Research ArticleUltra-fast formation control of high-order discrete-time multi-agent systems based on multi-step predictive mechanism

- Using the local neighbor-error knowledge, a multi-step predictive mechanism is established.
- Ultra-fast formation control for high-order multi-agent systems is achieved.
- The asymptotic convergence factor is improved by a power of q+1.
- A unified formation control framework is still kept.
- The new algorithm overcomes the influence of communication topology to the convergence speed.

This paper deals with the ultra-fast formation control problem of high-order discrete-time multi-agent systems. Using the local neighbor-error knowledge, a novel ultra-fast protocol with multi-step predictive information and self-feedback term is proposed. The asymptotic convergence factor is improved by a power of q+1 compared to the routine protocol. To some extent, the ultra-fast algorithm overcomes the influence of communication topology to the convergence speed. Furthermore, some sufficient conditions are given herein. The ones decouple the design of the synchronizing gains from the detailed graph properties, and explicitly reveal how the agent dynamic and the communication graph jointly affect the ultra-fast formationability. Finally, some simulations are worked out to illustrate the effectiveness of our theoretical results.