Finite-time Consensus Problem Research Articles

Event-Triggered Finite-Time Consensus of Second-Order Leader-Follower Multiagent Systems With Uncertain Disturbances.

In this article, for second-order multiagent systems with uncertain disturbances, the finite-time leader-follower consensus problem has been investigated. First, by considering that the leader's states are only available to part of the followers, a distributed estimator is constructed to estimate the state tracking errors between the leader and each follower. Then, an estimator-based control scheme is proposed under the event-triggered strategy to achieve finite-time leader-follower consensus. Besides, the event-triggered intervals are with a positive lower bound such that the Zeno behavior can be avoided. Note that the system is discontinuous under the event-triggered mechanism; thus, a nonsmooth analysis is performed. Numerical simulations are presented to demonstrate the effectiveness of our theoretical results.

Finite-time leader-following output consensus for multi-agent systems via extended state observer

In this paper, the finite-time leader-following output consensus problem is investigated for a multi-agent system subjected to directed topology and disturbance. Firstly, a distributed finite-time extended state observer (DFTESO) is designed to provide estimate for unmeasured consensus errors and disturbances. The sufficient condition is provided in terms of linear matrix inequality (LMI) to ensure that the error dynamics of the DFTESO is convergent in finite time. Then, based on the designed observer, the leader-following consensus protocol based on dynamic gain method is proposed under the directed topology. Finally, an example on the multi-spacecraft system is provided to illustrate the effectiveness of the proposed methodology.

Adaptive finite-time consensus for multiple mechanical systems with unknown backlash nonlinearity and uncertain dynamics

This paper studies the problem of finite-time consensus (FTC) for uncertain multiple mechanical systems with unknown backlash nonlinearity and external disturbance. Combining finite-time control technique and graph theory, a distributed adaptive FTC protocol is proposed. Radial basis function neural networks are employed to approximate the unknown functions. If the designed parameters of control algorithms and adaptive laws are appropriately chosen, then it can be proved that the position errors between arbitrary two mechanical systems will converge to a small region of zero in finite time as well as the velocity errors. Finally, the effectiveness of the proposed control scheme is verified by numerical simulation.

Fast finite-time tracking control for multi-agent systems with mismatched disturbances under directed communication graphs

In this paper, the fast finite-time consensus problem on multi-agent systems is considered. Multi-agent systems are affected by mismatched disturbances and the communication graph is directed. By a sliding mode observer and a fast nonsingular terminal sliding mode control method, the feedforward-feedback controller is presented for multiple second-order systems and multiple high-order systems to achieve consensus, respectively. The proposed control method can provide short convergence time and improved control input without strong chattering and singularity phenomenon. Finally, simulations are given to verify the availability of the methods.

Limited‐budget finite‐time average consensus design for multi‐agent systems

This study investigated the limited-budget finite-time average consensus problem of multi-agent systems. Different from the existing results about the guaranteed-cost asymptotical consensus, all agents can achieve the average consensus within a finite time and the limited budget can be given previously. Firstly, a novel consensus protocol is proposed with non-linear cost indexes to trade off the control energy consumption against the consensus regulation performance for the limited budget within a finite time. Then, sufficient conditions for limited-budget finite-time average consensus design and analysis are respectively given, where the limited budget is utilised to determine the value range of the control gain, and the consensus value obtained by all agents is the average of initial states. Moreover, for the case without giving the limited budget, guaranteed-cost finite-time average consensus design and analysis criteria are presented, respectively, in which an upper bound of the cost index is determined. Finally, a numerical simulation is shown to illustrate the effectiveness of theoretical results.

