Distributed Multi-Objective Fixed-time Optimization Algorithm Applied to Multi-Agent Systems

This paper addresses the multi-objective strongly convex optimization problem by designing a fixed-time optimization based on second-order integral multi-agent systems. The proposed algorithm includes a two-stage optimization process. In the first stage, each agent has a local objective controller that is designed to make each agent converge to the optimal state that minimizes respective local cost functions in a fixed time. Subsequently, the local optimal state obtained in the first stage is used as the initial state of the global objective controller, which allows to construct the global objective controller that makes the multiple agents’ states reach consensus in terms of the information interaction between neighboring agents and the Hessian matrix of the local cost function, where the consistency state is the global optimal state. In addition, the above optimization process is proved by the Lyapunov theory. Note that the designed controllers are not dependent on the initial state of the agents so that various tasks can be adapted. Finally, numerical simulation results are given to demonstrate the effectiveness of the proposed algorithm.