Spatial Iterative Learning Control: Systems with input saturation

This paper proposes a novel Iterative Learning Control (ILC) framework for spatial tracking. Spatial tracking means that the temporal component is not fixed which violates the standing assumption on time intervals in traditional ILC. The proposed framework allows for the length of the time interval to change with each iteration. To relate the spatial information from the past to the present iteration, the concept of spatial projection is proposed. A class of nonlinear uncertain systems with input saturation is chosen for demonstration. An a appropriate ILC control law, exploiting the spatial projection idea, is proposed and the corresponding convergence analysis, based on the Composite Energy Function, is carried out. It is shown that spatial tracking is achieved under appropriate assumptions related to spatial projection and provided that the desired trajectory is realizable within the saturation bound. Finally, simulation results illustrate the predicted convergence.