Multi-Agent Energy Optimization: Laplacian Weights Tuning using Fréchet Discrete Gradient

In this paper, we introduce a novel optimization strategy aimed at reducing energy consumption in multi-agent systems. We consider a network represented by a graph with time-varying edge weights and employ the Fréchet discrete gradient method to optimize these weights over a fixed time horizon. The objective is to minimize a cost function associated with the control input energy while preserving consensus performance. The proposed gradient-based approach effectively reduces energy consumption during the transient and guarantees convergence for any chosen step size. Simulation results are provided to demonstrate the effectiveness and validate the theoretical properties of the method.