Limited‐budget finite‐time average consensus design for multi‐agent systems

This study investigated the limited‐budget finite‐time average consensus problem of multi‐agent systems. Different from the existing results about the guaranteed‐cost asymptotical consensus, all agents can achieve the average consensus within a finite time and the limited budget can be given previously. Firstly, a novel consensus protocol is proposed with non‐linear cost indexes to trade off the control energy consumption against the consensus regulation performance for the limited budget within a finite time. Then, sufficient conditions for limited‐budget finite‐time average consensus design and analysis are respectively given, where the limited budget is utilised to determine the value range of the control gain, and the consensus value obtained by all agents is the average of initial states. Moreover, for the case without giving the limited budget, guaranteed‐cost finite‐time average consensus design and analysis criteria are presented, respectively, in which an upper bound of the cost index is determined. Finally, a numerical simulation is shown to illustrate the effectiveness of theoretical results.