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.

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.

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.

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.

Robustness and efficiency of voting consensus protocols within byzantine infrastructures

This paper investigates several voting consensus protocols with low computational complexity in noisy Byzantine infrastructures.Using computer simulations,we show that explicit randomization of the consensus protocol can significantly increase the robustness towards faulty and malicious nodes.We identify the optimal amount of randomness for various Byzantine attack strategies on different kinds of network topologies.

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.

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.

Maximizing Convergence Speed for Second Order Consensus in Leaderless Multi-Agent Systems

The paper deals with the consensus problem in a leaderless network of agents that have to reach a common velocity while forming a uniformly spaced string.Moreover,the final common velocity(reference velocity)is determined by the agents in a distributed and leaderless way.Then,the consensus protocol parameters are optimized for networks characterized by a communication topology described by a class of directed graphs having a directed spanning tree,in order to maximize the convergence rate and avoid oscillations.The advantages of the optimized consensus protocol are enlightened by some simulation results and comparison with a protocol proposed in the related literature.The presented protocol can be applied to coordinate agents such as mobile robots,automated guided vehicles(AGVs)and autonomous vehicles that have to move with the same velocity and a common inter-space gap.

T-PBFT: An EigenTrust-Based Practical Byzantine Fault Tolerance Consensus Algorithm

Blockchain with these characteristics of decentralized structure, transparent and credible, time-series and immutability, has been considering as a promising technology. Consensus algorithm as one of the core techniques of blockchain directly affects the scalability of blockchain systems. Existing probabilistic finality blockchain consensus algorithms such as PoW, PoS, suffer from power consumptions and low efficiency;while absolute finality blockchain consensus algorithms such as PBFT, HoneyBadgerBFT, could not meet the scalability requirement in a largescale network. In this paper, we propose a novel optimized practical Byzantine fault tolerance consensus algorithm based on EigenTrust model, namely T-PBFT, which is a multi-stage consensus algorithm. It evaluates node trust by the transactions between nodes so that the high quality of nodes in the network will be selected to construct a consensus group. To reduce the probability of view change, we propose to replace a single primary node with a primary group. By group signature and mutual supervision, we can enhance the robustness of the primary group further. Finally, we analyze T-PBFT and compare it with the other Byzantine fault tolerant consensus algorithms. Theoretical analysis shows that our T-PBFT can optimize the Byzantine fault-tolerant rate,reduce the probability of view change and communication complexity.

Finite-time consensus of heterogeneous multi-agent systems

We investigate the finite-time consensus problem for heterogeneous multi-agent systems composed of first-order and second-order agents.A novel continuous nonlinear distributed consensus protocol is constructed,and finite-time consensus criteria are obtained for the heterogeneous multi-agent systems.Compared with the existing results,the stationary and kinetic consensuses of the heterogeneous multi-agent systems can be achieved in a finite time respectively.Moreover,the leader can be a first-order or a second-order integrator agent.Finally,some simulation examples are employed to verify the efficiency of the theoretical results.

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.

Trajectory tracking and formation control based on consensus in high-dimensional multi-agent systems

This paper discusses consensus problems for high-dimensional networked multi-agent systems with fixed topology. The communication topology of multi-agent systems is represented by a digraph. A new consensus protocol is proposed, and consensus convergence of multigent systems is analyzed based on the Lyapunov stability theory. The consensus problem can be formulated into solving a feasible problem with bilinear matrix inequality （BMI） constrains. Furthermore, the consensus protocol is extended to achieving tracking and formation control. By introducing the formation structure set, each agent can gain its individual desired trajectory. Finally, numerical simulations are provided to show the effectiveness of our strategies. The results show that agents from arbitrary initial states can asymptotically reach a consensus. In addition, agents with high-dimensional can track any target trajectory, and maintain desired formation during movement by selecting appropriate structure set.

Integration of Fog Computing for Health Record Management Using Blockchain Technology

Internet of Medical Things (IoMT) is a breakthrough technologyin the transfer of medical data via a communication system. Wearable sensordevices collect patient data and transfer them through mobile internet, thatis, the IoMT. Recently, the shift in paradigm from manual data storage toelectronic health recording on fog, edge, and cloud computing has been noted.These advanced computing technologies have facilitated medical services withminimum cost and available conditions. However, the IoMT raises a highconcern on network security and patient data privacy in the health caresystem. The main issue is the transmission of health data with high security inthe fog computing model. In today’s market, the best solution is blockchaintechnology. This technology provides high-end security and authenticationin storing and transferring data. In this research, a blockchain-based fogcomputing model is proposed for the IoMT. The proposed technique embedsa block chain with the yet another consensus (YAC) protocol building securityinfrastructure into fog computing for storing and transferring IoMT data inthe network. YAC is a consensus protocol that authenticates the input datain the block chain. In this scenario, the patients and their family membersare allowed to access the data. The empirical outcome of the proposedtechnique indicates high reliability and security against dangerous threats.The major advantages of using the blockchain model are high transparency,good traceability, and high processing speed. The technique also exhibitshigh reliability and efficiency in accessing data with secure transmission. Theproposed technique achieves 95% reliability in transferring a large number offiles up to 10,000.

