Distributed Adaptive Event-Triggered Nash Equilibrium Seeking for Euler–Lagrange Systems Under Physical and Cyber Uncertainties

Distributed control of networked Euler–Lagrange systems has broad applications in industrial engineering. However, challenges, such as multiple uncertainties and resource-constrained networks, remain urgent issues to be resolved. This article addresses the issue of distributed Nash equilibrium seeking for Euler–Lagrange systems subject to physical and cyber uncertainties and limited communication resources. Specifically, considering uncertain parameters and time-varying uncertainties imposed on communication links, a new distributed strategy integrating an optimizer, a state regulator, a consensus algorithm, and an adaptive law is proposed for Euler–Lagrange systems, in which gains for consensus modules adaptively adjust to cope with the compromised communication weights caused by cyber uncertainties. Moreover, a dynamic gradient-based event-triggered scheme is put forward to enable information exchanges among neighbors and control updates when the predetermined triggered conditions are met. It is shown by theoretical analysis that the proposed event-triggered strategy is effective for significantly reducing the numbers of information transmission and control updates nearly without degrading convergence performance. Furthermore, the Zeno phenomenon is theoretically precluded under the proposed event-triggered scheme. Finally, the efficacy of the proposed method is validated through simulation cases on robotic manipulators.