Consensus Error Research Articles

Human-in-the-Loop Consensus Control for Multiagent Systems With External Disturbances.

In this article, the human-in-the-loop leader-follower consensus control problem is addressed for multiagent systems (MASs) with unknown external disturbances. A human operator is deployed to monitor the MASs' team by transmitting an execution signal to a nonautonomous leader in response to any hazard detected, with the control input of the leader unknown to all followers. For each follower, a full-order observer, in which the observer error dynamic system decouples the unknown disturbance input, is designed for asymptotic state estimation. Then, an interval observer is constructed for the consensus error dynamic system, where the unknown disturbances and control inputs of its neighbors and its disturbance are treated as unknown inputs (UIs). To process the UIs, a new asymptotic algebraic UI reconstruction (UIR) scheme is proposed based on the interval observer, and one of the significant features of the UIR is the capacity to decouple the control input of the follower. The subsequent human-in-the-loop asymptotic convergence consensus protocol is developed by applying an observer-based distributed control strategy. Finally, the proposed control scheme is validated through two simulation examples.

Switching adaptive dynamic event-triggered consensus of nonlinear multi-agent systems under DoS attacks and communication delay

This article addresses the issue of achieving security consensus in multi-agent systems (MASs) that are susceptible to denial-of-service attacks (DoS-As) and time-varying communication delays (TCD). We have developed a novel unified model to describe DoS-As and TCD. Firstly, a new switching adaptive dynamic event-triggered mechanism (SADETM) is proposed to conserve communication resources during DoS-As and TCD. The mechanism transforms into three event-triggered strategies adapted to highly dynamic MASs. Then, a consensus control protocol is designed through consensus errors based on SADETM. Finally, the sufficient conditions for ensuring the stability of MASs are solved by combining the Lyapunov-Krasovskii functional (LKF) method and the linear matrix inequality (LMI) technique. The effectiveness of this method is verified through simulation examples.

Nearly optimal fixed time sliding mode controller for leader–follower consensus problem with partially unknown nonlinear agents

This paper presents a conceptual framework for addressing the consensus problem in multi-agent systems with unknown nonlinear dynamics using reinforcement learning (RL) based nearly optimal sliding mode controller (SMC). The agents’ dynamics are assumed to have uncertainty and mismatched disturbance. An adaptive fixed-time estimator is introduced to estimate uncertain dynamics and disturbances for each agent at a certain time. The paper proposes two control strategies. In the first strategy, a controller is designed, incorporating adaptive SMC and an optimal controller. Adaption law in SMC estimates the bound of fixed time estimator error before convergence, ultimately achieving asymptotic convergence to the sliding surface and converting the agent’s dynamics to linear. This enables solving a linear consensus problem using an RL-based adaptive optimal controller through an on-policy critic–actor method. The second control strategy enhances the adaptive SMC into a fixed-time controller, reducing the time to reach the sliding surface regardless of initial conditions. Consequently, the convergence time of the consensus error to zero is diminished. This reduction in reaching time results in faster convergence of the consensus error to zero. The effectiveness of both strategies is validated through numerical experiments on two real system models, aligning with the theoretical proofs.

Adaptive fuzzy event-triggered control for a class of nonlinear time-delay multi-agent systems with dead zone and partial state constraints

This paper presents an adaptive fuzzy event-triggered control (ETC) method for a class of time-delay nonlinear multi-agent systems (MASs) with dead zone (DZ) and partial state constraints (PSCs). It should be pointed out that the states considered in this paper are unmeasurable and part of the system states are constrained by time-varying boundary. By utilizing fuzzy logic systems (FLSs) and backstepping design framework, a fuzzy state observer is constructed to estimate the unmeasured states, while the introduction of a time-varying barrier Lyapunov function (BLF) addresses the partial state constrained problem. Furthermore, during the design process of the state observer, compensation for the influence of the unknown DZ input on the system is achieved through utilization of known designed event-triggered input signal and adaptive parameter. Building upon this foundation, employing the Lyapunov stability theory and adaptive backstepping technique with ETC strategy, the developed distributed control mechanism demonstrates that all variables of the closed-loop system are bounded, the consensus error of the system can converge to a small region of origin and Zeno behavior can be ruled out. Finally, two simulation examples further illustrate the proposed control strategy and theorem.

