Prescribed‐Time Distributed Optimization for Multi‐agent Systems Over Unbalanced Directed Networks

ABSTRACT This paper investigates the prescribed‐time distributed convex optimization problem for multi‐agent systems with double‐integrator over unbalanced directed networks. In the continuous‐time setting, a prescribed‐time distributed optimization algorithm is proposed. By introducing an adjustment function, an estimator with prescribed‐time convergence is designed, which makes the algorithm independent of the left eigenvector associated with the zero eigenvalue of the Laplacian matrix. Additionally, we establish a prescribed‐time convergence theory, and then prove that the proposed algorithm converges to the optimal solution within the prescribed‐time and maintains optimality thereafter. Finally, two simulation experiments are employed to support the validity of the algorithm.