Prescribed Time Consensus Control of Multi-Agent Systems With Minimized Time-Varying Cost Function

In this note, a fully distributed and prescribed-time control approach is developed to achieve consensus for multiple agent systems (MAS) under certain optimal constraints. By virtue of local gradient information, a new estimator is first constructed to acquire global gradient information. Based on the well known result on fixed-time control, a novel prescribed time lemma is derived by specifying certain design parameters properly, with which the three objectives (consensus, estimation and optimization) are achieved within prescribed time irrespective of initial states or any other design parameters. The benefits and effectiveness are verified by numerical simulation.