Ultra-fast consensus of discrete-time multi-agent systems with multi-step predictive output feedback

Abstract

This article addresses the ultra-fast consensus problem of high-order discrete-time multi-agent systems based on a unified consensus framework. A novel multi-step predictive output mechanism is proposed under a directed communication topology containing a spanning tree. By predicting the outputs of a network several steps ahead and adding this information into the consensus protocol, it is shown that the asymptotic convergence factor is improved by a power of q + 1 compared to the routine consensus. The difficult problem of selecting the optimal control gain is solved well by introducing a variable called convergence step. In addition, the ultra-fast formation achievement is studied on the basis of this new consensus protocol. Finally, the ultra-fast consensus with respect to a reference model and robust consensus is discussed. Some simulations are performed to illustrate the effectiveness of the theoretical results.