Consensus Issues Research Articles

Prescribed-time leader-follower consensus and containment control for nonlinear multi-agent systems with event-triggered control protocols

This paper discusses the prescribed-time leader-follower consensus and containment control problems for a class of nonlinear multi-agent systems with external disturbances. First, an event-triggered control protocol with sign function is proposed, which can ensure that all agents achieve consensus within a prescribed time. Second, as the sliding mode control has the advantage of good robustness to external disturbances, an improved event-triggered control protocol is designed by using the integral sliding mode control method and some sufficient conditions are derived for achieving the prescribed-time leader-follower consensus. Moreover, the prescribed-time containment control problem for multi-agent systems with multiple leaders is investigated by using the event-triggered control strategy. It is shown that Zeno behavior can be excluded in the above consensus issues by choosing parameters appropriately. Finally, several numerical examples are given to demonstrate the effectiveness and reliability of the proposed approaches.

Model-independent event-based consensus of multiple Euler-Lagrange systems with input disturbances

This paper investigates leaderless consensus (LLC) and leader-follower consensus (LFC) issues of multiple Euler-Lagrange systems (MELSs) with uncertain system parameters and input disturbances. Firstly, by utilizing event-based control strategy, event-based consensus protocols are proposed to achieve LLC and LFC, respectively. Then, to confirm that no Euler-Lagrange (EL) system will exhibit Zeno behavior under the above event-based consensus protocols, we show that the low bound of event-triggering interval is strictly positive for any time instants. Distinct with the existing related works, the proposed event-triggered consensus protocols only rely on local sampled state, and are irrelevant to the system parameters. Finally, some simulation examples are presented to illustrate the feasibility of the proposed event-based consensus algorithms.

Consensus issues in multi-agent-based distributed control with communication link impairments

In multi-agent systems, achieving consensus among autonomous agents is a fundamental problem with wide-ranging applications, from autonomous robotics to distributed sensor networks. However, the real-world deployment of such systems often involves communication links prone to impairments, including packet loss, delays, and network congestion. These communication challenges present formidable obstacles to achieving consensus reliably and efficiently. In this paper, consensus protocols were introduced for network with and without communication impairments and convergence analysis were provided in all the cases. The intricate dynamics of consensus issues in multi-agent-based distributed control under the influence of communication link impairments, connectivity and consensus protocol were established. Undirected communication graphs used to model the topology for agents’ connectivity is significant to addressing consensus issues of communicating agents. The paper also discusses the tradeoffs and design considerations in developing consensus strategies resilient to communication failures while optimizing performance. Simulation results show that an isolated agent in a network can achieve consensus only when there is a reference value. It was also established that communication impairments significantly degrade the performance of distributed agents in a network.

Matrix-Weighted Consensus of Second-Order Discrete-Time Multiagent Systems.

In this article, we study the matrix-weighted consensus issues for second-order discrete-time multiagent systems on directed network topology. Under the designed matrix-weighted consensus algorithm, based on the eigenvalues of the Laplacian matrix, coupling gains, and discrete interval, we build some consensus conditions for reaching discrete-time consensus and deduce some simplified and straightforward consensus conditions for undirected network topology. Besides, for a given network topology, we theoretically analyze the influence of the coupling gains and discrete intervals on the consensus conditions of the network dynamics. Finally, we offer several simulation examples to validate the obtained results.

Adaptive fixed-time consensus control of nonlinear multiagent systems with dead-zone output

This paper proposes a fixed-time leader-follower consensus tracking control scheme for uncertain multiagent systems with unknown dead-zone output. First, a novel approximate dead-zone model was introduced to accurately represent the dead-zone phenomenon in the output channel of nonlinear multiagent systems. Furthermore, the model presented is a smooth function, which greatly simplifies the process of fusing it with the backstepping technique. Second, we present a Nussbaum function to compensate for the uncertain gain from the output dead-zone nonlinearity. Third, unlike previous works, we first consider practical fixed-time consensus issues for multiagent systems with output dead-zone. Finally, according to the fixed-time control theory, the tracking error of the multiagent systems converges to the region around zero within a fixed time, which is confirmed by the simulations.

Observer‐based event‐triggered consensus control for multi‐agent systems with nonlinearity and unknown inputs

AbstractThis article investigates observer‐based consensus issues for a class of Lipschitz nonlinear multi‐agent systems (MASs) with unknown input. To address the challenges because of the unmeasurable states and the unknown input of each agent system, an interval observer is utilized to design an unknown input observer (UIO). The UIO possesses the capability of generating asymptotically the estimations of both the system states and unknown input simultaneously. Subsequently, a distributed control protocol scheme is put forwarded. The distributed controller for each agent is designed by using the state estimation and the unknown input reconstruction (UIR). The unknown input is compensated thanks for the introduction of the UIR into the controller, and thus leads to a better control performance. Besides, the event‐triggered strategy is also considered such that agents communicate with each other discontinuously. In this way, an observer‐based event‐triggered distributed control protocol scheme is developed, and under the scheme, the asymptotic convergent MASs consensus is accomplished. Finally, the effectiveness of the proposed methods is verified by a simulation example.