Novel finite-time synchronization criteria for coupled network systems with time-varying delays via event-triggered control

This paper is concerned with the finite-time synchronization of coupled networks with time-varying delays. We work without applying the finite-time stability theorem, which is widely used in finite-time synchronization for complex networks or finite-time consensus problems for multi-agent systems. We construct a novel Lyapunov functional and apply some new analytical techniques. Sufficient conditions are obtained to ensure synchronization within a setting time with no Zeno behaviors. The obtained conditions do not contain any uncertain parameter. The controllers are presented based on event-driven strategies, which can significantly reduce the communication consumption and the frequency of the controller updates. And the setting time is related to initial values of the network. Finally, numerical examples are examined to illustrate the effectiveness of the analytical results.

Robust finite-time and fixed-time bipartite consensus problems for multi-agent systems via discontinuous protocol

This paper addresses the robust finite-time and fixed-time bipartite consensus problems for multi-agent systems under the signed graphs. A unified discontinuous control protocol is constructed to achieve both finite-time bipartite consensus (FINBC) and fixed-time bipartite consensus (FIXBC) only by adjusting the parameters, regardless of whether the signed graph is structurally balanced or unbalanced. By using discontinuous techniques, some simple sufficient conditions for FINBC/FIXBC are provided; moreover, the upper bounds of the settling times are explicitly estimated. Simulations show that the proposed control protocols are effective.

Finite-time output feedback leader-following consensus for high-order time-varying nonlinear multi-agent systems

This paper addresses the finite-time leader-following output-feedback consensus problem for a class of high-order nonlinear multi-agent systems. The agents dynamics are supposed to be in lower-triangular form and satisfy Lipschitz conditions with time-varying gains. Based on the dynamic output approach and dynamic gain control method, a new distributed output feedback consensus protocol is proposed with two online tuned gains such that the finite-time leader-following consensus is achieved. Different from some exiting observer-based output feedback approaches that the observers embedded in agents have to share full observation information with their neighbors, the proposed protocol only requires the output information of neighboring agents to be transmitted, and thus the network communication burden is reduced. In addition, compared to the traditional backstepping method that commonly used for finite time control of nonlinear system, the proposed controller can avoid the repeated derivation problem in backstepping control and thereby is simple and convenient for use. Finally, a numerical example is given to demonstrate the effectiveness of the proposed results.

Finite-time consensus for nonholonomic multi-agent systems with disturbances via event-triggered integral sliding mode controller

This paper investigates the finite-time consensus problem for nonholonomic multi-agent systems with unknown external disturbances. Firstly, the chained-form nonholonomic multi-agent systems are converted into two subsystems, one is first-order and another second-order. Then, the integral sliding mode-based finite-time event-triggered control laws are proposed to ensure that the states of the agents achieve consensus in finite time in spite of external disturbances. Furthermore, the inter-execution time is proved lower-bounded and the Zeno behavior is therefore naturally avoided. Finally, numerical simulations demonstrate the effectiveness of the proposed protocols.

Event-Based Finite-Time Consensus Control of Second-Order Delayed Multi-Agent Systems

This brief considers the event-based finite-time consensus problems for second-order multi-agent systems (MASs) with input delay. By backstepping design method, the controllers are developed to ensure true velocity track virtual velocity within a fixed time. Once the true velocity tracks on the virtual velocity, all agents can reach the agreement within a finite time. Moreover, an improved event-based control scheme is proposed by discontinuous communication. Besides, no Zeno behavior occurs. The efficiency of the proposed algorithms is illustrated by a detailed numerical example.

Distributed input observer-based finite-time consensus for the leader-following multi-agent systems

This paper mainly studies the problem of robust finite-time consensus for leader-following multi-agent systems in detail-balanced graphs. It is evident that the knowledge of the leader’s input will provide significant assistance to a follower in tracking the leader. For this reason, an observer is constructed to estimate the input of the leader for each follower. Compared with many existing works of leader-following consensus, we do not assume that the input of the leader is bounded, but assume instead that its derivative is bounded. Based on input observer, two discontinuous protocols are proposed firstly that require only the sign information of the differences between a given agent’s state and that of its neighbors. Then, the finite-time consensus and the upper-bound of the settling time are obtained by using matrix theory, Lyapunov control approach, and the algebraic graph theory. Finally, the availability of the theoretical results is demonstrated through an example.

