Fixed-time Leader-following Consensus Research Articles

Fixed-time leader–follower consensus for second-order multi-agent systems: Variable exponent sliding mode control approach

This paper investigates the fixed-time leader–follower consensus (LFC) problem of second-order multi-agent systems (MASs) with bounded disturbance under directed interaction topology. First, a sliding mode manifold (SMM) with consensus errors–dependent variable exponential coefficient is given. Then, two sliding mode control (SMC) protocols are proposed. The proposed control protocols can eliminate the singularity, while guaranteeing the fixed-time reachability of the consensus errors to the sliding mode surface (SMS) and the fixed-time convergence of the consensus errors toward the origin along the SMS. Finally, the validity of the obtained methodology is confirmed by two simulation examples.

Distributed Fixed-Time Leader-Following Consensus for Multi-Agent Systems: An Event-Triggered Mechanism

In this work, a fixed-time leader-following event-triggered (ET) consensus problem for multi-agent systems (MASs) with external disturbances is investigated. A distributed observer is developed to achieve the estimated state of the leader. By means of the observation information, the consensus error system for multi-agents is reformulated into a tracking error system, wherein individual follower agent aims to track the leader agent. Building upon Lyapunov technology and fixed-time stability theory, a new ET protocol is introduced to mitigate communication wastes. Notably, the proposed controller incorporates a strong robust fixed-time control form with lower complexity, and a reliable dynamic triggering condition also ensures the excellent performance of the system. Rigorous demonstrations underscore the stability and robustness of the ET method, while guaranteeing the avoidance of Zeno behavior. Finally, several numerical simulations are provided to underscore the efficacy of the proposed protocols.

Further Results on Fixed-Time Leader-Following Consensus of Heterogeneous Multiagent Systems With External Disturbances

Further Results on Fixed-Time Leader-Following Consensus of Heterogeneous Multiagent Systems With External Disturbances

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.

Disturbance observer-based fixed-time leader-following consensus control for multiple Euler–Lagrange systems: A non-singular terminal sliding mode scheme

This paper focuses on the fixed-time leader-following consensus problem for multiple Euler–Lagrange (EL) systems via non-singular terminal sliding mode control under a directed graph. Firstly, for each EL system, a local fixed-time disturbance observer is introduced to estimate the compound disturbance (including uncertain parameters and external disturbances) within a fixed time under the assumption that the disturbance is bounded. Next, a distributed fixed-time observer is designed to estimate the leader’s position and velocity, and the consensus problem is transformed into a local tracking problem by introducing such an observer. On the basis of the two types of observers designed, a novel non-singular terminal sliding surface is proposed to guarantee that the tracking errors on the sliding surface converge to zero within a fixed time. Furthermore, the presented control algorithm also ensures the fixed-time reachability of the sliding surface, while avoiding the singularity problem. Finally, the effectiveness of the proposed observers and control protocol is further verified by a numerical simulation.

Fixed-Time Consensus Tracking for Multi-Agent Systems With a Nonholomonic Dynamics

In this article, we investigate the control strategy of fixed-time leader-following consensus for chained-form systems with matched disturbances. A new decentralized observer is designed under a directed topology to estimate the leader state in a fixed time for each follower. Then, a novel control protocol is developed to track the estimated leader state in a prescribed finite time. Different from existing results, the bound we derive for the setting time does not depend on the initial conditions even in the presence of matching perturbations. Moreover, the chattering phenomenon of control output is effectively reduced as signum function gets smaller in the proposed method.

Fixed-Time Consensus Tracking of Multiagent System Under DOS Attack With Event-Triggered Mechanism

This paper focuses on fixed-time event-triggered consensus tracking of high-order MAS over digraph and under DOS attack. The considered DOS attack is divided into connectivity-maintained attack and connectivity-broken attack. To detect connectivity-broken attack under event-triggered environment, a new cyberattack detection algorithm is presented. Next, using cyberattack detection results, a fixed-time event-triggered distributed observer is developed to estimate the leader’s states in the presence of DOS attack, which conducts event-triggered update in the normal condition and under connectivity-maintained attack and stops updating in the presence of connectivity-broken attack. Then, an adaptive event-triggered prescribed-time dynamic surface consensus tracking control protocol is proposed to eliminate mismatched disturbances caused by estimation error and achieve prescribed-time convergence of the tracking error. Stability analysis proves fixed-time convergence of the developed consensus tracking strategy and non-zeno analysis shows the developed distributed observer and consensus tracking control strategy exclude zeno behavior. This paper contributes to proposing a fixed-time leader-follower consensus control strategy for MAS under DOS attack via event-triggered approach, which eliminates the effect of DOS attack, achieves consensus tracking within a fixed time and reduces resources consumption. Finally, simulation results show the effectiveness and superiority of the developed consensus tracking approach.

