Distributed predefined-time algorithms for optimal solution seeking in multi-agent systems subject to input disturbances

This paper presents a novel incremental consensus-based algorithm for solving a class of distributed optimization problems in multi-agent systems, considering input disturbances, equality constraints, and box constraints. Traditional methods rely on average consensus to maintain the satisfaction of equality constraints throughout the entire evolution process. However, in practical applications, input disturbances can disrupt these equality constraints, rendering traditional methods ineffective. To address this challenge, the proposed algorithm combines integration sliding mode control technology with the observer methodology, creating a unified framework capable of handling input disturbances and preventing the system state from deviating beyond the solution space defined by the equality and box constraints. Moreover, the proposed algorithm offers the advantage of ensuring that all agents reach the optimal solution within a predefined time frame. This settling time can be directly adjusted by modifying one or more parameters. Finally, several numerical examples are validated to demonstrate the effectiveness and performance of the proposed algorithm.