Distributed approximate aggregative optimization of multiple Euler–Lagrange systems using only sampling measurements

Abstract

This article studies the distributed aggregative optimization for multiple Euler–Lagrange systems over directed networks. First, a new class of auxiliary aggregative variables is proposed that only utilize sampling measurements of adjacent outputs. Then, by selecting a smoothing function, we can gradually integrate the sampling information into new variables within the sampling period. Given the proposed variables, a key theorem is derived to transform the approximate aggregative optimization problem into a regulation problem, such that classical control methods can be utilized to regulate the aggregative variables for more complex dynamics. In addition, an adaptive fuzzy distributed control law is constructed based on aggregative variables, deadzone function and fuzzy system to solve the aggregative optimization for fully actuated Lagrangian agents with bounded disturbance. Finally, a numerical experiment is conducted to demonstrate the validity and effectiveness of the theoretical results.