Model-Free Formation Control: Multi-Input Iterative Learning Super-Twisting Approach

This work proposes an economic model-free super twisting control (STWC) algorithm for the formation constrained tracking of a singularly perturbed multiagent system. Specifically, the intelligent model-free control framework is designed to be the sum of a multi-input STWC and an iterative learning control (ILC). First, time scales are artificially introduced into the STWC for the multiagent formation construction, without overestimating the control gains. Then, the input-output data collected from the iterative experiments are used to learn the model of unknown repeated uncertainties, and drive the whole system toward satisfactory consensus tracking performance. By utilizing the
$\epsilon $
-dependent Lyapunov method, the convergence properties of the STWC-type ILC are rigorously analyzed in both the iteration domain and the time domain. The selection method of the design parameters is also provided. Simulation results validate the effectiveness of the proposed controller in terms of formation construction, trajectory tracking, and robustness to system uncertainties.