Fuzzy prescribed-time self-triggered consensus control for nonlinear multi-agent systems with dead-zone output

This paper investigates the fuzzy prescribed-time self-triggered consensus control for nonlinear multi-agent systems (MASs) with dead-zone output. First, by proposing a dead-zone output approximation model and utilizing Nussbaum-type functions, an adaptive compensation mechanism is developed to alleviate the effect of unknown dead-zone output. Meanwhile, the fuzzy logic systems are incorporated to approximate the unknown functions of the nonlinear MASs. Next, by adopting a time-varying scaling function, a consensus control method is recursively established to steer the consensus errors into a small range within the prescribed time. Furthermore, a self-triggered scheme is established to conserve communication resources while avoiding continuously monitoring trigger conditions. It is illustrated that boundedness of all signals and practical prescribed-time leader-following consensus can be achieved. Finally, the simulation results show the effectiveness of the proposed method.

Output Reachable Set-Based Leader-Following Consensus of Positive Agents Over Switching Networks.

This work addresses the output reachable set-based leader-following consensus problem, focusing on a group of positive agents over directed dwell-time switching networks. Two types of non-negative disturbances, namely, 1) L1 -norm bounded disturbances and 2) L∞,1 -norm bounded disturbances are studied. Meanwhile, a class of directed dwell-time switching networks for modeling the communication protocol of positive agents is investigated. To deal with the presence of disturbances, an output-feedback control protocol is developed to achieve a robust consensus with positivity preserved based on the output reachable set. By exploiting the positive characteristics, switched linear copositive Lyapunov functions are adopted to establish output reachable set-based consensus conditions. These conditions can facilitate the control protocol design by solving a bilinear programming problem, and also generate hyperpyramidal regions to confine the output consensus error. A particle swarm optimization-based (PSO-based) algorithm is applied to compute the controller gains and optimize the volume of the hyperpyramids. The proposed methods are verified by the presented numerical case studies.

WITHDRAWN: Adaptive fuzzy fixed-time bipartite consensus control for stochastic nonlinear multi-agent systems with performance constraints

This paper investigates the fixed-time bipartite consensus control problem of stochastic nonlinear multi-agent systems (MASs) with performance constraints. A constraint scaling function is proposed to model the performance constraints with user-predefined steady-state accuracy and settling time without relying on the initial condition. Technically, the local synchronization error of each follower is mapped to a new error variable using the constraint scaling function and an error transformation function before being used to design the controller. To achieve fixed-time convergence of the local tracking error, a barrier function transforms the scaled synchronization error to a new variable to guarantee the prescribed performance. Then, an adaptive fuzzy fixed-time bipartite consensus controller is developed. The fuzzy logic system handles the uncertainties in the designing procedures, and one adaptive parameter needs to be estimated online. It is shown that the closed-loop system has practical fixed-time stability in probability, and the antagonistic network’s consensus error evolves within user-predefined performance constraints. The simulation results evaluate the effectiveness of the developed control scheme.

Data-driven leader-following consensus for nonlinear multi-agent systems against composite attacks: A twins layer approach

This paper studies the leader-following consensuses of uncertain and nonlinear multi-agent systems against composite attacks (CAs), including denial of service (DoS) attacks and actuation attacks (AAs). A double-layer control framework is formulated, where a digital twin layer (TL) is added beside the traditional cyber–physical layer (CPL), inspired by the recent Digital Twin technology. Consequently, the resilient control task against CAs can be divided into two parts: One is distributed estimation against DoS attacks on the TL, and the other is resilient decentralized tracking control against actuation attacks on the CPL. First, a distributed observer based on switching estimation law against DoS is designed on TL. Second, a distributed model-free adaptive control (DMFAC) protocol based on attack compensation against AAs is designed on CPL. Moreover, the uniformly ultimately bounded convergence of consensus error of the proposed double-layer DMFAC algorithm is strictly proved. Finally, the simulation verifies the effectiveness of the resilient double-layer control scheme.

