Distributed Optimal Resource Allocation in Prescribed-Time with Time-Varying Cost Functions

In this paper, we address time-varying resource allocation problems with heterogeneous Hessian matrices across agents. A novel prescribed-time convergent algorithm is proposed by integrating distributed average consensus estimators and a prediction-correction method. The global convergence is rigorously established via Lyapunov analysis. Numerical simulations on a battery energy storage system demonstrate the algorithm’s effectiveness in achieving optimal resource allocation within user-defined time horizons.