Distributed Robust Optimization for Disturbed Multiagent Systems With Fixed-Time Synchronized Convergence

This article investigates fixed-time synchronized convergence for disturbed second-order multiagent systems (MASs) in distributed optimization under the zero-gradient-sum (ZGS) scheme. A fixed-time ZGS distributed optimization method via sliding mode is first proposed for the second-order MASs, which avoids local minimization and rejects disturbances. To further achieve time-synchronized convergence, a hierarchical robust optimization method is then introduced. It employs a time-varying function-based local-minimization-free ZGS scheme within a virtual MAS to generate a reference signal that reaches the global cost function's minimizer and a fixed-time synchronized sliding mode tracking controller to drive the original second-order MAS to track this signal. Beyond the capabilities of the first protocol, this method also ensures the time-synchronized convergence of each agent's state components, low conservatism in terms of convergence time bounds, and privacy preservation. Numerical simulations demonstrate the effectiveness of the proposed methods.