Data-driven control for relative degree systems via iterative learning

Iterative learning control (ILC) is a kind of effective data-driven method that is developed based on online and/or offline input/output data. The main purpose of this paper is to supply a unified 2-D analysis approach for both continuous-time and discrete-time ILC systems with relative degree. It is shown that the 2-D Roesser system framework can be established for general ILC systems regardless of relative degree, under which convergence conditions can be provided to guarantee both asymptotic stability and monotonic convergence of the ILC processes. In particular, conditions for the monotonic convergence of ILC can be given in terms of linear matrix inequalities, and formulas for the updating law can be derived simultaneously. Simulation results are presented to illustrate the effectiveness of ILC determined through the 2-D design approach in dealing with the higher order relative degree problem of ILC systems, as well as the robustness of such ILC against uncertainties.