A distributed prescribed-time optimization analysis for multi-agent systems

This paper considers the distributed prescribed-time optimization problem of multi-agent systems (MASs). Considering the strongly convex function of time-invariant for each agent, the two-stage distributed prescribed-time optimization algorithm is designed based on the idea of zero-gradient-sum. Meanwhile, in order to save system resources, the event-triggered control mechanism is introduced into the algorithm in this paper. In the first stage, the distributed prescribed-time event-triggered algorithm is proposed to minimize the local objective functions of each agent at the prescribed-time interval. In the second stage, the algorithm is driven to optimize the global cost function while maintaining the gradient sum of all local cost functions to zero. The criteria for achieving the consensus and optimization of MASs are obtained by using Lyapunov stability theory and optimization theory. Moreover, it is proved in detail that using the two triggering functions will not result in Zeno behavior. The numerical example is given to demonstrate the correctness of the theoretical analysis and the effectiveness of the control algorithms.