Conic Input Mapping Design of Constrained Optimal Iterative Learning Controller for Uncertain Systems

In this article, we study the optimal iterative learning control (ILC) for constrained systems with bounded uncertainties via a novel conic input mapping (CIM) design methodology. Due to the limited understanding of the process of interest, modeling uncertainties are generally inevitable, significantly reducing the convergence rate of the control systems. However, huge amounts of measured process data interacting with model uncertainties can easily be collected. Incorporating these data into the optimal controller design could unlock new opportunities to reduce the error of the current trail optimization. Based on several existing optimal ILC methods, we incorporate the online process data into the optimal and robust optimal ILC design, respectively. Our methodology, called CIM, utilizes the process data for the first time by applying the convex cone theory and maps the data into the design of control inputs. CIM-based optimal ILC and robust optimal ILC methods are developed for uncertain systems to achieve better control performance and a faster convergence rate. Next, rigorous theoretical analyses for the two methods have been presented, respectively. Finally, two illustrative numerical examples are provided to validate our methods with improved performance.