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.