Distributed Optimization of Single-Integrator Systems With Prescribed-Time Convergence

This article considers the prescribed-time optimization problem of multiagent systems (MASs) under two types of control protocols, namely prescribed-time continuous protocol and its event-triggered extension. Firstly, the two-stage prescribed-time continuous protocol is designed to optimize the global cost function, which is the sum of all local objective cost functions. The event-triggered mechanism is then combined with continuous protocol from an energy saving perspective. Moreover, it is proved in detail that using the event-triggered function will not happen Zeno behavior. Secondly, to avoid using the global gradient information, the prescribed-time optimization protocols are designed based on the idea of zero-gradient-sum. Different from the existing finite/fixed-time optimization results, one of the advantages of the proposed protocols is that the settling time can be independent of the initial state and system parameters. Finally, the correctness and validity of theoretical results are proved by numerical examples.