Distributed Aggregative Optimization of Uncertain Multiple Euler–Lagrange Systems: Comparative Analysis of Two Optimization-Control Strategies

This paper addresses the distributed aggregative optimization challenge in uncertain multiple Euler- Lagrange (EL) systems, where each EL agent's local objective function depends on its own position and the aggregation of all EL agents' positions. The goal is to control all EL agents to reach their optimal positions as defined by the aggregative optimization problem. Two distributed aggregative optimization algorithms are proposed for uncertain EL systems, which are based on distinct optimization-control strategies, namely the open-loop optimization-control strategy and the closed-loop optimization-control strategy. To address the model uncertainty in EL systems, an auxiliary second-order system is introduced, integrating with adaptive compensation and tracking techniques to mitigate the uncertainty. Given the unique structure of the aggregative optimization problem, two distributed estimation protocols are developed for handling the aggregation terms in the optimization problem. Specifically, in the open-loop optimization-control strategy, the optimization gradient is derived from the position information of the auxiliary system; whereas, in the closed-loop optimization-control strategy, the optimization gradient relies on the real-time position of the EL system. The convergence of both algorithms is rigorously proved. Unlike existing studies that mainly concentrate on distributed optimization algorithms based on either open-loop or closed-loop strategies, this paper is dedicated to conducting a comprehensive comparative analysis of open-loop and closed-loop optimization-control strategies, with a special emphasis on the robustness of the closed-loop strategy in counteracting external disturbances and variations. Finally, the proposed distributed aggregative optimization algorithms are applied to the optimal localization problem of networked marine vehicles with parameter uncertainties. Comprehensive simulation comparisons are conducted to verify the theoretical results.