Finite-Time Consensus for Leader-Following Second-Order Multi-Agent Networks

IET Control Theory & Applications

2015

137

This study discusses the asymptotic consensus problem and finite-time leader-following consensus problem of second-order non-linear multi-agent systems (MASs) with directed communication topology. On the basis of the sliding mode control theory, a new distributed asymptotic consensus controller is proposed to ensure that the consensus of MAS can be reached as time goes to infinity. Another finite-time consensus control algorithm is also proposed based on terminal sliding mode control. The finite-time consensus controller can force the states of MAS to achieve the designed terminal sliding mode surface in finite time and maintain on it. The authors also can prove the consensus of MAS can be obtained in finite time on the terminal sliding mode surface if the directed topology has a directed spanning tree. Simulations are given to illustrate the effectiveness of the proposed approaches. IntroductionIn recent years, multi-agent systems (MASs) have attracted great attentions because of the wide practical applications. In many applications, a group of agents which can communicate with their neighbours are required to accomplish some challenging tasks together and the single agent can coordinate with the other agents by sharing its information with its neighbours. If all the agents in the group can reach an agreement, then the agents can reach the consensus. A consensus algorithm or protocol is an interaction rule that specifies the information exchange between an agent and all of its neighbours on the network [1]. The works on consensus problem have primarily studied the first-order MAS [2][3][4][5][6][7]. Compared with the first-order MAS, the consensus problem of the secondorder MAS is more difficult and complicated. As the consensus of second-order systems not only contains the position consensus like in first-order MAS but also contains the velocity consensus. A necessary condition presented in [8] to solve consensus problem of second-order MAS was that the graph had a (directed) spanning tree. The second-order consensus of MAS has been discussed in [9][10][11][12][13][14]. Most of works on MAS have a common feature that their systems are linear, for example [4, 9-11, 15, 16]. The consensus investigation of non-linear systems is more challenging than that of the linear systems. However, non-linearity is ubiquitous in physical phenomena, and many works have been done to research the nonlinear dynamic system, for example [17][18][19][20][21][22] and references therein. A class of non-linear system with unknown constant parameters was discussed in [17] and the backstepping technique was used to solve the robust adaptive failure compensation problem of hysteretic actuators. However, the unknown non-linear parts of the system in [17] were assumed to be linearly parameterised, that is, the unknown non-linear function of the dynamics model could be written in the form of a i f i where a i was the unknown constant and f i was the known non-linear function. In [20][21][22], the completely unknown non-linear dynamics were co...

Section: Introductionmentioning

confidence: 99%

“…So it is significant to investigate the finite-time leader-following consensus control of MAS. In recent years, a few of efforts have been taken to solve the finite time consensus control problem [11,12,[27][28][29][30][31][32][33][34]. However, most of them dealt with the consensus problem of linear MAS with directed or undirected communication topology.…”

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confidence: 99%

Sliding mode leader‐following consensus controllers for second‐order non‐linear multi‐agent systems

Ren

IET Control Theory & Applications

2015

137

“…Reaching agreement in a finite time allows the network to use precise information in the completion of other tasks. There have been some results related to finite-time synchronization (FTS) [20], [21]. Du et al [20] considered the FTS of a class of the second-order nonlinear multiagent systems using output feedback control, which showed that the systems output can reach synchronization in a finite time and the final consensus states are leader's states.…”

mentioning

confidence: 99%

“…Du et al [20] considered the FTS of a class of the second-order nonlinear multiagent systems using output feedback control, which showed that the systems output can reach synchronization in a finite time and the final consensus states are leader's states. Based on the graph theory, matrix theory, homogeneity with dilation and the LaSalles invariance principle, Guan et al [21] studied the leader-following finite-time consensus problem for the secondorder multiagent networks with fixed and switched topologies. Now, based on the well-known finite-time stability theory, the issue of FTS (including finite-time consensus) has been extensively studied under continuous or discontinuous control protocols [22]- [31].…”

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confidence: 99%

A Switching Approach to Designing Finite-Time Synchronization Controllers of Coupled Neural Networks

Liu

IEEE Trans. Neural Netw. Learning Syst.

2016

152

This paper is concerned with the finite-time synchronization issue of nonlinear coupled neural networks by designing a new switching pinning controller. For the fixed network topology and control strength, the newly designed controller could optimize the synchronization time by regulating a parameter α (0 ≤ α < 1). The control law presented in this paper covers both continuous controllers and discontinuous ones, which were studied separately in the past. Some criteria are discussed in detail on how to shorten the synchronization time for the strongly connected networks. Finally, the results are generalized to any network topologies containing a directed spanning tree, and one numerical example is given to demonstrate the effectiveness of the theoretical results.

“…Most of the existing consensus protocols for multi-agent systems mentioned previously only provided asymptotic convergence, which means that convergence rates of the considered systems are asymptotic with an infinite settling time and the goal of consensus cannot be achieved in a finite time. Actually, in practical applications, finite-time consensus (FTC) protocols are more desirable that holds not only the faster convergence rates but also better disturbance rejection properties and better robustness against uncertainties [16][17][18][19][20][21][22][23][24]. So far, existing research in FTC mainly concerns with continuous consensus protocols and discontinuous ones [25][26][27][28][29][30][31].…”

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confidence: 99%

Further results on finite‐time consensus of second‐order multi‐agent systems without velocity measurements

Liu

Intl J Robust & Nonlinear

et al. 2015

SUMMARYThis paper investigates the problem of finite-time consensus (FTC) for second-order nonlinear multi-agent systems when the velocity information is unavailable. Based on the global finite-time stability theory and homogeneity with dilation, a class of novel finite-time consensus protocols are proposed for the multi-agent systems. The protocol design is divided into two parts. First, when all the state information of the agents are measurable, a new continuous state feedback is designed to achieve FTC. Then, when the velocity information is unmeasurable, two finite-time convergent discontinuous observers are presented to estimate the velocities of the followers and the leader, respectively, which further ensure the final FTC for the multi-agent systems. Finally, one example is given to demonstrate the efficiency of the proposed method.