Data-Driven Iterative Learning Control of Nonlinear Systems by Adaptive Model Matching

Iterative learning control (ILC) has proven successful in the industry for enhancing tracking performance of repetitive tasks. The high accuracy and fast convergence of ILC algorithms hinge on: 1) the knowledge of the system model and 2) an effective learning algorithm. For general industrial systems with nonlinear dynamics, this raises technical challenges because acquiring a nonlinear dynamical model or several linearized models at different operating points may be difficult and costly. It is also nontrivial to determine the learning algorithm for the complex model obtained. To address these challenges, this article proposes a novel data-driven ILC algorithm for single-input-single-output nonlinear systems. Without explicit nonlinear models, our algorithm treats the nonlinear system as an unknown linear time-varying system linearized on a specified input–output (I/O) trajectory in each ILC iteration. A linearly parameterized time-varying adaptive filter is constructed in each ILC iteration so that, when cascading with the nonlinear plant, the I/O dynamics around the specified trajectory follow a linear time-invariant reference model. The ILC error trajectory is then filtered by the adaptive time-varying filter, which represents the inverse dynamics with a bandwidth specified by the reference model, to render fast convergence. The benefits of the proposed data-driven algorithm is demonstrated by comparing to a gradient and Hessian-based data-driven ILC algorithm on a prototypical two-degree-of-freedom nonlinear pendulum.