Distributed Time-Varying Resource Allocation Optimization Based on Finite-Time Consensus Approach

In this letter, we study the distributed algorithm to solve the optimal resource allocation problem with time-varying cost functions and resources for continuous-time multi-agent systems. Subject to a coupled linear equality constraint, all agents aim to minimize the sum of all local cost functions known only to each agent. Since the cost functions and resources are time varying, the optimal solutions are trajectories changing over time rather than some constants. By combining the prediction-correction method with the finite-time nonsmooth consensus idea, we propose a distributed continuous-time algorithm that ensures that the states of all agents will track the corresponding time-varying optimal trajectories with vanishing error when the cost functions have identical Hessians. Here each agent exchanges only local information through a fixed connected undirected graph in a distributed manner. We perform a simulation for the grid-connected battery energy storage system to illustrate the effectiveness of the proposed distributed continuous-time optimal resource allocation algorithm.