Model-free algorithm for consensus of discrete-time multi-agent systems using reinforcement learning method

In this work, we investigate consensus issues of discrete-time (DT) multi-agent systems (MASs) with completely unknown dynamic by using reinforcement learning (RL) technique. Different from policy iteration (PI) based algorithms that require admissible initial control policies, this work proposes a value iteration (VI) based model-free algorithm for consensus of DTMASs with optimal performance and no requirement of admissible initial control policy. Firstly, in order to utilize RL method, the consensus problem is modeled as an optimal control problem of tracking error system for each agent. Then, we introduce a VI algorithm for consensus of DTMASs and give a novel convergence analysis for this algorithm, which does not require admissible initial control input. To implement the proposed VI algorithm to achieve consensus of DTMASs without information of dynamics, we construct actor-critic networks to online estimate the value functions and optimal control inputs in real time. At last, we give some simulation results to show the validity of the proposed algorithm.

Intelligent Offloading in Blockchain-Based Mobile Crowdsensing Using Deep Reinforcement Learning

Mobile Crowdsensing (MCS) utilizes sensing data collected from users' mobile devices (MDs) to provide high-quality and personalized services, such as traffic monitoring, weather prediction, and service recommendation. In return, users who participate in crowdsensing (i.e., MCS participants) get payment from cloud service providers (CSPs) according to the quality of their shared data. Therefore, it is vital to guarantee the security of payment transactions between MCS participants and CSPs. As a distributed ledger, the blockchain technology is effective in providing secure transactions among users without a trusted third party, which has found many promising applications such as virtual currency and smart contract. In a blockchain, the proof-of-work (PoW) executed by users plays an essential role in solving consensus issues. However, the complexity of PoW severely obstructs the application of blockchain in MCS due to the limited computational capacity of MDs. To solve this issue, we propose a new framework based on Deep Reinforcement Learning (DRL) for offloading computation-intensive tasks of PoW to edge servers in a blockchain-based MCS system. The proposed framework can be used to obtain the optimal offloading policy for PoW tasks under the complex and dynamic MCS environment. Simulation results demonstrate that our method can achieve a lower weighted cost of latency and power consumption compared to benchmark methods.

Consensus Claims, Problems in Theory and Implimenting, and Obstacles to Ijtihad and Renewing

It is clear to islamic scholars that consensus (eijmaa) has an important place within the sources of islamic legislations, as our scholars counted it as one of the evidences which they agreed upon, and made it the third evidence after Quraan and the Sunna. So they talked about it in detail, especially in theoretical aspects of its definition and proves, its conditions, its types, the validity of each type, the judge on who violates the consensus, and so on.
 On the practical side, we find that the jurisprudential books are full of claims of its unanimity in hundreds of issues. While a professional reader and investigator of these issues finds it difficult to apply the theoretical conditions of consensus to the collected consensus issues. It is a must in its definition that the some of all scholars in one era have the same opinion, also scientifically known that the defined and its definition must be equal and neither of them must not be more specific or more general than the other, that is to say, it must be a collective interdiction, inclusive of all members of the defined. if we apply the fundamental definition of consensus to the codified collections of Islamic jurisprudence, we will see that there is inequality between the definition and the issues included in the true definition of consensus. The investigation reveals to us that hundreds of issues on which consensus is claimed are the opinion of most of the scholars and not everyone of them.
 Hence the idea of this research has developed to solve some issues including:
 - The distinction between fundamental consensus and jurisprudential consensus. With explaining of the proportion of righteousness in the consensuses that have been proven in the jurisprudential heritage.
 - Statement of the effects of excessive claims of consensus on the Islamic community. also clarifying the disadvantages of excess and neglection in these claims on Ijtihad and innovation, and thus on the flexibility of islamic legeslations (Shariaa) and its harmony with every time and place.
 - Statement of the problems related to practicing consensus according to the theory of islamic legeslations principles and to clarify that its impossible to practice these principles on consensus. also to propose alternatives to consensus, finally the most important results presented in the conclusion. only God is always the conciliator of righteousness.