Distributed iterative learning consensus tracking for singular partial differential multi-agent systems under fixed and iteration-varying topologies

This paper investigates the consensus tracking problems of singular partial differential multi-agent systems (SPD-MASs) with initial state errors under fixed and iteration-varying network topologies, where only certain follower agents have access the trajectory defined by virtual leaders. To solve this problem, a distributed iterative learning consensus protocol with initial state learning is proposed, ensuring accurate tracking of the leader's trajectory by all follower agents with initial state errors. The convergence conditions for consensus tracking error are derived through mathematical analysis between adjacent agents. Theoretical analysis shows that, under convergence conditions, the consensus error between any two agents can converge to zero along the iterative axis. Finally, numerical simulations show validate the effectiveness of the proposed distributed control protocol with initial state learning compared to traditional protocols without state learning.

Accuracy evaluation of Roche Accu‐Chek Performa blood glucose meters at low glucose concentrations: A nine‐year retrospective study

AbstractObjectiveTo evaluate the accuracy of Roche Accu‐Chek Performa glucose meters at a low glucose concentration of <5.55 mmol/L (100 mg/dL) over a 9‐year period.MethodsThe accuracy of the Roche Accu‐Chek Performa glucose meters at low glucose concentrations was evaluated using annual comparison data for 9 consecutive years from 2015 to 2023, according to the acceptability criteria specified in International Organization for Standardization (ISO) 15197:2013. Blood samples with low glucose concentrations of <5.55 mmol/L were prepared by incubation and glycolysis. The glucose concentration was detected using Roche Accu‐Chek Performa glucose meters and a biochemical analyzer in the central laboratory.ResultsA total of 2978 pairs of comparison results from 211 glucose meters at a low glucose concentration of <5.55 mmol/L were retrospectively analyzed from 2015 to 2023. The clinical use duration spanned from 1 to 9 years and 40.76% (86 out of 211 glucose meters) had been used for more than 2 years. The correlation coefficient r between glucose meter measurements and laboratory reference values was 0.98 (p < 0.001). The mean according to Roche Accu‐Chek Performa glucose meters was 0.05 mmol/L (0.9 mg/dL) higher than that of the biochemical analyzer (Z = −13.82, p < 0.0001). The results showed that 100.00% (211 out of 211) of the Roche Accu‐Chek Performa glucose meters met the acceptability criteria specified in ISO 15197:2013. At a low glucose concentration of <5.55 mmol/L, 99.90% (2975 out of 2978) of the comparative data pairs in the error distribution fell within the range of ±0.83 mmol/L (15 mg/dL). Parkes consensus error grid analysis showed that 100.00% (2978 out of 2978) of comparative data pairs fell within region A.ConclusionsThis study demonstrated that Roche Accu‐Chek Performa glucose meters successfully met the accuracy standards of ISO 15197:2013 for measuring blood glucose within the hypoglycemic range. Greater attention should be given to the performance of blood glucose monitoring systems in the low glycemic range, especially for patients with diabetes who are prone to hypoglycemia and require precise measurements.

Disturbance rejection based consensus controller for swarm system

This article introduces a robust controller designed to facilitate consensus among leader-follower agents in a swarm system. The method employs algebraic graph theory to establish a consensus framework and incorporates a sliding surface-based uncertainty and disturbance estimator (SUDE) to mitigate the effects of nonlinearities, external disturbances, and parametric uncertainty inherent in swarm systems. The stability of the SUDE controller is examined using Lyapunov theory. Importantly, this approach operates without prior knowledge of disturbance bounds, relying instead on the dynamics of disturbance error. Simulation studies demonstrate the effectiveness of the proposed control methodology, showing that the SUDE controller expedites consensus achievement while ensuring smooth and non-chattering control behavior. The proposed SUDE controller demonstrates a notable improvement in achieving position and velocity consensus in both the X and Y directions, with a 75% and 66% faster convergence rate, respectively, when compared to the conventional sliding mode controller (SMC). Additionally, the performance of the proposed controller is assessed under various external disturbances and parametric uncertainty conditions. Comparative analyses using root mean square error (RMSE) and integral absolute time error (IATE), both based on consensus error, confirm the effectiveness of the proposed SUDE consensus controller.

