Formation learning algorithms for mobile agents subject to 2-D dynamically changing topologies

In this paper, we consider a two-dimensional (2-D) formation problem for multi-agent systems subject to switching topologies that dynamically change along both a finite time axis and an infinite iteration axis. We present a distributed iterative learning control (ILC) algorithm via the nearest neighbor rules. By employing the 2-D approach, we develop both the asymptotic and exponentially fast convergence of our formation ILC, which can be guaranteed by conditions in terms of the spectral radius and the matrix norms, respectively.