Fixed-time Consensus Research Articles

Practical time-boundary consensus for fractional-order multi-agent systems under well-known and estimable topology

A framework for multi-agent systems with single-integrator dynamics to achieve practical fixed-time consensus has been developed under a well-known topology. However, the disagreement boundary in which is influenced by the initial values of the system. To avoid this, a practical time-boundary (PTB) consensus framework using a novel time-boundary-base generator (TBBG) is proposed in this paper, and it is extended to fractional-order multi-agent systems and estimable topology. A significant fractional differential equation is solved as the theoretical basis to achieve PTB consensus. Evolving from the time-base generator, this novel TBBG inherits the benefit of reducing the initial control input and saves energy consumption by optimizing four newly added adjustable parameters compared to the existing work. Additionally, outcomes are extended to quasi-PTB consensus and PTB-cluster consensus. The effectiveness and superiorities of the proposed approach are illustrated by two numerical examples.

Fixed-time sliding mode-based consensus of multi-agent systems with mismatched disturbances

This paper investigates the fixed-time consensus of second-order multi-agent systems subject to matched and mismatched disturbances. The derivatives of disturbances are assumed to be bounded. A novel integral sliding mode-based observer is presented by utilizing the super-twisting algorithm to estimate the agent states. The estimations can achieve the convergence to the leader in a fixed time. Furthermore, the corresponding fixed-time controller is developed to make the agents converge to the estimated states. As the estimated states converge to the leader, the agents will track the leader states with the help of estimated states. In addition, the overall convergence of multi-agent systems is non-monotonic due to the disturbances. It is theoretically shown that the proposed control approach can maintain a bounded convergence and get the consensus of multi-agent systems in a fixed time. Some simulations are presented to verify the effectiveness of the proposed control protocol.

Fixed-time output consensus for nonlinear heterogeneous multi-agent systems with disturbances

The fixed-time output consensus is considered in this article for heterogeneous nonlinear first-order and second-order multi-agent systems with disturbances. Firstly, we design a distributed observer by the fixed-time consensus theory, realizing distributed control of the system under directed graph. Secondly, designing a fixed-time controller for the first-order nonlinear system with disturbances by using constant exponential and time-varying exponential coefficient methods. For the second-order nonlinear system with both matched and mismatched disturbances, designing a fixed-time tracking controller by using the backstepping method and robust sliding mode control. The designed controller effectively suppresses the mismatched disturbance of system and makes the multi-agent system achieve output consensus in a fixed time. Finally, we demonstrate the effectiveness of the protocol through numerical examples.

Model-based event/self-triggered fixed-time consensus of nonlinear multi-agent systems

To address model-based event-triggered fixed-time consensus of nonlinear multi-agent systems with both fixed topology and switching topologies, a novel model-based event-triggered protocol is presented. In the proposed protocol, agents in multi-agent systems update controllers by utilizing estimated state values in the triggered intervals. And for reducing the burdens of bandwidth further, the model-based event-triggered protocol is extended to self-triggered protocol which does not need continuous communication in triggered intervals. It is proven that Zeno behavior is excluded. Our main contributions are giving a novel distributed model-based event-triggered protocol for fixed-time consensus and extending it into a self-triggered protocol. Finally, a couple of simulation examples are provided to verify the effectiveness of the proposed protocols.

Fixed-Time Prescribed Performance Consensus Control for Multiagent Systems With Nonaffine Faults

This paper studies the fixed-time consensus tracking control of nonlinear multi-agent systems (NNMASs) suffering from non-affine faults. A fixed-time command filter is constructed to solve the “explosion of complexity” issue, and a novel fixed-time error compensation mechanism is designed to eliminate filtering errors. The adaptive fuzzy control technique is introduced to deal with the unknown nonlinear terms containing non-affine fault functions. A new fixed-time fault-tolerant control scheme based on the modified prescribed performance technology is proposed for the NNMASs, which ensures that the closed-loop system satisfies the practical fixed-time stability. In addition, the consensus tracking errors of the NNMASs converge to a given range within a prescribed performance bound in a fixed time. Finally, comparative simulation results show the effectiveness of the proposed method.

Dynamic Event-Triggered Fixed-Time Consensus Control and Its Applications to Magnetic Map Construction

Dynamic Event-Triggered Fixed-Time Consensus Control and Its Applications to Magnetic Map Construction

Nonsingular Practical Fixed-Time Consensus Tracking for Multimotor System With Input Saturation

This article studies a novel fixed-time consensus tracking strategy for a multimotor system (MMS) with input saturation, suitable for most practical applications requiring stringent convergence time but with limited control input capability. First, a modified practical fixed-time stable theorem is proposed to guarantee that the actual system can reach a certain control precision in a fixed time, regardless of the initial states of the system. Then, an input saturation compensation system is also constructed to compensate for the input saturation to ensure fast convergence of the controller. Next, we propose a new distributed fixed-time consensus control algorithm for the MMS, which can render the time costs in both the reaching and sliding phases fixed. Inspired by the L'Hopital's rule, a hyperbolic tangent function is used to avoid the singularity of the controller. Besides, an experimental platform for verifying the algorithm is established. Finally, both simulation and experimental results demonstrate the effectiveness of our proposed strategy.

