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Distributed Containment Control for Multiple Unknown Second-Order Nonlinear Systems With Application to Networked Lagrangian Systems

机译:多个未知二阶非线性系统的分布式容纳控制及其在网络拉格朗日系统中的应用

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摘要

In this paper, we consider the distributed containment control problem for multiagent systems with unknown nonlinear dynamics. More specifically, we focus on multiple second-order nonlinear systems and networked Lagrangian systems. We first study the distributed containment control problem for multiple second-order nonlinear systems with multiple dynamic leaders in the presence of unknown nonlinearities and external disturbances under a general directed graph that characterizes the interaction among the leaders and the followers. A distributed adaptive control algorithm with an adaptive gain design based on the approximation capability of neural networks is proposed. We present a necessary and sufficient condition on the directed graph such that the containment error can be reduced as small as desired. As a byproduct, the leaderless consensus problem is solved with asymptotical convergence. Because relative velocity measurements between neighbors are generally more difficult to obtain than relative position measurements, we then propose a distributed containment control algorithm without using neighbors’ velocity information. A two-step Lyapunov-based method is used to study the convergence of the closed-loop system. Next, we apply the ideas to deal with the containment control problem for networked unknown Lagrangian systems under a general directed graph. All the proposed algorithms are distributed and can be implemented using only local measurements in the absence of communication. Finally, simulation examples are provided to show the effectiveness of the proposed control algorithms.
机译:在本文中,我们考虑了具有未知非线性动力学的多主体系统的分布式容纳控制问题。更具体地说,我们专注于多个二阶非线性系统和网络拉格朗日系统。我们首先研究了在具有未知非线性和外部干扰的情况下,具有多个动态领导者的多个二阶非线性系统的分布遏制控制问题,该图包含表征领导者和跟随者之间相互作用的一般有向图。提出了一种基于神经网络逼近能力的具有自适应增益设计的分布式自适应控制算法。我们在有向图上提出了一个必要和充分的条件,以便可以将容纳误差减小到所需的最小程度。作为副产品,无领导者共识问题通过渐近收敛得以解决。由于邻居之间的相对速度测量通常比相对位置测量更难获得,因此我们提出了一种不使用邻居速度信息的分布式遏制控制算法。基于李雅普诺夫的两步法用于研究闭环系统的收敛性。接下来,我们将这些思想应用于在一般有向图下处理网络未知拉格朗日系统的容纳控制问题。所有提出的算法都是分布式的,并且可以在没有通信的情况下仅使用本地测量来实现。最后,提供了仿真实例以说明所提出的控制算法的有效性。

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