ILC-Motivated Formation Algorithm for Multi-Agent Systems With Communication Time-Delays

In this paper, a high-precision formation control problem is addressed for multi-agent systems in the presence of switching topologies and communication time-delays. All agents are aimed at achieving the desired relative formation between each other over a finite-time interval which can be specified. Based on the nearest neighbor interaction rule, a cooperative iterative learning control (ILC) algorithm is proposed. It is shown that the resulting cooperative ILC process of multi-agent formation systems converges exponentially fast if and only if the union of interaction digraphs (without being affected by communication time-delays) jointly has a spanning tree for each time step along the iteration axis. In particular, if there exists a time-varying reference trajectory for a portion of agents, then not only can the relative formation between agents be guaranteed but also the formation shape can be regularized simultaneously.