Robust PID-Type Iterative Learning Control for Nonlinear Square and Nonsquare Systems

In this work, a novel PID-type adaptive iterative learning control (AILC) method is proposed for a class of nonlinear systems with unspecified control gain matrices and bounded iterative-varying uncertainties. Unlike the existing iterative learning method with accumulation of control information, the new PID-type AILC avoids control information accumulation in traditional iterative learning control (ILC), maintaining convergence based on error information and confining iteration to parameter estimation, suitable for amplitude- or frequency-limited controllers. Different from the existing approaches of P-type AILC, this work extends ILC advances to PID-type AILC for nonlinear square or nonsquare systems with unknown control gain matrices, enhancing robustness through simultaneous convergence of integral and proportional error terms over a larger range. This analysis method diverges from traditional approaches relying on contraction mappings or asymptotic stability theorems; error convergence is analyzed using inequalities of a composite energy function (CEF). The effectiveness of this work has been validated through two illustrated examples. The results show that compared with P-type AILC, the convergence speed can be increased by approximately two to three times.