Distributed prescribed-time optimization for multiple euler-lagrange systems

This article addresses distributed consensus and optimization problem for multiple Euler-Lagrange systems by proposing a novel distributed control scheme, which is motivated by the practical problems including source seeking and communication relay through coordination of multiple mobile robots. The proposed scheme ensures that each Euler-Lagrange agent reaches the optimal solution for the team's objective function in a prescribed time, overcoming the limitations of finite-time and fixed-time distributed optimization algorithms in estimating convergence time. The control algorithm employs a distributed estimator to calculate the gradient vector of the team's global cost function. Subsequently, distributed prescribed-time controllers for each Euler-Lagrange individual are designed based on the gradient descent method, enabling all the Euler-Lagrange agents' states achieve optimal solution for the team's objective function. The system's prescribed-time convergence is examined via theoretical analysis using Lyapunov stability theory, and simulation experiments are conducted to confirm the controller's effectiveness.