Prescribed-Time Robust Synchronization of Networked Heterogeneous Euler-Lagrange Systems

Abstract

In this paper, we propose a prescribed-time synchronization (PTS) algorithm for networked Euler-Lagrange systems subjected to external disturbances. Notably, the system matrix and the state of the leader agent are not accessible to all agents. The algorithm consists of distributed prescribed-time observers and local prescribed-time tracking controllers, dividing the PTS problem into prescribed-time convergence of distributed estimation errors and local tracking errors. Unlike most existing prescribed-time control methods, which achieve prescribed-time convergence by introducing specific time-varying gains and adjusting feedback values, we establish a class of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\mathcal {K}}_{T}$ </tex-math></inline-formula> functions and incorporate them into comparison functions to represent time-varying gains. By analyzing the properties of class <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\mathcal {K}}_{T}$ </tex-math></inline-formula> and comparison functions, we ensure the prescribed-time convergence of distributed estimation errors and local tracking errors, as well as the uniform boundedness of internal signals in the closed-loop systems. External disturbances are handled and dominated by the time-varying gains that tend to infinity as time approaches the prescribed time, while the control signal is still guaranteed to be bounded. Finally, a numerical example and a practical experiment demonstrate the effectiveness and innovation of the algorithm. Note to Practitioners—This paper aims to address the issue of prescribed-time synchronization for networked Euler-Lagrange systems. Existing research on asymptotic and finite-time convergence reveals that the settling time for synchronization is significantly influenced by the system’s initial values and controller parameters, making it challenging to be freely pre-designed. In contrast, our proposed prescribed-time synchronization algorithm ensures that all Euler-Lagrange systems achieve synchronization within a prescribed time. The effectiveness of our algorithm has been validated through numerical simulations and physical experiments. In practical applications, our algorithm can be utilized for cooperative control in robotic manipulators and drones. Compared to traditional PD controllers, our proposed algorithm not only offers the advantage of arbitrary settling time configuration in cooperation but also ensures faster response speeds and higher control accuracy, owing to the incorporation of time-varying gains.