Adaptive expected-time tracking consensus control for multiagent systems with external disturbances and time delays

This paper studies the expected-time tracking control problem for multiagent systems with disturbances and time delays. The expected-time control scheme can ensure that control objectives can be completed within the desired time. In the other words, the output signal can track the reference signal in an expected time. Based on a special error and the adaptive technology, the expected-time tracking consensus control scheme is achieved. Moreover, by using the neural networks technique, the unknown nonlinear functions which often exist in the dynamic of the system are handled. According to the Lyapunov stability theorem and the Lyapunov–Krasovskii function, it is proved that the consensus errors are semi-globally uniformly ultimately bounded. At last, the feasibility of the control method is verified by a simulation example.

Adaptive Neural Network Finite-Time Prescribed Performance Consensus Control for a Class of Second-Order Multi-Agent Systems

This research investigates the semi-global practical finite-time prescribed performance consensus control issue for a class of second-order multi-agent systems with unknown nonlinear functions. Unlike the previous finite-time control set by a finite-time performance function, we give finite-time control by constraining the terminal sliding manifold in a performance function. In addition, an adaptive neural network control scheme is designed, which simplifies the controller and avoids the chattering issue existing in traditional sliding mode control. Eventually, a novel adaptive finite-time prescribed performance consensus control strategy is designed, which ensures that all system variables are semi-globally practical finite-time stable and consensus errors of the multi-agent systems converge within the prescribed region in finite time. The effectiveness and practicality of the presented control strategy are evaluated by conducting simulation cases.

Distributed formation control of multi-UAV systems using relative information

An adaptive distributed control strategy is designed for the formation of multiple unmanned aerial vehicle (UAV) groups by using only relative measurement information. A distributed estimator is first designed to get the estimate of the consensus error. Then, an adaptive distributed controller is proposed to realize the formation tracking with the relative measurements. Based on the position and velocity information, a control barrier function (CBF) algorithm is applied to achieve the UAV formation under safe position constraints. In addition, in order to break up and reorganize multiple UAV groups, the proposed controller is designed based on the time-varying network topology. It is proved that the closed-loop system is uniformly asymptotically stability. Simulation and experiment results indicate that the proposed strategy can achieve formation control of multiple UAVs under safety constraints based on the measurement of relative measurement information.

#2103 Accuracy of a continuous glucose monitor in people with diabetes on peritoneal dialysis

Abstract Background and Aims Globally 40% of people receiving peritoneal dialysis (PD) have a diagnosis of diabetes. Good glycaemic control can by complicated by the obligate glucose load associated with PD. Monitoring and treatment of people with diabetes (PwD) on PD has been limited by reduced reliability of traditional markers of glycaemia such as HbA1c in end-stage kidney disease. Continuous glucose monitors (CGMs) have been increasingly used in the care of PwD over the last 20 years. Monitors worn on the upper arm or abdomen measure glucose in interstitial fluid at regular intervals over the 24 hour period. CGMs are currently unlicensed in PD populations as they have not been tested in large scale studies. Concerns remain around accuracy in the presence of potentially interfering substances generated by the breakdown of osmotic agents used in PD fluid (e.g. Icodextrin). We aimed to assess the analytical and clinical accuracy of the FreeStyle Libre(FSL) CGM system in PwD on maintenance PD. Method We conducted a single centre observational study of 10 PwD who had been on PD for at least 3 months. For the 10 day study period participants wore a blinded research model FSL monitor which measured interstitial glucose levels every 15 minutes. Results from the FSL were compared with; Analytical accuracy was assessed using three methods; Clinical accuracy was assessed using the Parkes consensus error grid to assign each pair of readings to one of five risk zones and quantify the clinical implications of any difference between the two measurements. The International Organisation for Standardisation guidelines stipulates 99% of pairs should be in zones A and B, denoting little or no effect on clinical actions. Results Of 11 recruited participants, 10 completed the 10 day study period resulting in 76 paired CGM-YSI measurements and 375 paired CGM-CBG measurements. 7 participants were on APD and 3 on CAPD. All participants were prescribed a PD regime that included one daily dwell with Icodextrin. The aggregate MARD was 9.4% (95% CI 7.9, 10.4) for CGM-YSI matched pairs and 17.6% (95% CI 17, 19.3) for CGM-CBG matched pairs. Spearman's r was 0.94 (p < 0.0001) for CGM-YSI and 0.89 (p < 0.0001) for CGM-CBG. From Bland-Altman analysis, the systematic error of the CGM compared with YSI and CBG was −0.81 mmol/l (SD 0.81) and −1.6 mmol/l (SD 1.9) respectively. Parkes consensus error grid analysis showed that compared with YSI and CBG respectively, 100% and 99.9% of sensor values were in the clinically acceptable zones A and B (Fig. 1). Conclusion We have demonstrated satisfactory performance of the FSL monitoring system by both analytical and clinical metrics in this cohort of PD patients using treatment regimens including Icodextrin based fluids. CGMs provide much more information for the PwD and their clinical care team compared with random CBGs (which in themselves have been shown to exhibit significant between user variability) and time averaged markers such as HbA1c. They allow detection of asymptomatic hypoglycaemia and direct monitoring of the systemic effects of any change to the PD prescription resulting in a larger or smaller glucose load. These results should be reassuring for clinicians wishing to utilise the greater depth of information provided by CGMs to improve clinical care for their patients with diabetes on PD.

