Multi-Input Enhanced Data-Driven Discrete-Time Adaptive ILC

Abstract

In Chap. 7, a data-driven DAILC is presented via an iterative dynamical linearization (IDL) approach and achieves a perfect convergence even though the initial states and desired trajectories are iteratively varying. However, the IDL approach employed in Chap. 7 merely makes use of control information from an immediately past one sample instant even if the original system itself is of higher order in control input. In other words, the dynamic effect on the system output from the control input at earlier time instants is not considered. Another weakness of the IDL in Chap. 7 is that the resulting linear data model includes only one parameter representing the whole system uncertainties consisting of disturbances, noises, nonlinearities, structural uncertainties, etc. In other words, all dynamical characteristics of the original nonlinear system are represented by a single scalar parameter only. As a result, it may fail to capture the desired dynamics when the complexity of a process is increased significantly. More recently, a multi-lagged-input-based IDL technique Chi et al. (2015) is developed and a linear input-output data model is built along the iteration direction by using multi-lagged inputs and their corresponding parameters. The complexity of the original systems is reduced by using multi-dimension components of the parameter vector. However, the controller analysis and synthesis in Chi et al. (2015) requires that the target reference is identical among all iterations.