A Novel Improved Artificial Bee Colony and Blockchain-Based Secure Clustering Routing Scheme for FANET

Flying Ad hoc Network(FANET)has drawn significant consideration due to its rapid advancements and extensive use in civil applications.However,the characteristics of FANET including high mobility,limited resources,and distributed nature,have posed a new challenge to develop a secure and ef-ficient routing scheme for FANET.To overcome these challenges,this paper proposes a novel cluster based secure routing scheme,which aims to solve the routing and data security problem of FANET.In this scheme,the optimal cluster head selection is based on residual energy,online time,reputation,blockchain transactions,mobility,and connectivity by using Improved Artificial Bee Colony Optimization(IABC).The proposed IABC utilizes two different search equations for employee bee and onlooker bee to enhance convergence rate and exploitation abilities.Further,a lightweight blockchain consensus algorithm,AI-Proof of Witness Consensus Algorithm(AI-PoWCA)is proposed,which utilizes the optimal cluster head for mining.In AI-PoWCA,the concept of the witness for block verification is also involved to make the proposed scheme resource efficient and highly resilient against 51%attack.Simulation results demonstrate that the proposed scheme outperforms its counterparts and achieves up to 90%packet delivery ratio,lowest end-to-end delay,highest throughput,resilience against security attacks,and superior in block processing time.

Finite-time Consensus for Multi-agent Systems via Nonlinear Control Protocols

This paper investigates the fnite-time consensus problem of multi-agent systems with single and double integrator dynamics,respectively.Some novel nonlinear protocols are constructed for frst-order and second-order leader-follower multi-agent systems,respectively.Based on the fnite-time control technique,the graph theory and Lyapunov direct method,some theoretical results are proposed to ensure that the states of all the follower agents can converge to its leader agent s state in fnite time.Finally,some simulation results are presented to illustrate the efectiveness of our theoretical results.

CF-BFT:A Dual-Mode Byzantine Fault-Tolerant Protocol Based on Node Authentication

The consensus protocol is one of the core technologies in blockchain,which plays a crucial role in ensuring the block generation rate,consistency,and safety of the blockchain system.Blockchain systems mainly adopt the Byzantine Fault Tolerance(BFT)protocol,which often suffers fromslow consensus speed and high communication consumption to prevent Byzantine nodes from disrupting the consensus.In this paper,this paper proposes a new dual-mode consensus protocol based on node identity authentication.It divides the consensus process into two subprotocols:Check_BFT and Fast_BFT.In Check_BFT,the replicas authenticate the primary’s identity by monitoring its behaviors.First,assume that the systemis in a pessimistic environment,Check_BFT protocol detects whether the current environment is safe and whether the primary is an honest node;Enter the fast consensus stage after confirming the environmental safety,and implement Fast_BFT protocol.It is assumed that there are 3f+1 nodes in total.If more than 2f+1 nodes identify that the primary is honest,it will enter the Fast_BFT process.In Fast_BFT,the primary is allowed to handle transactions alone,and the replicas can only receive the messages sent by the primary.The experimental results show that the CF-BFT protocol significantly reduces the communication overhead and improves the throughput and scalability of the consensus protocol.Compared with the SAZyzz protocol,the throughput is increased by 3 times in the best case and 60%in the worst case.

Bitcoin:a new proof‑of‑work system with reduced variance

Since its inception,bitcoin has used the popular consensus protocol proof-of-work(PoW).PoW has a well-known flaw:it distributes all rewards to a single miner(or pool)who inserts a new block.Consequently,the variance of rewards and the mining enter-prise risk are extremely high.In 2016,Shi proposed addressing this problem with a theoretical algorithm.We introduce an easily-implemented PoW variant that improves Shi’s idea.The network must not find a single nonce but a few to insert a block.This simple change allows for a fairer distribution of rewards and also has the effect of regularizing the insertion time of blocks.This method would facilitate the emergence of small pools or autonomous miners.

Second-Order Consensus in Networks of Agents with Delayed Dynamics

This paper proposes second-order consensus protocols and gives a measure of the robustness of the protocols to the time-delays existing in the dynamics of agents with second-order dynamics. By employing a frequency domain method, it is proven that the information states achieve second-order consensus asymptotically for appropriate time-delay if the topology of the network is connected. Particularly, a nonconservative upper bound on the fixed time-delay that can be tolerated is found. The consensus protocols are distributed in the sense that each agent only needs information from its neighboring agents, which makes the proposed protocols scalable. It reduces the complexity of connections among agents significantly. Simulation results are provided to verify the effectiveness of the theoretical results for second-order consensus in networks in the presence of time-delays existing in the dynamics of agents.

CONSENSUS CONTROL FOR LEADER-FOLLOWING MULTI-AGENT SYSTEMS WITH MEASUREMENT NOISES

This work is concerned with consensus control for a class of leader-following multi-agentsystems (MASs).The information that each agent received is corrupted by measurement noises.Toreduce the impact of noises on consensus,time-varying consensus gains are adopted,based on whichconsensus protocols are designed.By using the tools of stochastic analysis and algebraic graph theory,asufficient condition is obtained for the protocol to ensure strong mean square consensus under the fixedtopologies.This condition is shown to be necessary and sufficient in the noise-free case.Furthermore,by using a common Lyapunov function,the result is extended to the switching topology case.