Fully distributed adaptive practical fixed-time consensus protocols for multi-agent systems

This paper investigates the practical fixed-time consensus problem for a multi-agent system in networks with an undirected topology. Both node-based and edge-based fully distributed adaptive protocols are proposed to achieve the practical fixed-time consensus for the single integrator-type multi-agent systems, i.e., fixed-time attractiveness of a residual set as well as asymptotic consensus. Most notably, the settling time estimate can be computed without using any global information, which is distinctive from the existing fixed-time protocols. Furthermore, a scaling technique is applied for the proposed protocol such that the fixed-time attraction region can be contracted by only tuning a scaling parameter and the original settling time estimate remains unchanged. Finally, a numerical simulation example is given to validate the proposed protocols.

Fixed-time consensus-based distributed Nash equilibrium seeking for noncooperative game with second-order players

This paper aims to study the Nash equilibrium (NE) seeking algorithm of noncooperative game with second-order system under strongly connected digraph. In the algorithm, velocity information is not directly accessible to players, in order to avoid the need for additional velocity observers. Meanwhile, for position information, the position estimation of all the other players under local communication is completed in fixed time. To address the aforementioned concern, a NE seeking algorithm with a two-time-scale structure is designed. (1) For reduced system, a second-order velocity estimation model based on state observer is introduced to avoid direct acquisition of velocity information; (2) For fast compensation mechanism, each player uses leader-following consensus protocol to estimate the position of all the other players. The fixed-time consensus protocol is utilized to ensure that the position is estimated in fixed time. Then, aiming to reduce the communication costs and communication burden among players, the event-triggered mechanism is introduced into the above algorithm, and Zeno behavior is excluded. Lastly, a self-organized network problem involving autonomous vehicles is presented to validate the efficacy of the proposed theoretical results.

Finite-Time and Fixed-Time Consensus Tracking of Multiple Euler–Lagrange Systems via Hierarchical Control Approach

Finite-Time and Fixed-Time Consensus Tracking of Multiple Euler–Lagrange Systems via Hierarchical Control Approach

On novel distributed fixed-time formation tracking of multiple hypersonic flight vehicles with collision avoidance

This paper aims to achieve collision-free formation tracking for multiple hypersonic flight vehicles without introducing conventional approximators such as fuzzy logic systems and neural networks. By relying on the hierarchical control theory, a globally fixed-time distributed formation control protocol with guaranteed tracking behaviors is proposed. Firstly, for the purpose of deriving the virtual control commands in the three-dimensional translational dynamics, a fixed-time consensus control input is presented. Then, by designing a comprehensive performance-preserving feedback control law, the actual control commands are derived, so that the virtual control inputs can be tracked timely and accurately. Meanwhile, with resort to a novel exponential-type artificial potential function, a collision-free control input is proposed to avoid close proximity between adjacent hypersonic flight vehicles. Summarily, the outstanding advantage of the proposed protocol is that it simultaneously realize the collision-free formation tracking, fixed-time stability and performance-preserving control for multiple hypersonic flight vehicles with uncertain dynamics. Lyapunov stability criterion verifies the closed-loop stability, showing that the error signals can attenuate to a tiny region around the origin within a user-specified time. Finally, comparative numerical simulations are performed to further demonstrate the theoretical results.

The fixed-time consensus of leader-following nonlinear multi-agent systems under event-triggered impulsive control

This paper studies the leader-following fixed-time consensus problem for a class of first-order nonlinear multi-agent systems via event-triggered impulsive control where the communication topologies are general undirected. For each agent, the controller is updated only when some state-dependent errors exceed a tolerable bound, and the impulsive control time sequence is produced by the event triggered mechanism. This original control protocol can substantially improve the convergence speed, obtain the lower energy consumption and reduce the update times of the controller. Also, it is shown that continuous communication of neighboring agents can be avoided and there is no Zeno-behavior. The results are verified by a numerical simulation.

Distributed optimization of networked marine surface vehicles: A fixed-time estimator-based approach

This paper focuses on the fixed-time consensus problem of the networked marine surface vehicles (NMSVs) while minimizing the sum of the cost functions. To tackle this complex problem, we propose a fixed-time optimization hierarchical control approach that transforms the problem into two sub-problems: a distributed fixed-time optimization estimation problem and a local fixed-time tracking problem respectively. Specifically, the proposed approach leverages a distributed fixed-time optimization estimator to enable the NMSVs to estimate the state and velocity of a virtual leader while minimizing the sum of cost functions. Additionally, the above estimated signal will be tracked by the NMSVs under a fixed-time local tracking controller. We demonstrate the effectiveness of our proposed approach through simulation experiments on a network of four marine surface vehicles, and present the sufficient conditions for stability through Lyapunov stability analysis.

