Distributed Approximate Aggregative Optimization of Unknown Pure-Feedback Systems With Sampled Neighbor Information.

This article addresses the distributed aggregative optimization (DAO) problem for high-order nonlinear systems with unknown pure-feedback dynamics over directed unbalanced networks, with the key contribution being the extension of DAO methods to high-order nonlinear systems. To achieve this, we first introduce auxiliary aggregative variables that integrate agent output and sampled neighbor information, progressively updated through a smoothing function. Using these variables and drawing inspiration from the dynamic average consensus-based approach, a pivotal theorem is introduced to facilitate the transformation of the DAO problem into a regulation problem, enabling the application of classical control methods to manage complex high-order dynamics. Furthermore, we present a control law based on prescribed performance functions and aggregative variables to solve the approximate aggregative optimization problem for high-order nonlinear agents with bounded disturbances. Finally, numerical examples are provided to validate the effectiveness of the proposed control scheme.