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Distributed finite-time containment control for second-order nonlinear multi-agent systems

机译：二阶非线性多智能体系统的分布式有限时间约束控制

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This paper considers the finite-time containment control problem for a class of second-order nonlinear multi-agent systems with external disturbances under the directed topology graph. The considered nonlinear systems are composed of multiple dynamic leaders, and they have only a subset of the followers with their accessing to the leaders. Firstly, by using the one-hop neighbors' information, a second-order finite-time distributed observer estimator protocol is constructed to achieve accurate estimation of the weighted average of the velocities and positions of the leaders. Furthermore, it is proved that the proposed estimator protocol can guarantee accurate estimation of the weighted average of the velocities and positions of the leaders in the finite-time. Then, we design a new continuous nonlinear control protocol by means of the nonsingular terminal sliding mode. It is shown that by using proposed control protocol, the states of the followers can converge to the convex hull spanned by those of the leaders in the finite-time. In addition, the finite convergence time can be also explicitly estimated. Finally, the effectiveness of the obtained theoretical results is illustrated by the numerical simulation. (C) 2015 Elsevier Inc. All rights reserved.
机译：本文研究了有向拓扑图下一类具有外部干扰的二阶非线性多主体系统的时滞控制问题。所考虑的非线性系统由多个动态领导者组成，并且他们只有一部分跟随者可以访问领导者。首先，通过使用一跳邻居的信息，构建了二阶有限时间分布式观察者估计器协议，以实现对引导者的速度和位置的加权平均值的准确估计。此外，证明了所提出的估计器协议可以保证在有限时间内准确估计领导者的速度和位置的加权平均值。然后，我们通过非奇异终端滑模设计了一种新的连续非线性控制协议。结果表明，利用所提出的控制协议，随从的状态可以在有限的时间内收敛到由领导者跨越的凸包。此外，还可以明确估计有限的收敛时间。最后，通过数值模拟说明了所获得理论结果的有效性。 （C）2015 Elsevier Inc.保留所有权利。

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