Time-varying formation of double-integrator discrete-time multi-agent systems with switching topology and time-delay

摘要

Time-varying formation problem for discrete-time multi-agent systems with double-integrator dynamics is investigated in this article, where the transmission delays and switching topology are discussed. The transmission time-delay can be nonuniform and the graph of the topology is not required to include a spanning tree all the time. A time-varying formation problem is defined; the corresponding formation vector and formation reference function are given. Based on the neighboring states, a linear formation protocol is presented. Using the state transformation method and properties of the stochastic matrix, sufficient conditions for the discrete-time multi-agent systems to complete the specified time-varying formation are given. A formation problem of four agents in a two-dimensional surface is simulated to illustrate the effectiveness of the protocol considering delays and switching topology.