On General Linear Encoding-Decoding Pairs for Quantized Iterative Learning Control

As control systems increasingly rely on limited-bandwidth networks, quantization and data rate constraints present significant challenges for iterative learning control (ILC). This study aims to design a general framework of linear encoding-decoding pairs for quantized ILC under channel transmission constraints. We first develop a unified mathematical framework that integrates existing encoding-decoding schemes within the quantized ILC loop, enabling both the linear encoder and decoder designs to be parameterized by a common set. By employing a p-type controller, we derive a convergence criterion for quantized ILC using the general linear encoding-decoding pair. Furthermore, we introduce a control signal fidelity metric (CSFM) to quantify the discrepancy between the control signal generated with and without a general linear encoding-decoding pair. Based on the CSFM, we provide systematic guidelines for selecting the parameters of the linear encoding-decoding pair. Finally, we establish practical selection rules for the parameters of linear encoding-decoding pairs when finite-level quantizers are used. These rules ensure that no saturation occurs while minimizing both the steady-state output tracking error and the CSFM, thus facilitating the practical quantizer selection in quantized ILC. The theoretical findings are validated through simulations involving industrial robot joint models.