Finite-Time Consensus of Finite Field Networks With Stochastic Time Delays

This brief aims to solve the finite-time consensus problem of finite field networks (FFNs) with stochastic time delays. An algebraic state space representation (ASSR) approach is introduced for the investigation of this problem. Firstly, the concept of finite-time consensus with probability one is defined for FFNs with two kinds of stochastic time delays. Secondly, the dynamics of FFNs with time delays is converted into an ASSR, based on which, the dynamics of FFNs with probabilistic time delay is converted into a linear discrete-time stochastic system. It is shown that the finite-time consensus of FFNs with probabilistic time delay is equivalent to the finite-time set stability of the obtained system. Thirdly, a verifiable criterion is put forward for the finite-time consensus of FFNs with probabilistic time delay. Finally, using the dummy matrix, the dynamics of FFNs with Markov jump time delay is also converted into a linear discrete-time stochastic system, and the corresponding criterion is proposed for the finite-time consensus of FFNs with Markov jump time delay.

Finite-time consensus algorithms of leader-follower higher-order multi-agent systems with uncertain nonlinearities

In this paper, the finite-time consensus problem of leader-follower higher-order multi-agent systems with uncertain nonlinearities is studied, where the uncertainties are assumed to satisfy Hölder conditions. To solve this problem, distributed adding a power integrator method, feedback domination technique and integral sliding-mode control are combined together. Firstly, by using distributed adding a power integrator method, a distributed recursive control scheme is proposed. In the recursive control design, based on feedback domination method, the Hölder conditions of the unknown nonlinearities are introduced into the virtual controllers design. Secondly, on the basis of the designed recursive controllers, integral sliding-mode surfaces are designed and then the corresponding distributed sliding-mode controllers are proposed. The designed sliding-mode controllers guarantee that the finite-time leader-follower consensus problem is solved without using a distributed observer. The stability analysis of the closed-loop systems is presented based on finite-time stability theory. Moreover, simulations show the effectiveness of the proposed consensus algorithms.

Finite-Time Observer-Based Leader-Following Consensus for Nonlinear Multiagent Systems With Input Delays.

This article studies the finite-time observer-based leader-following consensus problem for a class of nonlinear multiagent systems with nonuniform time-varying input delays. Existing works usually assume that input delays are the same constants and the input of the leader is available for each follower. In this article, we propose a new distributed consensus algorithm to relax the conservative condition. A novel finite-time distributed observer is designed for each follower, which can accurately estimate the state information of the leader in a setting time. By means of the observer, the distributed controller is proposed for each follower, and it depends only on the state information of the follower and the estimated-state information of its neighbor agents. Based on the Lyapunov stability theory, it is strictly proved that all agents can achieve a consensus. Finally, the effectiveness of the theoretical results is verified by numerical simulation on a group of single-link manipulators.

Finite-Time Consensus for Power Regulation of Parallel PV Grid-Connected Inverters

Several small photovoltaic (PV) grid-connected inverters (GCIs) connected to a single PV array are applied in parallel in large-capacity applications since the power generation efficiency can be improved through appropriate control strategies. The control problem for parallel inverters is challenging due to DC voltage regulation and power sharing issues. This brief considers the problem of finite-time consensus of power sharing for parallel PV GCIs with a novel leader-follower structure. A primary droop controller at the DC side and a secondary finite-time controller are introduced in each follower to achieve power sharing with fast regulation and strong disturbance rejection. The test results for five 100 kW GCIs are presented to demonstrate the performance of the method.

