An iteratively learned preview control scheme: Nonlinear systems with time-variant parameters in uncertainty

Abstract

Iterative learning control (ILC) and preview control are well-established methods for enhancing tracking performance. Their integration presents a promising approach for systems with time-varying uncertainties and previewable reference trajectories. This study proposes a novel iterative learning preview control (ILPC) framework for a class of linear parameter-varying (LPV) nonlinear systems with time-varying delays. The core design challenge addresses robust tracking under imperfect state information. To this end, an augmented error system (AES) is constructed by synthesizing the LPV plant dynamics, an observer for unmeasured states, the tracking error, and the previewable reference signal. This formulation transforms the tracking problem into a stability problem for the AES. A composite controller is then designed, utilizing the observer states, tracking error, and previewed future reference information. By employing a parameter-dependent Lyapunov function and linear matrix inequality (LMI) techniques, novel and less conservative sufficient conditions are derived to guarantee the asymptotic stability of the AES, ensuring robust tracking performance. The effectiveness and superiority of the proposed ILPC scheme are validated through numerical simulations, demonstrating its capability in handling time-varying uncertainties and delays.