A New Intermittent Control Approach to Practical Fixed-Time Consensus With Input Delay

This paper addresses the practical fixed-time consensus problem of delayed disturbed multi-agent systems (MASs) under aperiodically intermittent control. Different from existing periodic intermittent controllers, the proposed intermittent controller is designed in an aperiodic way, which is more general. A new intermittent-based criterion for the delayed disturbed MASs is given. Based on the given criterion, the consensus of the MASs is obtained in a fixed time, which is unrelated to the initial conditions. Finally, a simulation example is provided to verify the effectiveness of theoretical results.

Dynamic event-triggered fixed-time consensus control of multi-agent systems with unknown bounded disturbances

This paper investigates the fixed-time consensus control for a class of multi-agent systems subject to unknown bounded disturbances under undirected topology. Firstly, the nonlinear controllers and the measurement errors are designed based on the hyperbolic tangent function to avoid the non-differential problem. Secondly, a distributed fixed-time control protocol is designed, which can realise the fixed-time convergence and improve the system convergence rate independent of the system’s initial state. Thirdly, the dynamic event-triggered mechanism is proposed, such that the triggering frequency of events is reduced and communication energy consumption can be saved. The stability analysis is presented by employing the Lyapunov theory and the Zeno phenomenon is excluded. Finally, the simulation examples are presented to show the effectiveness and advantages of the proposed method in this paper.

Fixed-time consensus control for nonlinear multi-agent systems via fully distributed edge-based adaptive protocols

In this paper, we mainly concern the fixed-time consensus control problem for nonlinear leader-following multi-agent systems(MASs). An edge-based adaptive control protocol is presented with part of parameters updated by relative information of system state. Compared with the common node-based adaptive protocols, the proposed edge-based adaptive control protocol assigning different time-varying weights to different communication edges is more accurate. By selecting special Lyapunov functions and theoretical analysis, the obtained conclusions indicate that both sufficient conditions and the settling time of the fixed-time consensus are independent of the system's global information such as the spectrum of Laplacian matrix, which implies that the given protocol is fully distributed. Finally, numerical simulation is illustrated to support the correctness of the main theoretical results.

Fixed-time consensus of second-order multi-agent systems with nonlinear dynamics

The authors mainly discuss finite-time tracking consensus and fixed-time tracking consensus of multi-agent systems for second-order with inherent nonlinear function and disturbance under a directed interaction graph in this work. By sliding mode control theory, consensus tracking controllers are proposed to ensure that sliding mode can be reached and maintain on it in finite time and fixed time. By using some theoretical knowledge of control, such as graph theory and Lyapunov theory, we make the system to reach consensus in finite time and fixed time by choosing the right parameters. In addition, the calculation leads to the conclusion that settling time of finite-time consensus is associated to initial state, while settling time of fixed-time consensus is interrelated to parameters but not to the initial state. The feasibility of the theory is proved by simulation experiments.

Observer-based fixed-time consensus tracking for second-order multi-agent systems with disturbances

This paper researches into a fixed-time consensus tracking problem for a class of second-order multi-agent systems (MASs) subject to external disturbances based on a fixed-time observer. First, we adopt a state observer to change the states of each agent from unknown to known. The observer is designed so that observed states and the leader’s state reach consensus. Second, according to the designed controller, states of each agent and observed states achieve consensus, namely leader-following consensus is realized and the setting time of which is obtained without depending on initial states. By employing Lyapunov stability theory, some sufficient criteria are obtained to achieve fixed-time consensus tracking for second-order MASs with disturbances. Finally, the validity of the design is verified by numerical arithmetic examples.

Fixed-Time Consensus for Multiple Mechanical Systems With Input Dead-Zone and Quantization Under Directed Graphs

Fixed-Time Consensus for Multiple Mechanical Systems With Input Dead-Zone and Quantization Under Directed Graphs

Fixed-time sliding-mode distributed consensus and formation control of disturbed fractional-order multi-agent systems

In this paper, fixed-time consensus and formation control for fractional-order multi-agent systems with a dynamic virtual leader in the presence of external disturbances is investigated. Consensus is achieved in fixed-time, i.e., with a finite settling time whose upper bound is independent of the initial conditions of the agents’ states. A new distributed sliding-mode control with neighborhood-based error variable is proposed to track a virtual leader in order to achieve a desired consensus in the presence of disturbances. Furthermore, the fractional Lyapunov stability theorem has been employed to prove the fixed-time stability and to estimate the upper bound of convergence. The formation of agents has also been investigated for the agents of fractional-order. Finally, several numerical simulations are provided to determine the effectiveness of the design method.