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.

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.

Second-Order Consensus of Multiple Agents with Coupling Delay

In this paper, we investigate two kinds of second-order consensus algorithms for multiple agents with coupling delay under general fixed directed information topology. Stability analysis is performed based on Lyapunov- Krasovskii functional method. Delay-dependent asymptotical stability condition in terms of linear matrix inequalities （LMIs） is derived for the second-order consensus algorithm of delayed dynamical networks. Both delay-independent and delay-dependent asymptotical stability conditions in terms of LMIs are derived for the second-order consensus algorithm with information feedback.

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.

Fixed-time group consensus of second-order multi-agent systems based on event-triggered control

The problem of fixed-time group consensus for second-order multi-agent systems with disturbances is investigated.For cooperative-competitive network,two different control protocols,fixed-time group consensus and fixed-time eventtriggered group consensus,are designed.It is demonstrated that there is no Zeno behavior under the designed eventtriggered control.Meanwhile,it is proved that for an arbitrary initial state of the system,group consensus within the settling time could be obtained under the proposed control protocols by using matrix analysis and graph theory.Finally,a series of numerical examples are propounded to illustrate the performance of the proposed control protocol.

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 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.

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.

Bipartite consensus problems of Lurie multi-agent systems over signed graphs: A contraction approach

This paper examines the bipartite consensus problems for the nonlinear multi-agent systems in Lurie dynamics form with cooperative and competitive communication between different agents. Based on the contraction theory, some new conditions for the nonlinear Lurie multi-agent systems reaching bipartite leaderless consensus and bipartite tracking consensus are presented. Compared with the traditional methods, this approach degrades the dimensions of the conditions, eliminates some restrictions of the system matrix, and extends the range of the nonlinear function. Finally, two numerical examples are provided to illustrate the efficiency of our results.

CRBFT:A Byzantine Fault-Tolerant Consensus Protocol Based on Collaborative Filtering Recommendation for Blockchains

Blockchain has been widely used in finance,the Internet of Things(IoT),supply chains,and other scenarios as a revolutionary technology.Consensus protocol plays a vital role in blockchain,which helps all participants to maintain the storage state consistently.However,with the improvement of network environment complexity and system scale,blockchain development is limited by the performance,security,and scalability of the consensus protocol.To address this problem,this paper introduces the collaborative filtering mechanism commonly used in the recommendation system into the Practical Byzantine Fault Tolerance(PBFT)and proposes a Byzantine fault-tolerant(BFT)consensus protocol based on collaborative filtering recommendation(CRBFT).Specifically,an improved collaborative filtering recommendation method is designed to use the similarity between a node’s recommendation opinions and those of the recommender as a basis for determining whether to adopt the recommendation opinions.This can amplify the recommendation voice of good nodes,weaken the impact of cunningmalicious nodes on the trust value calculation,andmake the calculated resultsmore accurate.In addition,the nodes are given voting power according to their trust value,and a weight randomelection algorithm is designed and implemented to reduce the risk of attack.The experimental results show that CRBFT can effectively eliminate various malicious nodes and improve the performance of blockchain systems in complex network environments,and the feasibility of CRBFT is also proven by theoretical analysis.

Leveraging Sharding-Based Hybrid Consensus for Blockchain

The advent of blockchain technology has transformed traditional methods of information exchange,shifting reliance from centralized data centers to decentralized frameworks.While blockchain’s decentralization and security are strengths,traditional consensus mechanisms like Proof of Work(PoW)and Proof of Stake(PoS)face limitations in scalability.PoW achieves decentralization and security but struggles with scalability as transaction volumes grow,while PoS enhances scalability,but risks centralization due to monopolization by high-stake participants.Sharding,a recent advancement in blockchain technology,addresses scalability by partitioning the network into shards that process transactions independently,thereby improving throughput and reducing latency.However,cross-shard communication,essential for transactions involving multiple shards,introduces challenges in coordination and fault tolerance.This research introduces a shard-based hybrid consensus model,PoSW,which combines PoW and PoS to mitigate the limitations of both mechanisms.By integrating PoW’s fairness with PoS’s scalability in a shard-based blockchain,the proposed model addresses key issues of scalability and monopolization.We evaluate the model against state-of-the-art consensus algorithms,including Monoxide and Practical Byzantine Fault Tolerance(PBFT).The results show that the proposed PoSW model reduces communication overhead compared to PBFT and improves resource utilization over Monoxide.In addition to performance gains,the security analysis demonstrates that the PoSW model provides robust defense against common blockchain attacks such as the 51%and Sybil attacks,etc.The proposed approach is particularly suited for applications like decentralized finance(DeFi)and supply chain management,which require both high scalability and robust security.The contributions of this research include the development of the PoSW hybrid consensus mechanism,its comparative evaluation with leading algorithms,and a thorough security analysis.These contributions represent a significant step forward in addressing blockchain’s scalability,fairness,and security challenges.