Prescribed fixed-time consensus control of multiple second-order systems with communication connectivity assurance

The leader-following consensus tracking problem is investigated for multiple second-order agent systems subject to communication range constraints in this paper. First, a novel fixed-time convergent performance function is developed to quantitatively characterize the consensus tracking performance. Then, an auxiliary state variable is defined by integrating the position and velocity consensus tracking errors with the potential function for removing the communication range constraints. Based on this auxiliary state variable, a fixed-time leader-following consensus controller is devised to guarantee the preassigned consensus tracking performance and communication preservation simultaneously. Compared with the existing consensus control methods, the prominent advantage of the proposed one is that the fixed-time convergence rate of the position and velocity tracking errors can be guaranteed without applying discontinuous control techniques. And the communication connectivity among the multiple agents is assured simultaneously via adding a potential function into the auxiliary state. Finally, two groups of illustrative examples are organized to validate the effectiveness of the proposed consensus control method.

Continuous Distributed Fixed-Time Attitude Controller Design for Multiple Spacecraft Systems With a Directed Graph

This brief addresses the fixed-time leader-following attitude consensus problem for multiple spacecraft systems on a directed graph. A distributed continuous observer is designed to estimate the angular velocity of the leader within a fixed time. Based on the fixed-time observer and adding a power integrator method, a continuous distributed adaptive controller is developed to achieve the consensus tracking control in a fixed time which is regardless of the initial conditions. The proposed continuous fixed-time scheme works well when the systems are subject to model uncertainties and external disturbances. The simulation results show the effectiveness of the proposed control scheme.

Fixed-time leader-following consensus of multi-agent systems with intermittent control

In this article, the intermittent-based fixed-time (IBFT) consensus matter is researched for nonlinear multi-agent systems (MASs). By designing a novel IBFT control protocol, the follower can achieve consensus with the leader’s state within a settling time. To deal with the fixed-time (FT) consensus matter, a new differential inequality is proposed, which provides a way to analyze the IBFT stability. Some properties are given to ensure the FT consensus of the nonlinear MASs. Furthermore, we extend our results to the directed communication situation of agents. The FT leader-following consensus problem with directed topology via intermittent control is solved as well. The settling time achieved is relative to the protocol parameters and independent of the initial states. Three examples demonstrate the feasibility and effectiveness of the suggested control protocols, including two application examples, the Chua’s circuit system, a spring-mass-damper (SMD) system, and one numerical example.

Fixed-Time Leader-Following Consensus Tracking Control for Nonliear Multi-Agent Systems under Jointly Connected Graph.

This paper researches the fixed-time leader-following consensus problem for nonlinear multi-agent systems (MASs) affected by unknown disturbances under the jointly connected graph. In order to achieve control goal, this paper designs a fixed-time consensus protocol, which can offset the unknown disturbances and the nonlinear item under the jointly connected graph, simultaneously. In this paper, the states of multiple followers can converge to the state of the leader within a fixed time regardless of the initial conditions rather than just converging to a small neighborhood near the leader state. Finally, a simulation example is given to illustrate the theoretical result.

Fixed-time leader-following consensus of multiple uncertain nonholonomic systems: An adaptive distributed observer approach

This paper discusses the fixed-time leader-following consensus problem for multiple uncertain nonholonomic systems, which are widely used in engineering models. According to our literature review, either the system is assumed to be known, or the uncertainty only contains state information, which does not meet the actual requirements. For this reason, this paper investigates more general nonholonomic systems with uncertainties driven by inputs and states. First, a fixed-time adaptive distributed observer is proposed to estimate the leader’s state and structural parameters, which ensures that the estimation errors converge to zero within a fixed time. Second, two regulator equations based on the idea of cooperative output regulation are constructed, and a novel observer-based distributed switching control law is proposed. This control law overcomes the nonholonomic constraints and appropriately relaxes the assumptions of uncertain functions in the existing references. Finally, the simulation results verify the effectiveness of the proposed control scheme.

Fixed-time leader-follower quantized output consensus of high-order multi-agent systems over digraph

This paper is concerned with fixed-time leader-follower consensus of high-order multi-agent system (MAS) under quantized communication and directed communication graph. First, dynamic encoder, quantizer and decoder are presented to encode and quantize the transmitted states at the sending end and decode the transmitted states at the receiving end. Next, a new distributed observer is proposed to estimate the leader’s states within a fixed time under quantized communication environment and directed communication graph. Practical fixed-time convergence of the proposed distributed observer is proved based on nonsmooth stability analysis. Then, a new predefined-time control scheme is developed to achieve practical predefined-time convergence of tracking error dynamics. Finally, simulation results show the validity of the strategy developed in achieving fixed-time leader-follower consensus and formation.

Fixed-time leader-following/containment consensus for a class of nonlinear multi-agent systems

This study focuses on the fixed-time leader-following consensus problem for a class of multi-agent system with multi-dimensional nonlinear dynamics. First, the distributed static fixed-time control protocol is put forward to settle this issue. Different from the existing fixed-time control methods, the proposed control protocol is continuous such that the chattering phenomenon can be avoided. Note that the proposed static fixed-time controller is dependent on the global information of network topology. To address above issue, the fully distributed adaptive fixed-time controller is further proposed. Moreover, the results in fixed-time leader-following consensus are extended to containment consensus. And the case of directed graph is also considered. Finally, several examples are provided to illustrate the feasibility of the theoretical results.

