Robust H∞ Iterative Learning Control to Enhance Learning Speed and Reduce Remaining Error in Uncertain Linear Time-Invariant Systems

Iterative learning control (ILC) is a control scheme used in repetitive operations to reduce tracking errors by progressively refining the feedforward control input over multiple iterations. It is essential for ILC to guarantee convergence and accelerate the learning process while ensuring that the remaining error is reduced to improve tracking performance. However, in practical applications, achieving these objectives simultaneously is challenging, because model uncertainties can deteriorate the convergence rate and limit the achievable error reduction. To address these challenges, this paper presents a robust H∞ ILC framework for linear time-invariant systems subject to unstructured norm-bounded uncertainties. Both the convergence condition and the transfer function from the desired trajectory to the remaining error are formulated as a linear fractional transformation form composed of the nominal system, system uncertainty, and learning controllers. Based on this formulation, criteria are established to ensure not only robust convergence but also reduction of the remaining error. Unlike heuristic approaches, a systematic design algorithm is then proposed based on H∞ synthesis techniques with frequency domain weighting functions. This approach enables the synthesis of learning controllers that achieve faster convergence while maintaining the remaining error at a low level. The effectiveness of the proposed method is verified through a numerical example. The results demonstrate that the proposed algorithm significantly enhances tracking performance, achieving a reduction in the remaining error of more than 40 dB in terms of RMS compared to existing methods.