Evidence-based expert consensus on clinical management of safety of Bruton’s tyrosine kinase inhibitors(2024)

Bruton’s tyrosine kinase inhibitors(BTKis)have revolutionized the treatment of B-cell lymphomas.However,safety issues related to the use of BTKis may hinder treatment continuity and further affect clinical efficacy.A comprehensive and systematic expert consensus from a pharmacological perspective is lacking for safety issues associated with BTKi treatment.A multidisciplinary consensus working group was established,comprising 35 members from the fields of hematology,cardiovascular disease,cardio-oncology,clinical pharmacy,and evidencebased medicine.This evidence-based expert consensus was formulated using an evidence-based approach and the Delphi method.The Joanna Briggs Institute Critical Appraisal(JBI)tool and Grading of Recommendations Assessment,Development,and Evaluation(GRADE)approach were used to rate the quality of evidence and grade the strength of recommendations,respectively.This consensus provides practical recommendations for BTKis medication based on nine aspects within three domains,including the management of common adverse drug events such as bleeding,cardiovascular events,and hematological toxicity,as well as the management of drug-drug interactions and guidance for special populations.This multidisciplinary expert consensus could contribute to promoting a multi-dimensional,comprehensive and standardized management of BTKis.

A Bitcoin Address Multi-Classification Mechanism Based on Bipartite Graph-Based Maximization Consensus

Bitcoin is widely used as the most classic electronic currency for various electronic services such as exchanges,gambling,marketplaces,and also scams such as high-yield investment projects.Identifying the services operated by a Bitcoin address can help determine the risk level of that address and build an alert model accordingly.Feature engineering can also be used to flesh out labeled addresses and to analyze the current state of Bitcoin in a small way.In this paper,we address the problem of identifying multiple classes of Bitcoin services,and for the poor classification of individual addresses that do not have significant features,we propose a Bitcoin address identification scheme based on joint multi-model prediction using the mapping relationship between addresses and entities.The innovation of the method is to(1)Extract as many valuable features as possible when an address is given to facilitate the multi-class service identification task.(2)Unlike the general supervised model approach,this paper proposes a joint prediction scheme for multiple learners based on address-entity mapping relationships.Specifically,after obtaining the overall features,the address classification and entity clustering tasks are performed separately,and the results are subjected to graph-basedmaximization consensus.The final result ismade to baseline the individual address classification results while satisfying the constraint of having similarly behaving entities as far as possible.By testing and evaluating over 26,000 Bitcoin addresses,our feature extraction method captures more useful features.In addition,the combined multi-learner model obtained results that exceeded the baseline classifier reaching an accuracy of 77.4%.

Fully Completed Spherical Fuzzy Approach-Based Z Numbers(PHIModel)for Enhanced Group Expert Consensus

This study aims to establish an expert consensus and enhance the efficacy of decision-making processes by integrating Spherical Fuzzy Sets(SFSs)and Z-Numbers(SFZs).A novel group expert consensus technique,the PHImodel,is developed to address the inherent limitations of both SFSs and the traditional Delphi technique,particularly in uncertain,complex scenarios.In such contexts,the accuracy of expert knowledge and the confidence in their judgments are pivotal considerations.This study provides the fundamental operational principles and aggregation operators associated with SFSs and Z-numbers,encompassing weighted geometric and arithmetic operators alongside fully developed operators tailored for SFZs numbers.Subsequently,a case study and comparative analysis are conducted to illustrate the practicality and effectiveness of the proposed operators and methodologies.Integrating the PHI model with SFZs numbers represents a significant advancement in decision-making frameworks reliant on expert input.Further,this combination serves as a comprehensive tool for decision-makers,enabling them to achieve heightened levels of consensus while concurrently assessing the reliability of expert contributions.The case study results demonstrate the PHI model’s utility in resolving complex decision-making scenarios,showcasing its ability to improve consensus-building processes and enhance decision outcomes.Additionally,the comparative analysis highlights the superiority of the integrated approach over traditional methodologies,underscoring its potential to revolutionize decision-making practices in uncertain environments.

