Distributed event-triggered adaptive finite-time consensus control for second-order multi-agent systems with connectivity preservation

https://doi.org/10.1016/j.jfranklin.2021.05.028Get rights and content

Highlights

  • A novel finite-time sliding mode manifold is developed, which removes the need for the fractional-order signum function and reduces the computational burden.

  • An adaptive distributed finite-time controller is proposed by combining artificial potential function with sliding mode technique.

  • The presented controller is capable of achieve finite-time consensus, connectivity preservation, and event-triggered transmission simultaneously.

Abstract

In this paper, we consider the robust finite-time consensus problem for second-order multi-agent systems (MASs) with limited sensing range and weak communication ability. As a stepping stone, a novel distributed finite-time sliding mode manifold is developed for MASs. Then, by combining artificial potential function technique with the presented sliding mode manifold, a robust distributed control scheme is proposed to enable the finite-time consensus of MASs while preserving the prescribed communication connectivity. Furthermore, the sampling frequency and implementation burden of the proposed controller can be reduced with resort to the event-triggered methodology. Finally, numerical examples are given to show the effectiveness of the proposed method.

Introduction

During the past decade, cooperative control of multiple autonomous agents has become undoubtedly one of the most concerned themes due to its potential applications such as power electronic systems [1], [2], [3], [4], aeronautic and aerospace engineering [5], [6], [7], [8], multi-robot systems [9], [10], [11], [12], and so on. Up to now, several related projects aimed at demonstrating the cooperative control ability of multi-agent systems have been put forward, including ESA’s Laser Interferometer Space Antenna (LISA) mission [13], AFRL’s Technology Satellite of the 21st Century (Techsat-21) program [14], DARPA’s Collaborative Operations in Denied Environment (CODE) program [15] etc. An attracting problem in cooperative control is how to reach an agreement upon various physical and virtual quantities of interest in a distributed manner. Through the lens of consensus problem, a myriad of existing results have been devoted to MASs. Initially, the asymptotic consensus results were obtained in [16], [17], [18]. Note that one important performance indicator of consensus study is the convergence rate, which contributes to the research on finite-time consensus. Then, finite-time convergence and anti-disturbance robustness related to consensus problems were investigated in [19], [20], [21], [22], [23], [24], [25]. Lin and Zheng [19] focused on the finite-time consensus problem of a switched MASs, which is composed of continuous-time and discrete-time subsystems. Ning and Han [20] dealt with the prescribed finite-time consensus tracking problem for MASs with nonholonomic chained-form dynamics. In [21], a finite-time consensus fault-tolerant tracking control protocol was investigated for a class of nonstrict nonlinear MASs. In [22], a novel distributed saturated consensus control scheme was designed for second-order MASs. Liu et al. [23] investigated the problem of finite-time robust consensus for second-order nonlinear MASs with external disturbances. However, it should be pointed out that the aforementioned works suffer from the assumption that agents are under a static network topology during the whole motion evolution, which is generally hard to maintain in practical engineering.

Considering the limited communication capabilities of devices equipped on multiple agents, connectivity preservation has become another research topic in the consensus study of MASs. In practice, the sensing and communication ranges between two adjacent agents are always bounded due to transmit power constraints [26]. For example, the communication connection of multiple underwater unmanned vehicles depend on a group of wireless sensor networks, which generally suffer from limited power supplies and susceptible underwater acoustic environments [27]. Therefore, the connectivity of communication topology network can only be preserved within a close distance, which drives us to study the distributed control of MASs with connectivity preservation. The predefined network topology must be maintained during the motion process to achieve the consensus of MASs [28], [29], [30], [31], [32], [33]. Sun et al. [28] considered the robust finite-time connectivity preserving coordination problem for second-order MASs with limited sensing range. Feng et al. [29] proposed a nonlinear control protocol for a class of leader-follower multi-robot systems with connectivity preservation. With the same author, a fault-tolerant coordination algorithm with connectivity preservation and collision avoidance was proposed in [32] for a group of unknown Lagrange systems. The fixed-time connectivity-preserving average tracking problem for MASs under communication constraints was proposed in [30]. Yoo and Part [31] addressed a distributed connectivity-preserving synchronized tracking problem of multiple uncertain nonholonomic mobile robots with an approximation-based local adaptive scheme.