Dynamic event-triggered fixed-time consensus control for coupled multi-permanent magnet synchronous motors stochastic system with prescribed performance

With the ubiquity of permanent magnet synchronous motors (PMSM), multi-PMSMs are increasingly being elastically coupled to achieve greater output power. The authors establish a general mathematical model of coupled multi-PMSMs system. The dynamic analysis of the coupled multi-PMSMs system is analyzed using coupled three-PMSMs system as an example, and a dynamic event-triggered fixed-time consensus controller with prescribed performance is constructed for coupled PMSMs stochastic system. In addition, Interval Type-3 Fuzzy System (IT3FS) is employed to estimate unknown functions, the computing cost is reduced by updating the weights based on only one adaptive law per PMSM. To enhance the efficiency of communication resource utilization, a dynamic event-triggered mechanism is introduced, where the triggering condition depends on a dynamic auxiliary variable. Moreover, fixed-time control technical is applied to guarantee the setting time and a novel fixed-time prescribed performance function (PPF) is constructed to constrain consensus errors. To cope with the “complexity explosion”, a fixed-time tracking differentiator (TD) is introduced and the corresponding filtered error compensation signals is designed. Finally, the authors demonstrate the system is fixed-time stabilized in probability by applying fixed-time stabilization Lyapunov stability criterion, and the simulation results of a coupled three-PMSMs stochastic system show that the presented algorithm is feasible.

Quantised adaptive consensus control of heterogeneous nonlinear multi-agent systems under external disturbance

This paper is primarily devoted to the distributed consensus tracking control for heterogeneous nonlinear multi-agent systems (MASs) with a directed communication topology. Taking the considered heterogeneous nonlinear MASs own unknown nonlinear term and quantised input signals, the adaptive radial basis function neural networks (RBFNNs)-based approximator is utilised to tackle these interesting challenges. Next, considering the boundness of disturbances, the upper bound of time-varying disturbance is utilised in the controller design. Then, a distributed dynamic compensator is developed to complete coordination task, which only requires to exchange output information via the communication network. In addition, the compensator transforms the adaptive output consensus problem into asymptotic tracking problem, without needing extra stability conditions. Finally, by means of the Lyapunov stability theory, the satisfying result of the consensus error converging to zero asymptotically can be obtained. Through simulations, the effectiveness of the developed protocol is illustrated.

Continuous Glucose Monitoring Using the Dexcom G6 in Cardiac Surgery During the Postoperative Period