Decentralised finite‐time consensus for second‐order multi‐agent system under event‐triggered strategy

In this technical note, the authors address the finite-time consensus problem of a second-order multi-agent system (SOMAS) under an event-triggered control strategy. This problem arises from the case where actuators in a SOMAS fail to follow the ideal controller behaviour exactly, due to either the failure of an embedded processor to maintain the desired update rate or a large time constant in the actuators, while still trying to maintain some performance merits from the finite-time control theory. A decentralised event-triggered non-linear protocol is proposed based on only local information for the undirected and connected communication graph. The rigorous proof is then presented and shows that the consensus can be achieved in finite time even under event-triggered schemes. Owing to the event-triggered strategy, they proposed a technique that bounds the steady errors of agent states into a small region around zero in finite time and reduces the update frequency of actuators while excluding the Zeno behaviour. Finally, simulation results are provided to validate the correctness and effectiveness of the proposed method and demonstrate that it can adjust a composed performance metrics with respect to the convergent rate, consensus accuracy, and update frequency of actuators by tuning the parameters in the control protocol.

Distributed Event-Triggered Control for Prescribed Finite-Time Consensus of Linear Multi-Agent Systems

In this paper, the prescribed finite-time consensus problem of linear multi-agent systems (MASs) is considered based on distributed event-triggered control strategies. It has been presented in the literatures that the prescribed finite time is independent of initial conditions or any other parameters, and can be pre-specified by the designer. Different from the existing prescribed finite-time consensus control rules that are based on continuous communication between agents and their neighbors, the proposed control laws in this paper are built on event-triggered mechanism. Furthermore, because the control schemes involve a time-varying scaling function, the Zeno behavior is hard to be excluded by the traditional approaches. To solve this problem, a dynamical event-triggered controller concerning time-varying variables to agents is proposed. Numerical simulations demonstrate the effectiveness of theoretical results.

Finite-Time Output Consensus of Higher-Order Multiagent Systems With Mismatched Disturbances and Unknown State Elements

This paper studies the finite-time output consensus problem of higher-order multiagent systems subject to both mismatched disturbances and unknown state elements, where the disturbances are allowed to be fast time-varying. To solve this problem, an active anti-disturbance control approach is developed based on the disturbance estimation/compensation and the baseline feedback consensus protocols. First, to estimate the matched/mismatched disturbances and the agents unknown state elements, a finite-time generalized state observer is constructed for each agent. Second, by integrating the distributed adding a power integrator feedback control method and the estimates of the matched/mismatched disturbances and the agents unknown state elements together, composite consensus protocols are developed for both leaderless and leader–follower cases. In both cases, the proposed protocols guarantee that the agents outputs reach consensus in finite time. Simulations show the effectiveness of the proposed consensus algorithms.

Finite-Time Consensus for Linear Multi-Agent Systems Using Data-Driven Terminal ILC

In this brief, the finite time consensus problem for a class of unknown linear multi-agent systems is considered. Firstly, a linear mapping relationship between the agent’s terminal output and the control input along the iteration domain is established. Then, a novel distributed data-driven iterative learning consensus protocol is constructed only using the I/O data of each agent and its neighbors. Meanwhile, a convergence condition that does not depend on model information is derived for the multi-agent system. It is shown that the proposed protocol can guarantee that all agents achieve the finite-time consensus objective. Finally, an example of numerical simulation is given to verify the effectiveness of the proposed design.

Finite-time and fixed-time consensus problems for second-order multi-agent systems with reduced state information

This paper studies the fixed-time consensus (FixTC) and connectivity-preserving finite-time consensus (FinTC) protocol designs for second-order multi-agent systems using output information only.Herein, a distributed FixTC protocol based on the Lyapunov stability and bi-limit homogeneity approaches is proposed with the aid of an auxiliary system. Then, when the graph is state-dependent, i.e., the agents have limited sensing and communication ranges, a connectivity-preserving FinTC is proposed by designing a mechanism suitable for this purpose.Theoretical analysis and several simulations are presented to verify the effectiveness of the proposed protocols.