In this article, an iterative learning approach is proposed for the formation control of discrete-time multi-agent systems, where the trial length of each learning iteration is randomly varying. In particular, a modified state error related to the prescribed formation is defined by taking into account the nonuniform actual trial length that could be different from the desired one. Then, a P-type iterative learning protocol is established for switching networks of agents subject to nonuniform trial lengths, and the convergence analyses are given for the fixed and the iteration-varying initial conditions respectively. It shows that through iterative learning, the given formation will be maintained among multiple agents in the entire time interval of one trial. In the end, simulations are done to demonstrate the correctness of the obtained theoretical results.

Two challenging problems are addressed in this work for the convergence analysis of iterative learning control (ILC), that is, the rigorous assumption on repetitive conditions and the severe dependence on linear or nonlinear parametric models. Consequently, a data‐based analysis method of ILC is presented for a general multi‐input multi‐output nonaffine nonlinear system in the existence of multiple nonrepetitive uncertainties in initial states, external disturbances, reference trajectories, and plant models. An extended iterative dynamic relationship is constructed to extract the linear relationship of I/O dynamics for a nonaffine nonlinear system between two different iterations. The data‐based double dynamics analysis method is developed for analyzing that the tracking error is convergent and the I/O sequence is bounded. The tracking error is shown to converge to a finite bound related to nonrepetitive uncertainties and achieve a perfect convergence if nonrepetitive uncertainties are also iteratively convergent to zero. Notably, the presented analysis method merely uses the I/O data without relying on the plant model. Simulations validate the effectiveness of our theoretical results.