This paper aims to solve the problems of energy shaping-based consensus control in networked underactuated Euler–Lagrange systems (NUELSs) in the presence of communication and input delays. By appropriately introducing the auxiliary sliding mode variable describing local communication interaction among agents and the corresponding adaptive velocity observer in energy-shaping framework, two decentralized time-varying consensus tracking schemes are proposed for NUELSs. The developed schemes systematically integrate the energy of three parts: the system model energy of actuated and underactuated components, the energy of the controller dynamics and the energy of the adaptive update law, as the total energy. Then this total energy formulates the resultant Lyapunov function that can fully guarantee the distributed time-varying consensus tracking of NUELSs having time-varying communication and input delays. Furthermore, simulation examples of multiple flexible-joint manipulator systems characterized by NUELSs demonstrate the potential advantages of the proposed consensus schemes in stability, adaptability, and robustness. The effects of communication and input delays on cooperative tracking performance are also numerically investigated for NUELSs.

中文翻译：

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具有通信和输入延迟的网络欠驱动欧拉-拉格朗日系统中基于能量整形的共识控制

本文旨在解决存在通信和输入延迟的网络欠驱动欧拉-拉格朗日系统（NUELS）中基于能量整形的共识控制问题。通过在能量整形框架中适当引入描述代理之间本地通信交互的辅助滑模变量和相应的自适应速度观测器，提出了两种分散式时变共识跟踪方案。所开发的方案系统地整合了三部分的能量：驱动和欠驱动部件的系统模型能量、控制器动力学的能量和自适应更新律的能量，作为总能量。然后，这个总能量公式化得到的李亚普诺夫函数，可以充分保证具有时变通信和输入延迟的NUELS的分布式时变共识跟踪。此外，以NUELS为特征的多柔性关节机械臂系统的仿真例子证明了所提出的共识方案在稳定性、适应性和鲁棒性方面的潜在优势。还对 NUELS 的通信和输入延迟对协作跟踪性能的影响进行了数值研究。