Distributed Asynchronous Optimization of Multiagent Systems: Convergence Analysis and Its Application

This article focuses on solving a distributed convex optimization problem of multiagent systems with multiple inequality constraints. Considering communications between agents are prone to failures and not synchronized among themselves in some cases, a novel asynchronous adaptive step sizes-DIGing algorithm is proposed through integrating the projection operators and logic-
and
framework. In specific, a bilaterally adjustable adaptive step size mechanism is introduced to automatically abandon the irrational evolutionary route which relieves the limitations of traditional DIGing algorithm. By adopting the operator theory, the almost sure convergence of the proposed algorithm under asynchronous communication is proved. Finally, the theoretical and simulation results for the plantwide optimization problem in the ethylene production process illustrate the effectiveness of the proposed algorithm.