This paper studies a class of robust cooperative learning control problems for directed networks of agents (a) with nonidentical nonlinear dynamics that do not satisfy a global Lipschitz condition and (b) in the presence of switching topologies, initial state shifts and external disturbances. All uncertainties are not only time-varying but also iteration-varying. It is shown that the relative formation of nonlinear agents achieved via cooperative learning can be guaranteed to converge to the desired formation exponentially fast as the number of iterations increases. A necessary and sufficient condition for exponential convergence of the cooperative learning process is that at each time step, the network topology graph of nonlinear agents can be rendered quasi-strongly connected through switching along the iteration axis. Simulation tests illustrate the effectiveness of our proposed cooperative learning results in refining arbitrary high precision relative formation of nonlinear agents. (C) 2016 Elsevier Ltd. All rights reserved.