Finite-time consensus for leader-following second-order multi-agent system

Sun, Fenglan; Guan, Zhi‐Hong

doi:10.1080/00207721.2011.618641

Cited by 57 publications

(28 citation statements)

References 29 publications

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“…Remark 4: For the special case that the non-linear function is a constant, we can design a distributed controller by the existing results. When the constant is known, the non-linear MAS becomes linear MAS, so we can design the finite-time consensus controller as [28,[31][32][33]. When the constant is unknown, we can apply the adaptive algorithm and design the finite-time consensus controller as [7].…”

Section: Finite-time Leader-following Consensus Control Design and Anmentioning

confidence: 99%

“…. , N u i = u ai + u bi + u ci (32) where (see (33)(34)(35)) where c 1 , c 2 and α = p/q are positive parameters. p and q are positive odd integers satisfying the following condition: 1 < p/q < 2. ω and g have been defined in Theorem 1.…”

Section: Finite-time Leader-following Consensus Control Design and Anmentioning

confidence: 99%

“…The time costs in the reaching phase and sliding phase are both finite. In addition, compared with finite-time consensus control in [28,[31][32][33], the second-order MAS are extended from linear systems to non-linear systems. Compared with [7,29,30,36], the finite-time consensus control approach in this paper proposes a milder condition to the inherent nonlinear dynamics of the systems, that is, the condition that non-linear dynamics must be bounded by a known constant is not required.…”

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%

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

Ren

Chen

2015

IET Control Theory & Applications

131

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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...

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Section: Finite-time Leader-following Consensus Control Design and Anmentioning

confidence: 99%

Section: Finite-time Leader-following Consensus Control Design and Anmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

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

Ren

Chen

2015

IET Control Theory & Applications

131

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“…Especially, consensus and tracking problems for multi-agent systems has been intensively investigated (Cui & Jia, 2012;Du, Li, & Shi, 2012;Hong, Hu, & Gao, 2006;Hu, 2010;Park, Lee, Son, Kwon, & Cha, 2013;Qin, Gao, & Zheng, 2011;Shen, Jiang, Shi, & Zhao, 2013;Sun & Guan, 2013;Xie, Liu, Wang, & Jia, 2009;Xie & Wang, 2012;Yu, Chen, Cao, & Kurths, 2010;Zhang & Tian, 2013). Specifically, Zhang and Tian (2013), studies the consensus problem of multi-agent systems with multiple time delays and Shen et al (2013), proposes a fuzzy tracking control scheme which can minimise the time delay due to fault diagnosis and reduce the adverse effect on tracking performance.…”

Section: Introductionmentioning

confidence: 97%

Sliding mode control for multi-agent systems under a time-varying topology

Dong

Chai

Zhang

et al. 2014

International Journal of Systems Science

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This paper addresses the tracking problem of a class of multi-agent systems under uncertain communication environments which has been modelled by a finite number of constant Laplacian matrices together with their corresponding scheduling functions. Sliding mode control method is applied to solve this nonlinear tracking problem under a time-varying topology. The controller of each tracking agent has been designed by using only its own and neighbours' information. Sufficient conditions for the existence of a sliding mode control tracking strategy have been provided by the solvability of linear matrix inequalities. At the end of this work, numerical simulations are employed to demonstrate the effectiveness of the proposed sliding mode control tracking strategy.

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Robust fixed‐time connectivity preserving consensus of nonlinear multi‐agent systems with disturbance

Sun

Wang

Liu

et al. 2021

Intl J Robust & Nonlinear

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This article studies the fixed-time tracking consensus of second-order nonlinear multi-agent systems with disturbance. To make the fixed-time tracking consensus, a consensus protocol based on the integral sliding mode surface is proposed, which can ensure the adjacent agents remain within a limited communication range in the communication process. By adopting Lyapunov stability theory and matrix theory, sufficient conditions for the fixed-time tracking consensus are given, and a bound of the settling time is obtained. Finally, a simulation example is presented to verify the potential correctness of the obtained results.

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Finite-time consensus for leader-following second-order multi-agent system

Cited by 57 publications

References 29 publications

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

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

Sliding mode control for multi-agent systems under a time-varying topology

Robust fixed‐time connectivity preserving consensus of nonlinear multi‐agent systems with disturbance

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