Distributed Consensus Protocol Research Articles

Modelling the Raft Distributed Consensus Protocol in mCRL2

Modelling the Raft Distributed Consensus Protocol in mCRL2

Blizzard: A Distributed Consensus Protocol for Mobile Devices

We present Blizzard, a Byzantine fault tolerant (BFT) distributed ledger protocol that is aimed at making mobile devices first-class citizens in the consensus process. Blizzard introduces a novel two-tier architecture by having the mobile nodes communicate through online brokers, and includes a decentralized matching scheme to ensure each node connects to a certain number of random brokers. Through mathematical analysis, we derive a guaranteed safety region (i.e., the set of ratios of malicious nodes and malicious brokers for which the safety is assured) for the Blizzard protocol. Liveness is shown as well. We analyze the performance of Blizzard in terms of its throughput, latency, and message complexity. Through experiments based on a software implementation, we show that Blizzard is capable of throughput on the order of several thousand transactions per second per shard and sub-second confirmation latency.

Distributed Adaptive Output Feedback Consensus for Nonlinear Stochastic Multiagent Systems by Reference Generator Approach.

This article investigates the distributed leader-following consensus for a class of nonlinear stochastic multiagent systems (MASs) under directed communication topology. In order to estimate unmeasured system states, a dynamic gain filter is designed for each control input with reduced filtering variables. Then, a novel reference generator is proposed, which plays a key role in relaxing the restriction on communication topology. Based on the reference generators and filters, a distributed output feedback consensus protocol is proposed by a recursive control design approach, which incorporates adaptive radial basis function (RBF) neural networks to approximate the unknown parameters and functions. Compared with existing works on stochastic MASs, the proposed approach can significantly reduce the number of dynamic variables in filters. Furthermore, the agents considered in this article are quite general with multiple uncertain/unmatched inputs and stochastic disturbance. Finally, a simulation example is given to demonstrate the effectiveness of our results.

Optimal Consensus Control for Continuous-Time Linear Multiagent Systems: A Dynamic Event-Triggered Approach.

This article investigates the optimal consensus problem for general linear multiagent systems (MASs) via a dynamic event-triggered approach. First, a modified interaction-related cost function is proposed. Second, a dynamic event-triggered approach is developed by constructing a new distributed dynamic triggering function and a new distributed event-triggered consensus protocol. Consequently, the modified interaction-related cost function can be minimized by applying the distributed control laws, which overcomes the difficulty in the optimal consensus problem that seeking the interaction-related cost function needs all agents' information. Then, some sufficient conditions are obtained to guarantee optimality. It is shown that the developed optimal consensus gain matrices are only related to the designed triggering parameters and the desirable modified interaction-related cost function, relaxing the constraint that the controller design requires the knowledge of system dynamics, initial states, and network scale. Meanwhile, the tradeoff between optimal consensus performance and event-triggered behavior is also considered. Finally, a simulation example is provided to verify the validity of the designed distributed event-triggered optimal controller.

Distributed Consensus Protocol for Multi-Agent Differential Graphical Games

Distributed Consensus Protocol for Multi-Agent Differential Graphical Games

Dispatcher: Resource-aware Nakamoto Blockchain via Hierarchical Topology and Adaptive Incentives

Mainstream blockchain systems such as Bitcoin and Ethereum are revolutionizing the financial industry by adopting the Nakamoto consensus protocol, i.e., Proof-of-Work (PoW). Only nodes with sufficient computing resources can work out the PoW difficulties, thereby increasing the mining cost of malicious attackers and ensuring the security of blockchain systems. Such an assumption of having abundant resources leads to drawbacks of low throughput and risk of centralization. In this paper, we present Dispatcher, a novel distributed consensus protocol that takes resource heterogeneity into account to ensure resource-aware PoW with high efficiency. Dispatcher introduces a hierarchical topology to offer flexible PoW difficulties tailored for different nodes’ resources. In particular, it utilizes the limited resource of each node to jointly maximize the performance by concurrent mining. Moreover, we design an adaptive incentive mechanism to fit the available resource of blockchain nodes to rewards. Our experiments show that Dispatcher enjoys a substantial performance margin over the state-of-the-art. We can achieve a 50% throughput improvement compared with OHIE.