Data-Driven Event-Triggered Bipartite Consensus for Multi-Agent Systems Preventing DoS Attacks

This paper considers event-triggered bipartite consensus issues for discrete-time nonlinear networked multi-agent systems with antagonistic interactions and denial-of-service (DoS) attacks. Firstly, a pseudo partial derivative technology is applied to obtain an equivalent dynamic linearization model of the controlled system. The signed graph theory is employed to analyze the coopetition relationships among agents. Next, a distributed combined measurement error function is formulated to transform the bipartite consensus issue into a consensus issue. Then, an output predictive compensation scheme is proposed to offset the influence of DoS attacks. Furthermore, a dead-zone operator is designed to improve the flexibility of the proposed event-triggered mechanism. Additionally, a data-driven event-triggered resilient bipartite consensus scheme is formulated. Then, the convergence of the proposed method is strictly proved by using the Lyapunov theory and the contraction mapping principle, which indicates that the bipartite consensus error could be cut to a small region around zero. Finally, hardware tasks are conducted to verify the effectiveness of the proposed method.

Model-Free Event-Triggered Consensus Algorithm for Multiagent Systems Using Reinforcement Learning Method

In this article, we study the consensus issues of multiagent systems (MASs) without any information of the system model by using the reinforcement learning (RL) method and event-based control strategy. First, we design an adaptive event-based consensus control protocol using the local sampled state information so that the consensus errors of all agents are uniformly ultimately bounded. The validity of the above event-triggered adaptive control protocol is confirmed by excluding the Zeno behavior within finite time. Then, based on the RL approach, we present a model-free algorithm to get the feedback gain matrix, and accomplish constructing the adaptive event-triggered control strategy without the knowledge of model information. Distinct with the existing related works, this RL-based event-triggered adaptive control algorithm only relies on the local sampled state information, irrelevant to any model information or global network information. Finally, we provide some examples to demonstrate the validity of the above adaptive event-based consensus algorithm.

Promoting the physician–patient consensus with a hesitant fuzzy linguistic consensus method based on betweenness relation

As the relationship between physicians and patients faces increasing challenges, physician–patient relation has gradually become the common concern of the whole society. To relieve this kind of pressure, the mechanism that reaches a consensus between physicians and patients on treatment choices needs to be discussed. Considering that there always exist uncertainties during the medical treatment process, this paper aims to develop a decision-making method to address the consensus issues under a hesitant fuzzy linguistic environment. Since patients and physicians possess different backgrounds and multiple specialties, they are allowed to evaluate alternatives under the individual set of criteria. Then, a Simos–Roy–Figueira method is proposed to derive the weights of criteria with hesitant fuzzy linguistic information. The ELECTRE III method is introduced to obtain the ranking of alternatives from each decision maker’s opinions. Further, a novel consensus method based on betweenness relation is developed to address the obtained rankings. Finally, the process to determine the treatment plan for a hepatocellular carcinoma patient is solved by the proposed method. The obtained result is considered reasonable by experts involved in the consultation, which illustrates the effectiveness of the method. Then, some simulation experiments are designed to show the features of the method. The short running time of the proposed method shows its high efficiency.

General Second-Order Consensus of Discrete-Time Multiagent Systems via Q-Learning Method

A consensus control issue is studied for general second-order multiagent systems via Q-learning method in this article. A novel second-order type with discrete-time dynamics is investigated to solve the corresponding consensus issues. Under fixed directed topology, in order to achieve general second-order consensus for the systems, a model-free Q-learning method is proposed, which can derive the coupling gains matrix without any information from the system dynamics. Moreover, applying the obtained coupling gains matrix, this general second-order multiagent systems can achieve consensus. Then, for undirected graphs, a similar corollary is obtained for this system to achieve general second-order consensus by means of the Q-learning method. Finally, the correctness of the new method is confirmed by several simulation examples.

John Lewis and the Durability of Transcendent Race Politics

AbstractJohn Lewis's civil rights activism in the 1960s often obscures the fact that he won elective office as a racially moderate politician. Scholars have long noted the efficacy of using deracialized, or racially transcendent, campaign strategies to get elected, despite normative concerns. These strategies were critical to electing Black governors, senators, and even President Obama. However, in the age of Black Lives Matter, some have questioned the continued usefulness of the strategy. Using Rep. Lewis's life as a guide, I examine the ways that some Black politicians continue to use deracialization, even in this racially charged social and political moment, and I explain how younger cohorts of Black politicians challenge this approach. Ultimately, I argue that while deracialization is a contested strategy, its efficacy has not diminished. Rather, Black politicians have expanded the boundaries of what constitutes racially transcendent politics to include consensus issues like voting rights, which while highly racialized, are not likely to induce an erosion of support among non-Black Democratic voters.