Transperineal laser ablation of the prostate as a treatment for benign prostatic hyperplasia and prostate cancer: The results of a Delphi consensus project

Objective: To evaluate transperineal laser ablation (TPLA) with Echolaser® (Echolaser® TPLA, Elesta S.p.A., Calenzano, Italy) as a treatment for benign prostatic hyperplasia (BPH) and prostate cancer (PCa) using the Delphi consensus method.Methods: Italian and international experts on BPH and PCa participated in a collaborative consensus project. During two rounds, they expressed their opinions on Echolaser® TPLA for the treatment of BPH and PCa answering online questionnaires on indications, methodology, and potential complications of this technology. Level of agreement or disagreement to reach consensus was set at 75%. If the consensus was not achieved, questions were modified after each round. A final round was performed during an online meeting, in which results were discussed and finalized.Results: Thirty-two out of forty invited experts participated and consensus was reached on all topics. Agreement was achieved on recommending Echolaser® TPLA as a treatment of BPH in patients with ample range of prostate volume, from <40 mL (80%) to >80 mL (80%), comorbidities (100%), antiplatelet or anticoagulant treatment (96%), indwelling catheter (77%), and strong will of preserving ejaculatory function (100%). Majority of respondents agreed that Echolaser® TPLA is a potential option for the treatment of localized PCa (78%) and recommended it for low-risk PCa (90%). During the final round, experts concluded that it can be used for intermediate-risk PCa and it should be proposed as an effective alternative to radical prostatectomy for patients with strong will of avoiding urinary incontinence and sexual dysfunction. Almost all participants agreed that the transperineal approach of this organ-sparing technique is safer than transrectal and transurethral approaches typical of other techniques (97% of agreement among experts). Pre-procedural assessment, technical aspects, post-procedural catheterization, pharmacological therapy, and expected outcomes were discussed, leading to statements and recommendations.Conclusion: Echolaser® TPLA is a safe and effective procedure that treats BPH and localized PCa with satisfactory functional and sexual outcomes.

Overlapping approach Proton Pump Inhibitors/Nux vomica-Heel as new intervention for gastro-esophageal reflux management:Delphi consensus study

BACKGROUND Gastro-esophageal reflux disease(GERD)may affect the upper digestive tract;up to 20%of population in Western nations are affected by GERD.Antacids,histamine H2-receptor antagonists,and Proton Pump Inhibitors(PPIs)are considered the referring medications for GERD.Nevertheless,PPIs must be managed carefully because their use,especially chronic,could be linked with some adverse effects.An effective and safe alternative pharmacological tool for GERD is needed.After the identification of potentially new medications to flank PPIs,it is mandatory to revise and improve good clinical practices even through a consensus process.AIM To optimize diagnosis and treatment guidelines for GERD through a consensus based on Delphi method.METHODS The availability of clinical studies describing the action of the multicomponent/multitarget medication Nux vomica-Heel,subject of the consensus,is the basic prerequisite for the consensus itself.A modified Delphi process was used to reach a consensus among a panel of Italian GERD specialists on the overlapping approach PPIs/Nux vomica-Heel as a new intervention model for the management of GERD.The Voting Consensus group was composed of 49 Italian Medical Doctors with different specializations:Gastroenterology,otolaryngology,geriatrics,and general medicine.A scientific committee analyzed the literature,determined areas that required investigation(in agreement with the multiple-choice questionnaire results),and identified two topics of interest:(1)GERD disease;and(2)GERD treatment.Statements for each of these topics were then formulated and validated.The Delphi process involved two rounds of questioning submitted to the panel experts using an online platform.RESULTS According to their routinary GERD practice and current clinical evidence,the panel members provided feedback to each questionnaire statement.The experts evaluated 15 statements and reached consensus on all 15.The statements regarding the GERD disease showed high levels of agreement,with consensus ranging from 70%to 92%.The statements regarding the GERD treatment also showed very high levels of agreement,with consensus ranging from 90%to 100%.This Delphi process was able to reach consensus among physicians in relevant aspects of GERD management,such as the adoption of a new approach to treat patients with GERD based on the overlapping between PPIs and Nux vomica-Heel.The consensus was unanimous among the physicians with different specializations,underlying the uniqueness of the agreement reached to identify in the overlapping approach between PPIs and Nux vomica-Heel a new intervention model for GERD management.The results support that an effective approach to deprescribe PPIs through a progressive decalage timetable(reducing PPIs administration to as-needed use),should be considered.CONCLUSION Nux vomica-Heel appears to be a valid opportunity for GERD treatment to favor the deprescription of PPIs and to maintain low disease activity together with the symptomatology remission.

Mean nocturnal baseline impedance in gastro-esophageal reflux disease diagnosis:Should we strictly follow the Lyon 2 Consensus?