ObjectiveCardiac surgery is associated with hyperglycemia, which in turn is associated with adverse postsurgical outcomes such as wound infections, acute renal failure, and mortality. This pilot study seeks to determine if Dexcom G6Pro continuous glucose monitor (Dexcom G6Pro CGM) is accurate during the postoperative cardiac surgery period when fluid shifts, systemic inflammatory response syndrome, and vasoactive medications are frequently encountered, compared to standard glucose monitoring techniques. MethodsThis study received institutional review board approval. In this prospective study, correlation between clinical and Dexcom glucose readings was evaluated. Clinical glucose (blood gas, metabolic panel, and point of care) data set included 1428 readings from 29 patients, while the Dexcom G6Pro CGM data included 45 645 data points following placement to upper arm. Additionally, average clinical measurements of day and overnight temperatures and hemodynamics were evaluated.Clinical and Dexcom data were restricted to being at least 1 hour after prior clinical reading Matching Dexcom G6Pro CGM data were required within 5 minutes of clinical measure. Data included only if taken at least 2 hours after Dexcom G6Pro CGM insertion (warm-up time) and analyzed only following intensive care unit (ICU) admission. Finally, a data set excluding the first 24 hours after ICU admission was created to explore stability of the device. Patients remained on Dexcom G6Pro CGM until discharge or 10 days postoperatively. ResultsThe population was 71% male, 14% with known diabetes; 66% required intravenous insulin infusion. The Clarke error grid plot of all measures post-ICU admission showed 53.5% in zone A, 45.9% in zone B, and 0.6% (n = 5) in zones D or E. The restricted dataset that excluded the first 24 hours post-ICU admission showed 55.9% in zone A, 43.9% in zone B, and 0.2% in zone D. Mean absolute relative difference between clinical and Dexcom G6Pro CGM measures was 20.6% and 21.6% in the entire post-ICU admission data set, and the data set excluding the first 24 hours after ICU admission, respectively. In the subanalysis of the 12 patients who did not have more than a 5-minute tap in the operating room, a consensus error grid, demonstrated that after ICU admission, percentage in zone A was 53.9%, zone B 45.4%, and zone C 0.7%. Similar percentages were obtained removing the first 24 hours post-ICU admission. These numbers are very similar to the entire cohort.A consensus error grid created post-ICU admission demonstrated: (zone A) 54%, (zone B) 45%, (zone C) 0.9%, and the following for the dataset created excluding the first 24 hours: (zone A) 56%, (zone B) 44%, (zone C) 0.4%, which demonstrated very close agreement with the original Clarke error grid. No adverse events were reported. ConclusionsAlmost 100% of Dexcom G6Pro CGM and clinical data matching points fell within areas considered as giving clinically correct decisions (zone A) and clinically uncritical decisions (zone B). However, the relatively high mean absolute relative difference precludes its use for both monitoring and treatment in the clinical context. As technology evolves, interstitial glucose monitoring may become an important tool to limit iatrogenic anemia and mitigate glycemic fluctuations.

Communication topology for AUV formation consensus based on optimal cost control under time-varying communication and input delays

This study investigates the optimal communication topology for consensus in autonomous underwater vehicle (AUV) formations, considering both leader-following and leaderless scenarios. Initially, a second-order dynamic model of the AUV is established using the feedback linearization method. To address time-varying delays, a universal predictor-based consensus protocol is introduced, capable of operation with or without a designated leader. Subsequently, two global quadratic cost functions are formulated based on distinct consensus errors. Utilizing linear quadratic regulator (LQR) theory and matrix theory, the optimal communication topologies and associated gain matrices are deduced. Specifically, for leader-following AUV formations, the optimal communication topology is identified as an unevenly weighted star-shaped directed spanning tree. Conversely, for leaderless formations, the optimal topology adopts a complete digraph, which indicates high interaction requirements. To accommodate practical constraints, a suboptimal topology is devised, featuring a directed spanning tree. These findings offer a theoretical framework for selecting communication topologies in AUV formations, with numerical examples provided to validate the proposed approaches.

Novel consensus framework on discrete-time positive multi-agent systems

This paper investigates the consensus of discrete-time positive multi-agent systems. A framework on the consensus of positive multi-agent systems is constructed. By introducing a finite point and a self-feedback term, a novel consensus protocol is proposed to drive all states to common nonnegative finite values. An improved error model is established for positive multi-agent systems. Based on the consensus error model, the consensus of the agents is transformed into the stability of the error systems. Under the proposed consensus protocol and the new consensus error model, the consensus of agents is realized. A copositive Lyapunov function is chosen to derive the consensus of the multi-agent systems. Such a consensus approach is extended for time-delay multi-agent systems. All positivity and consensus conditions can be solved by virtue of linear programming. The main novelties of this paper lie in that: (i) A novel consensus error model is established, (ii) A finite value consensus is achieved, and (iii) Linear programming-based conditions are presented for the consensus design. Finally, two illustrated examples are given to verify the validity of the theoretical findings.