Pre-specified-time coordination algorithm for convex optimization problems over weight-unbalanced networks

This paper investigates a group of convex optimization problems for swarm systems with directed and weight-unbalanced topologies, such as the economic dispatch problems with equality constraints. By using the multi-step planning method, a new pre-specified-time coordination algorithm is proposed to seek the optimal value of global objective function in a distributed manner. Here, the specified time represents the moment when convex optimization problem gets solution, which can be appointed in advance without additional fuzzy estimation. In addition, the convergence time of the proposed algorithm is calculated precisely with the aid of Kronecker matrix algebra and Lyapunov stability theory. Finally, some simulations are shown to demonstrate the usefulness and superiority of the new designed optimization algorithms.