Managing Consistency and Consensus Issues in Group Decision-Making with Self-Confident Additive Preference Relations and Without Feedback: A Nonlinear Optimization Method

Managing Consistency and Consensus Issues in Group Decision-Making with Self-Confident Additive Preference Relations and Without Feedback: A Nonlinear Optimization Method

Fixed degree of decentralization DPoS consensus mechanism in blockchain based on adjacency vote and the average fuzziness of vague value

The Delegated Proof of Stake (DPoS) consensus mechanism is the fastest, most effective, most decentralized, and most flexible consensus model. The DPoS consensus uses the power of stakeholders to agree to vote in resolving consensus issues in a fair and democratic manner. However, in a traditional DPoS consensus mechanism, the degree of decentralization is undefined, and the number of agent nodes is fixed in advance. In this paper, a new fixed degree of decentralization for the DPoS consensus mechanism is proposed based on the adjacency vote and the average fuzziness of vague value. Moreover, the degree of decentralization is defined and discussed. As nodes are dynamically added and withdrawn, the total number of nodes in the blockchain changes. The proposed new consensus mechanism can automatically determine the number of agent nodes to be selected, based on the degree of decentralization and the total number of nodes in the blockchain. The adjacency vote and the average fuzziness of vague value are used to select agent nodes, and this method improves the fairness and security of the blockchain. We analyze five agent nodes, selected from 15 nodes, using the balloting distribution results. The feasibility and effectiveness of our new consensus mechanism are confirmed based on two test examples.

H-Rank Consensus Models for Fuzzy Preference Relations Considering Eliminating Rank Violations

Fuzzy preference relations (FPRs) have been widely used when ranking alternatives using pairwise comparison. However, when the FPRs have rank violations, the ranking results tend to contradict the decision makers’ (DMs) preferences. To date, no studies have examined the elimination of these FPR rank violations. Further, traditional consensus models utilizing distance measures between individual preferences are not suitable to manage classification-based consensus problems. To overcome these problems, this article develops several optimization models to address rank violations and h-rank consensus issues. First, the conditions that satisfy the FPRs’ preservation of order preferences (POPs) are analyzed and a system of constraints derived to ensure that the POPs are explicitly controlled by the optimization model, after which a mixed integer linear optimization model is developed to assist DMs to satisfy both the POP conditions and acceptable consistency. Finally, a linear model for the h-rank ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$h \geq 2$</tex-math></inline-formula> ) consensus reaching process is designed to ensure that each individual FPR also satisfies the POP conditions and acceptable consistency. The feasibility of the proposed models is illustrated using numerical examples, with extensive comparisons further validating the usefulness of the proposed models for group decision-making problems.

Consensus of the Hybrid Multiagent System Under Impulse Control

In this brief, we focus on two types of consensus issues of hybrid multiagent system under impulse control. Firstly, the hybrid multiagent system is introduced under impulse control, which includes continuous and discrete dynamic interactions. We use the characteristic of the impulse controller to transform the hybrid system into a single system. By using relevant knowledge of graph theory and matrix theory, the necessary and sufficient conditions for the consensus of the hybrid multiagent system are established. Secondly, taking advantage of impulse control, an index function for evaluating the performance between agents is introduced. It is shown that the hybrid multiagent system can achieve the consensus with guaranteed position performance by combining the coupling weights. Finally, two numerical examples are presented to verify the validity of the main results.

Fixed-time leader-following/containment consensus of nonlinear multi-agent systems based on event-triggered mechanism

This study focuses on the fixed-time event-triggered leader-following consensus issue for nonlinear multi-agent system with uncertain disturbances. First, two distributed fixed-time controllers based on event-triggered mechanism are put forward to address this issue. Different from the existing finite-time control techniques, the proposed controller can guarantee that the settling time does not depend on the initial conditions and the continuous controller updates cannot be required. Moreover, compared with the existing fixed-time control methods, the fixed-time event-triggered tracking problem for multi-dimensional nonlinear multi-agent system with uncertain disturbances is considered for the first time in this paper. To avoid continuous communication among agents, a novel triggering mechanism is further proposed. Furthermore, the fixed-time event-triggered containment consensus with multiple leaders is considered. No agent exhibits the Zeno behavior in these two consensus issues. The effectiveness of main theoretical findings is demonstrated by two illustrative examples finally.

Fully distributed event-triggered consensus protocols for multi-agent systems with physically interconnected network

In this study, the novel fully distributed asynchronous event-triggered protocols that use sampled state information are developed to address the leader-follower and leaderless consensus issues for the general linear multi-agent systems with physically interconnected network. By designing the state estimate of each follower agent, the protocols avoid the requirements for the continuous communication. Meanwhile, this paper proves that the designed protocols don’t exhibit the Zeno behavior in any finite time by giving a strictly positive lower-bound of the minimum inter-event interval. In contrast to the existing related papers, the salient features of this study are that both physically interconnected network and communication network of the multi-agent systems are considered and the developed protocols don’t require global network information, which reduce the conservativeness of previous systems modeling and protocols. Finally, two simulation results are provided to display the performance and effectiveness of the protocols.