Tracking control over a finite interval for multi-agent systems with a time-varying reference trajectory

In this paper, the tracking control problem for multi-agent systems is considered, where all agents in a directed graph are enabled to track a time-varying reference trajectory perfectly over a finite interval. A unified algorithm is presented for agents described by both discrete-time and continuous-time models through using the iterative learning approach. Even under the condition that the reference trajectory is available to not all but only a portion of agents, all agents can be guaranteed to (1) obtain the finite-time tracking except the initial time step in the discrete-time domain and (2) follow the reference trajectory with constant shifts at all the time in the continuous-time domain. If an initial rectifying action is used to continuous-time agents, then the finite-time tracking can be derived on an interval that can be specified. The proposed algorithms are also extended to achieve the formation control for multi-agent systems. Moreover, design conditions are developed for all algorithms, and two examples are given to demonstrate the effectiveness of the theoretical results.