free protocol to describe this situation.First,we calculate consensus probabilities based on the information of the interaction networks.Then,sufficient conditions are obtained for all agents converging to a same value with probability one.Finally,numerical simulation results are given to verify the above results.

CHB-Consensus:一种基于一致性哈希算法的区块链共识机制研究

区块链中的共识协议使得网络中相互不信任的节点对全网的交易状态达成一致的确认。当前的共识协议在"去中心化、安全性、能耗"3个方面存在矛盾,无法同步优化。针对该问题,本文基于一致性哈希算法,设计实现了全新的区块链共识协议,称为"CHB-Consensus"。该共识协议在"诚实"节点创建新区块时不耗费多余的"算力"资源,但是"恶意"节点进行新块创建攻击或"双花"攻击时需要耗费海量算力。"CHB-Consensus"形成的区块链网络与比特币系统基于同样的安全性假设,因此,"CHB-Consensus"节省了海量算力的同时没有牺牲去中心化和安全性的优势。本文分析了"CHB-Consensus"共识协议可能存在的攻击过程,并给出了严格但可调整的验证策略。"CHB-Consensus"共识过程引入了CA,CA数字证书只作为共识过程的准入凭证,CA对区块链网络及区块链数据结构不具有任何特殊的管理控制权限,但有交易隐私泄露的风险,这取决于CA的安全性和可信性。本文最后分析了"CHB-Consensus"的健壮性及对应不同网络环境的优化策略。