Autonomous and non-autonomous fixed-time leader–follower consensus for second-order multi-agent systems

This paper addresses the problem of consensus tracking with fixed-time convergence, for leader–follower multi-agent systems with double-integrator dynamics, where only a subset of followers has access to the state of the leader. The control scheme is divided into two steps. The first one is dedicated to the estimation of the leader state by each follower in a distributed way and in a fixed-time. Then, based on the estimate of the leader state, each follower computes its control law to track the leader in a fixed-time. In this paper, two control strategies are investigated and compared to solve the two mentioned steps. The first one is an autonomous protocol which ensures a fixed-time convergence for the observer and for the controller parts where the Upper Bound of the Settling-Time (UBST) is set a priory by the user. Then, the previous strategy is redesigned using time-varying gains to obtain a non-autonomous protocol. This enables to obtain less conservative estimates of the UBST while guaranteeing that the time-varying gains remain bounded. Some numerical examples show the effectiveness of the proposed consensus protocols.

Distributed fixed-time leader-following consensus tracking control for nonholonomic multi-agent systems with dynamic uncertainties

The problem of distributed fixed-time leader-following consensus tracking control for nonholonomic chained-form dynamic systems with nonlinear disturbances is considered in this paper. Compared with the existing works, this paper considers a class of more general nonholonomic multi-agent systems where both the leader and the followers have nonlinear uncertainties. For undirected graphs, a distributed observer for each follower is investigated such that both the leader state and input can be estimated by the followers in a fixed time. Based on the distributed observers, a consensus tracking controller is proposed to ensure that the tracking errors convergence to zero within a fixed time. Lyapunov analysis proves the stability of the closed-loop system. A simulation example of wheeled mobile robots is given to demonstrate the effectiveness of the proposed controllers.

Fixed-Time Leader–Follower Consensus of Networked Nonlinear Systems via Event/Self-Triggered Control

This brief addresses the fixed-time event/self-triggered leader-follower consensus problems for networked multi-agent systems subject to nonlinear dynamics. First, we present an event-triggered control strategy to achieve the fixed-time consensus, and a new measurement error is designed to avoid Zeno behavior. Then, two new self-triggered control strategies are presented to avoid continuous triggering condition monitoring. Moreover, under the proposed self-triggered control strategies, a strictly positive minimal triggering interval of each follower is given to exclude Zeno behavior. Compared with the existing fixed-time event-triggered results, we propose two new self-triggered control strategies, and the nonlinear term is more general. Finally, the performances of the consensus tracking algorithms are illustrated by a simulation example.

Adaptive controller design for fixed-time leader-following consensus of multi-agent systems with discontinuous dynamics

This paper investigates the adaptive fixed-time consensus of a class of multi-agent systems with discontinuous dynamics. First, under the framework of Filippov solutions, a new theorem is established to achieve fixed-time consensus of discontinuous multi-agent systems using the proposed control protocol. Furthermore, an adaptive control protocol is provided in the second theorem that highly improves the control signals of the system. Finally, numerical simulations are worked out to illustrate the effectiveness of our theoretical results.

Fixed-Time Leader-Following Consensus for High-Order Time-Varying Nonlinear Multiagent Systems

This article investigates the fixed-time leader-following consensus problem for high-order nonlinear multiagent systems dominated by the lower triangular model with a time-varying gain. Based on the fixed-time distributed observer and dynamic gain control approach, a new dynamic controller is developed with two online tuned gains such that the fixed-time leader-following consensus is achieved. It is mathematically proved that the upper bound of the convergence time only depends on system parameters and controller parameters, which makes it possible to obtain a prescribed convergence time regardless of the initial conditions. Simulation results are given to demonstrate the proposed results.

Adaptive Neural Network Fixed-Time Leader-Follower Consensus for Multiagent Systems With Constraints and Disturbances.

This article is concerned with fixed-time leader-follower consensus problem for multiagent systems (MASs) with output constraints, unknown control direction, unknown system dynamics, unknown external disturbance, and dead-zone control input. First, a fixed-time distributed observer is presented for each follower to estimate the leader's states. Next, using a modified nonlinear mapping, an output-constrained system is transformed into an unconstrained system. Then, by adopting adding a power integrator technique, radial basis function neural network (RBFNN) approximation, and adaptive method, the ideal fixed-time stable virtual control protocol is derived and the issues of unknown control direction, unknown system dynamics, and unknown external disturbance are addressed. Finally, the actual control protocol is developed using the bound of dead-zone parameters. It is shown that the proposed control scheme achieves fixed-time leader-follower consensus of the studied MAS. The presented control protocol is applied to the leader-follower consensus of inverted pendulums and simulation results verify its effectiveness.