Clinical practice guidelines drive clinical practice and clinicians rely to them when trying to answer their most common questions.One of the most important position papers in the field of gastro-esophageal reflux disease(GERD)is the one produced by the Lyon Consensus.Recently an updated second version has been released.Mean nocturnal baseline impedance(MNBI)was proposed by the first Consensus to act as supportive evidence for GERD diagnosis.Originally a cut-off of 2292 Ohms was proposed,a value revised in the second edition.The updated Consensus recommended that an MNBI<1500 Ohms strongly suggests GERD while a value>2500 Ohms can be used to refute GERD.The proposed cut-offs move in the correct direction by diminishing the original cut-off,nevertheless they arise from a study of normal subjects where cut-offs were provided by measuring the mean value±2SD and not in symptomatic patients.However,data exist that even symptomatic patients with inconclusive disease or reflux hypersensitivity(RH)show lower MNBI values in comparison to normal subjects or patients with functional heartburn(FH).Moreover,according to the data,MNBI,even among symptomatic patients,is affected by age and body mass index.Also,various studies have proposed different cut-offs by using receiver operating characteristic curve analysis even lower than the one proposed.Finally,no information is given for patients submitted to on-proton pump inhibitors pH-impedance studies even if new and extremely important data now exist.Therefore,even if MNBI is an extremely important tool when trying to approach patients with reflux symptoms and could distinguish conclusive GERD from RH or FH,its values should be interpreted with caution.

A multi-scale second-order autoregressive recursive filter approach for the sea ice concentration analysis

To effectively extract multi-scale information from observation data and improve computational efficiency,a multi-scale second-order autoregressive recursive filter(MSRF)method is designed.The second-order autoregressive filter used in this study has been attempted to replace the traditional first-order recursive filter used in spatial multi-scale recursive filter(SMRF)method.The experimental results indicate that the MSRF scheme successfully extracts various scale information resolved by observations.Moreover,compared with the SMRF scheme,the MSRF scheme improves computational accuracy and efficiency to some extent.The MSRF scheme can not only propagate to a longer distance without the attenuation of innovation,but also reduce the mean absolute deviation between the reconstructed sea ice concentration results and observations reduced by about 3.2%compared to the SMRF scheme.On the other hand,compared with traditional first-order recursive filters using in the SMRF scheme that multiple filters are executed,the MSRF scheme only needs to perform two filter processes in one iteration,greatly improving filtering efficiency.In the two-dimensional experiment of sea ice concentration,the calculation time of the MSRF scheme is only 1/7 of that of SMRF scheme.This means that the MSRF scheme can achieve better performance with less computational cost,which is of great significance for further application in real-time ocean or sea ice data assimilation systems in the future.

Opinion consensus incorporating higher-order interactions in individual-collective networks

In the current information society, the dissemination mechanisms and evolution laws of individual or collective opinions and their behaviors are the research hot topics in the field of opinion dynamics. First, in this paper, a two-layer network consisting of an individual-opinion layer and a collective-opinion layer is constructed, and a dissemination model of opinions incorporating higher-order interactions(i.e. OIHOI dissemination model) is proposed. Furthermore, the dynamic equations of opinion dissemination for both individuals and groups are presented. Using Lyapunov's first method,two equilibrium points, including the negative consensus point and positive consensus point, and the dynamic equations obtained for opinion dissemination, are analyzed theoretically. In addition, for individual opinions and collective opinions,some conditions for reaching negative consensus and positive consensus as well as the theoretical expression for the dissemination threshold are put forward. Numerical simulations are carried to verify the feasibility and effectiveness of the proposed theoretical results, as well as the influence of the intra-structure, inter-connections, and higher-order interactions on the dissemination and evolution of individual opinions. The main results are as follows.(i) When the intra-structure of the collective-opinion layer meets certain characteristics, then a negative or positive consensus is easier to reach for individuals.(ii) Both negative consensus and positive consensus perform best in mixed type of inter-connections in the two-layer network.(iii) Higher-order interactions can quickly eliminate differences in individual opinions, thereby enabling individuals to reach consensus faster.

Fixed-Time Antidisturbance Consensus Tracking for Nonlinear Multiagent Systems With Matching and Mismatching Disturbances

In this paper,fixed-time consensus tracking for mul-tiagent systems(MASs)with dynamics in the form of strict feed-back affine nonlinearity is addressed.A fixed-time antidistur-bance consensus tracking protocol is proposed,which consists of a distributed fixed-time observer,a fixed-time disturbance observer,a nonsmooth antidisturbance backstepping controller,and the fixed-time stability analysis is conducted by using the Lyapunov theory correspondingly.This paper includes three main improvements.First,a distributed fixed-time observer is developed for each follower to obtain an estimate of the leader’s output by utilizing the topology of the communication network.Second,a fixed-time disturbance observer is given to estimate the lumped disturbances for feedforward compensation.Finally,a nonsmooth antidisturbance backstepping tracking controller with feedforward compensation for lumped disturbances is designed.In order to mitigate the“explosion of complexity”in the tradi-tional backstepping approach,we have implemented a modified nonsmooth command filter to enhance the performance of the closed-loop system.The simulation results show that the pro-posed method is effective.