In conventional consensus control settings, the sensors are assumed to take samples as fast as possible at all time intervals and the actuators act accordingly. It is generally unrealistic in practical applications, especially when computation resources, communication bandwidth and channels are limited in networked systems [34], [35]. More specifically, the typical IEEE 802.15.4-standard communication protocol used in ZigBee systems supports data transmission rates from 20250kb/s within a range up to 20m [36]. As a result, the economic dispatch in smart grid may fail in communicating over a network environment once the link is congested. In addition, in load frequency control of circuit systems, the embedded communication networks also induce undesirable phenomena [37]. Thus, it is necessary to develop an alternative scheme to reduce the sampling frequence and save network transmission resources [38], [39]. Li et al. [40] studied the event-triggered security consensus problem for time-varying MASs against false data-injection attacks and parameter uncertainties. Liu et al. [41] proposed two kinds of fixed-time event-triggered consensus controllers for uncertain nonlinear MASs. The fixed-time event/self-triggered leader-follower consensus problem for networked multi-agent systems subject to nonlinear dynamics was addressed in [42]. With the same author, the event-triggered fixed-time consensus problems for a class of second-order MASs subject to uncertain disturbance were addressed in [43], [44]. In [45], a distributed finite-time event-triggered consensus control protocol was presented for MASs with undirected communication topology. Dong and Tang [46] investigated the event-triggered consensus problem of nonlinear MASs with unknown external disturbances. To the best of authors’ knowledge, few existing works have investigated the finite-time consensus, connectivity preservation, and event-triggering strategy for MASs, simultaneously, in the presence of external disturbances.

Motivated by the foregoing observation, this work aims at designing a distributed event-triggered adaptive finite-time consensus control protocol for second-order MASs with connectivity preservation and event-triggering condition. The contributions of this work are summarized as follows.

  • 1.

    A novel distributed sliding mode manifold is developed, with which the practical consensus performance of MASs can be achieved in finite time. The presented finite-time sliding mode manifold provides a concise form and removes the needs for fractional power state and signum function, which can reduce the computational burden effectively.

  • 2.

    By combining artificial potential function with the presented sliding mode manifold, an adaptive event-triggered control protocol is proposed. Compared with the existing works, the proposed controller is capable of achieving the finite-time consensus and connectivity preservation, whilst reducing the data transmission rate and the actuator implementation burden.

The reminder of the text is organized as follows. Section 2 gives the problem formulation and preliminaries. In Section 3, the novel sliding mode manifold and the distributed control protocol are constructed. Section 4 provides the numerical simulation results. Finally, Section 5 concludes the work.

Notations: Rm, Rm×n, and R+ denote the sets of mdimensional vectors, m×ndimensional matrices, and nonnegative numbers, respectively. · represents the Euclidean norm of a vector or induced 2norm of a matrix. |·| denotes the absolute value. Given a vector x=[x1,x2,,xn]T, diag(x) denotes a n×n diagonal matrix with entries xi(i=1,2,,n). Denote Im to be the mdimensional identity matrix and refers to the Kronecker product.

Section snippets

Graph theory

In this study, an undirected graph G={W,E,A} is utilized to describe the information exchange topology of MASs, where W={w1,w2,,wn} denotes the set of nodes, EW×W denotes the set of edges, and A=[aij]Rn×n denotes the adjacent matrix of G. An edge (wi,wj)E indicates that agents wj and wi can exchange information with each other. For (wi,wj)E, then aij=aji=1; otherwise, aij=aji=0. Let aii=0 for i{1,2,,n}. If there is a sequence of edges (wi,wi1),(wi1,wi2),,(wik,wj),wimW(m=1,2,,k), then

Finite-time sliding manifold design

The following consensus errors are defined ase1i=j=1naij(xixj)+bi(xix0)e2i=j=1naij(vivj)+bi(viv0)

In view of Eqs. (13) and (14), we have{e1=[(L+B)Im]x˜e2=[(L+B)Im]v˜where e1=[e11T,e12T,,e1nT]T, e2=[e21T,e22T,,e2nT]T, x˜=[x˜1T,x˜2T,,x˜nT]T, v˜=[v˜1T,v˜2T,,v˜nT]T, x˜i=xix0, v˜i=viv0(i=1,2,,n).

Based on Eqs. (13) and (14), the following sliding manifold is designedsi=k1Tanh(k2e2i)+k3(e1i)where Tanh(k2e2i)=[tanh(k2e2i,1),tanh(k2e2i,2),,tanh(k2e2i,m)]T, k1>0, k2>0, k3>0. (e1i)Rm is

Simulation results

To verify the effectiveness of the proposed method, two simulation scenarios are carried out. In Section 4.1, simulations with the control of second-order MASs Eq. (9) are performed to show the performance of the proposed approach, and the nonsingular finite-time consensus approach (NFTCA) method [43] is employed as comparative test. In Section 4.2, simulation scenario of multiple mobile robots with nonlinear dynamics [28] is considered, and the robust finite-time connectivity preserving

Conclusions

In this paper, the finite-time consensus problem of second-order MASs is investigated in the presence of external disturbances, connectivity preservation and event-triggering condition. Firstly, a novel distributed sliding manifold is proposed to achieve the finite-time convergence performance. Then, by combining artificial potential function technique with the well-designed sliding mode manifold, a distributed finite-time event-triggered control is developed for MASs. Compared with the

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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