Global Reachability of Heterogeneous Multiagent Systems Under Collaborative Interaction Topology and Unknown Delays

The multi-agent rendezvous problem for single- and double-integrator agents in the presence of unknown constant input and communication delays is investigated in this paper. Existing works address the rendezvous problem by incorporating negative gain(s) into the distributed consensus protocol and showing that negative gain(s) expands the reachable set beyond the initial configuration of the agents' convex hull. On the contrary, the present control protocol ensures global reachability of a network of agents with a directed communication topology having non-negative edge weights. This is accomplished with the help of a dynamic distributed control protocol, where the information exchange among agents occurs in the internal controller states. For homogeneous delays, the analytical expression of the rendezvous point confesses the non-dependency of the point with delays, which in turn signifies that rendezvous can be achieved with unknown and arbitrarily large but bounded delays. The very structure of the control protocol ensures rendezvous at any desired point, even if the input delays are heterogeneous and unknown. However, heterogeneity in communication delays has an effect on the rendezvous point, and hence, global reachability of agents can be established if these delays are exactly known. For heterogeneous multi-agent systems composed of single- and double-integrator agents, tuning of the design parameters gets simplified due to the single-integrator based internal controller structure for all agents. Numerical simulations are provided to validate the robustness of the protocol against delays.

Adaptive Finite-Time Consensus for Stochastic Multiagent Systems With Uncertain Actuator Faults

This paper aims to develop fully distributed adaptive protocols and establish the finite-time consensus criteria for nonlinear stochastic multi-agent systems that are subjected to serious multiple uncertainties not only in the agents' states and inherent nonlinearities but also in their actuators. Firstly, we propose a new continuous fully distributed consensus protocol for leaderless stochastic multi-agent systems by leveraging the adaptive technology, enabling the agents to achieve the finite-time consensus in probability efficiently. Secondly, we develop an adaptive protocol for leader-following multi-agent systems, and remarkably our protocol contains only one dynamic gain, which is adequate to resist serious multiple uncertainties and to ensure the realization of finite-time consensus in probability. Finally, we provide numerical simulations to verify the effectiveness of our protocols.

Conceptualization, Realization, and Validation of Distributed Cyber-Physical Systems for Sensing and Automation

Abstract This paper investigates the feasibility of the pragmatic implementation of distributed algorithms in real-world cyber-physical systems (CPSs). We detail how distributed (and parallel) computing systems can be realized using existing system-design software for CPS development. A series of experiments is devised and used to verify the information-exchange capacity of the computing nodes and the synchronous and real-time operational effectiveness of the overall distributed computing system development framework. Finally, an actual distributed computing system is realized and validated by executing a fundamental distributed consensus protocol.

Dissipativity-Based Consensus Tracking Control of Nonlinear Multiagent Systems With Generally Uncertain Markovian Switching Topologies and Event-Triggered Strategy.

This article focuses on the dissipativity-based consensus tracking control (DBCTC) problems of time-varying delayed leader-following nonlinear multiagent systems (LFNMASs) with the event-triggered transmission strategy. The switching topologies of the LFNMASs are subject to the uncertain and partially unknown generally Markovian jumping process. The control inputs of the following agents are updated according to the proposed event-triggered transmission strategy, which could reduce the communication burden. Based on the event-triggered transmission condition and distributed consensus protocol, some dissipativity-based criteria obtained by adopting the delay-product-term Lyapunov-Krasovskii functional (DPTLKF) and higher order polynomial-based relaxed inequality (HOPRII) are proposed to guarantee the LFNMAS consensus. The validity of the main results is verified by two simulation examples.

