A Predefined-Time Consensus Algorithm of Multi-Agent System for Distributed Constrained Optimization

This article proposes a multi-agent system with predefined-time consensus to solve distributed optimization problem subject to inconsistent constraint sets. Under some derived conditions, the predefined-time consensus of multi-agent system is guaranteed. Meanwhile, the states of agents are convergent with consensus to an optimal solution of the distributed constrained optimization. Compared to the system with finite time consensus, the proposed system has a fixed time consensus that can be estimated in advance. The suggested system for distributed constrained optimization not requires objective functions have a specific form and smooth. It suitable for the problem with bounded sub-differential of objective function and unbound gradient of objective function. Simulation results validate the theoretical analysis.