Predefined-Time Distributed Optimization Algorithm for MASs with Unknown Disturbances

This paper proposes a distributed optimization algorithm for first-order multi-agent systems with unknown external disturbances. The objective is to minimize a global cost function, defined as the sum of all local cost functions, through local information exchange. A novel approach is introduced, combining an Extended State Observer (ESO) and a Time Base Generator (TBG), resulting in a predefined-time active disturbance rejection optimization method. The convergence and stability of the method are rigorously analyzed via Lyapunov theory, demonstrating that the algorithm ensures all agents’ states converge to an arbitrarily small neighborhood of the global minimum within a predefined time when disturbances are bounded. Numerical simulations confirm the algorithm’s effectiveness.