A Continuous-Time Algorithm for Distributed Optimization With Nonuniform Time-Delay Under Switching and Unbalanced Digraphs

This paper studies the distributed optimization of continuous-time multi-agent systems with time-delay under switching digraphs. An auxiliary system which only requires the information of the number of adjacent agents is first constructed, then a class of new distributed optimization algorithms are proposed. As an application, we extend above algorithms to address distributed economic dispatch issues for smart grids. It is theoretically shown that the new illustrated distributed control strategies can asymptotically realize optimal consensus for multi-agent systems and optimal economic dispatch for smart grids, where the communication time-delay can be nonuniform, and the switching digraphs are uniformly jointly strongly connected. Finally, two simulation examples are provided to validate theoretical results.