RAFT Consensus Reliability in Wireless Networks: Probabilistic Analysis

The centralized system becomes less efficient, secure, and resilient as the network size and heterogeneity increase due to its inherent single point of failure issues. Distributed consensus mechanisms characterized by decentralization, autonomy, parallelism and fault-tolerance can meet the increasing demands of safety and security in critical interconnected systems. This paper establishes a Node and Link probabilistic failure model in the presence of node and communication link failures for a representative crash fault tolerant distributed consensus protocol: RAFT. The analytical results in terms of the probability density function and the mean value of consensus reliability are derived. Two important reliability performance indicators, Reliability Gain and Tolerance Gain are proposed to indicate the linear relationship between the consensus reliability and two basic parameters, i.e. the joint failure rate and the maximum number of tolerant faulty nodes, which provide the theoretical guidance for quickly deploying a RAFT system. The special case of a distributed consensus network with already a certain number of failures and its adverse impact are evaluated. The Markov probabilistic models, definitions of Reliability Gain and Tolerance Gain, and the analysis methods proposed in this paper can be extended to other consensus mechanisms.

AUTHENTICATED KEY AGREEMENT SCHEME BASED ON BLOCKCHAIN FOR AMI COMMUNICATION SECURITY

Security is the basis for the normal operation of advanced measurement infrastructure (AMI). As an important part of key management scheme, key establishment is indispensable in meeting AMI communication security requirements. Most proposed key management schemes rely on a trusted third party (TTP). Once there is a problem with TTP, the security of these schemes will be greatly reduced. Furthermore, the data concentrators (DCs) in traditional AMI architectures all manage smart meters (SMs) in their respective regions, and the lack of interaction between the DCs exposes a serious single point of failure. To alleviate these problems, we propose a blockchain-based authenticated key agreement scheme to secure the communication of AMI. In this scheme, the blockchain comprises DCs as network nodes that interact with the SMs. The proposed key agreement and distributed consensus protocol ensure the authenticity and validity of the communication content without relying on TTP. We analyse the resistance of the proposed protocol to multiple known attacks and evaluate its performance. The proposed protocol has higher security or better performance than other schemes.

Lag Group Consensus of High-Order Multiagent Systems in Directed Network Settings

This article studies lag group consensus problems of multiagent systems with directed information transformations. Agents in the network are divided into finite groups, and modeled by high-order systems. Distributed consensus protocols with constant lags are presented to realize the lag group consensus: the states of the agents in a group approach to a consensus value asymptotically, while there exist given ratios between the final values of different groups. Necessary and sufficient criteria for the lag group consensus are obtained by the Laplace transformation. Finally, theoretical results are proved to be effective by several simulation results.

Distributed Active Fault-Tolerant Cooperative Control for Multiagent Systems With Communication Delays and External Disturbances.

This article investigates the distributed active fault-tolerant cooperative control problem for leader-follower multiagent systems (MASs) in the presence of multiple faults, communication delays, and external disturbances. A new distributed consensus protocol is put forward to ensure the state consensus of MASs, which can be served as a nominal controller in fault-free cases with communication delays and external disturbances. A novel distributed time-delay intermediate observer, which can estimate system states and multiple faults simultaneously, is derived based on the time-delay closed-loop system equation. By integrating a fault compensation mechanism into the nominal controller, a distributed active fault-tolerant consensus controller is constructed for the follower agents to eliminate the adverse effects of multiple faults. Simulation examples are provided to demonstrate the effectiveness of the proposed method.

Hierarchical control strategy of thermostatically controlled load considering multiple factors

In this article, a distributed hierarchical control strategy of thermostatically controlled loads (TCLs) is proposed, which can effectively utilize TCLs to provide power dispatching service in a microgrid composed of buildings. Firstly, the distributed consensus protocol of TCLs is studied, and the state space of a TCL is established. The optimal control performance is achieved by selecting coupling strength and control gain. Then, the dispatching power of each building is reasonably distributed through pinning control, and consensus coefficient and proportional coefficient are determined according to the heterogeneity of building parameters. Finally, the case studies were conducted to validate the proposed novel distributed hierarchical control scheme, which can provide effective power dispatching services and realize the fair distribution of the dispatching requirements among all TCLs. The proposed strategy also takes into account the multiple factors of each TCL such as heterogeneous parameters, communication burden and user's actual conditions, which improves the feasibility and expansibility of the dispatching process.

