A Specified-Time Convergent Multiagent System for Distributed Optimization With a Time-Varying Objective Function

This technical note presents a specified-time convergent multiagent system for distributed optimization with a time-varying objective function subject to equality constraints. Different from the static optimal solutions to most existing distributed optimization problems, the optimal solutions are time varying due to the time-varying objective function in this problem. A distributed protocol law is designed to ensure all the agents' convergence to feasible and suboptimal solutions within a specified settling time and keep tracking the time-dependent optimal solutions. The specified-time convergence of the system and the asymptotic optimality of the solution generated by the system are proved based on the Lyapunov theory. A salient feature of the multiagent system is that its upper bound of settling time can be specified in advance. Two examples are presented to illustrate the theoretical results.