Distributed Predefined-Time Optimization for Basic Source Estimation

This paper introduces a distributed optimization algorithm for achieving formation control in multi-agent systems utilizing the zero-gradient sum property and the predefined-time stabilization framework. The distributed optimization scheme offers the flexibility to assign the settling time according to desired requirements, distinguishing it from existing finite and fixed-time schemes. Moreover, the algorithm eliminates the need for agents to exchange local gradients or Hessians of the cost functions. The algorithm’s effectiveness is validated through an application to a basic case of distributed source localization.