Distributed consensus of heterogeneous switched nonlinear multiagent systems with input quantization and DoS attacks

In this paper, the consensus tracking control problem is investigated for a class of heterogeneous switched nonlinear multiagent systems (MASs) with input quantization under denial-of-service (DoS) attacks, where first-order agents and second-order agents exist simultaneously, and each agent shows the switching characteristic. Due to the prevalence of DoS attacks in communication channels, a DoS attack model is constructed in this study, and the upper bounds on the duration and frequency of DoS attacks are given. Meanwhile, taking the chattering phenomena of control inputs into account, a hysteresis quantizer is introduced to overcome the issue of the undesirable input chattering. Hence, a new anti-attack distributed consensus protocol is developed such that MASs with input quantization can effectively resist the impact of DoS attacks. Based on the Lyapunov stability theory, the boundedness of all signals in the closed-loop system is verified and the consensus target can be achieved. Finally, the effectiveness of the proposed control scheme is demonstrated by two simulation examples.

Distributed optimal consensus protocol for high-order integrator-type multi-agent systems

Optimal consensus control of high-order multi-agent systems (MASs) modeled by multiple integrator-type dynamics is studied. A fully distributed optimal control protocol that achieves the specific consensus behavior is designed for MASs with linear dynamics, where topology-dependent conditions are removed. Further, a distributed consensus protocol for high-order nonlinear MASs with one-sided Lipschitz continuity is presented using the optimization approach, and the optimal solution can be obtained by solving a standard algebraic Riccati equation. Some numerical examples are finally provided to illustrate the effectiveness of the presented approaches.

Consensus of Multi-Agent Systems With Asymmetric Input Saturation Over Directed Graph

In this brief, the consensus issue of continuous-time first-order multi-agent systems (MASs) subject to asymmetric input saturation under the directed graph containing a directed spanning tree is investigated. First, a fully distributed consensus protocol is proposed. We discuss the scenario where there are zeros in the partial saturation bounds. Based on the contradiction method and the graph theory, a necessary and sufficient criterion for guaranteeing the global consensus is given. After that, we extend the above findings to the discrete-time case, where an upper bound of the sample time is explicitly formulated. Finally, simulation examples verify the effectiveness of our proposed strategy.

Cooperative Control of Multi-Time-Scale Agent Networks Under Digraphs

This paper addresses cooperative control for a class of multi-agent networks. An interesting feature of such network is that each agent possesses the characteristic of multi-time-scale. By developing the relative states or the relative outputs based consensus protocols, some well-conditioned consensus criteria in terms of linear matrix inequalities are derived successively based on the ε-strict Lyapunov function. Compared with undirected graphs or strongly connected digraphs in existing works, a more general digraph that it contains at least a directed spanning tree is considered herein. Moreover, a fully distributed consensus protocol with time-varying coupling strength is proposed to avoid using global information. Finally, the obtained theoretical results are validated by two examples including standard and nonstandard agents.

Performance‐prescribed consensus for uncertain nonlinear multi‐agent systems under directed graph

AbstractWhether or not system performance can be prescribed by users is one core issue for almost all control problems, of course for multi‐agent control systems. But it could pose stern constraints on or exceptions to systems and control methods. How can one guarantee the prescribed performance while covering much more systems? It deserves deep study and particularly entails the integration/reformation of the related techniques. In the paper, we are concerned with the leaderless consensus with a prescribed convergence rate, aiming at ‐dimensional multi‐agent systems typically with unknown heterogeneous nonlinearities under a directed graph. In view of the essence of the problem, we resort to a powerful time‐varying high‐gain method, that is, funnel control. Specifically, to suppress unknown system nonlinearities and guarantee the prescribed performance, funnel gains are devised by utilizing the relative states and a time‐varying design function. Integrating them as well as a series of intermediate variables, a distributed consensus protocol is obtained without involving any global graph information. Remark that besides being used to construct funnel gains, the time‐varying design function is also introduced as a part of the protocol, substantially enhancing the control effect and playing a key role in forcing the relative states to ultimately converge to zero. It is shown that under the proposed protocol, the desired consensus is achieved with a prescribed convergence rate. A simulation example is given to illustrate the effectiveness of the theoretical result.