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Variable Gain Iterative Learning Control with Initial Error Correction

For a class of nonlinear continuous multivariable (NCM) systems, a variable gain iterative learning control (ILC) algorithm with initial error correction is proposed to solve the tracking error of the system in a finite time interval. In this algorithm, system runtime period is divided into two sections, in the first section, ILC controller corrects the initial error of system from zero, and the run-time of this section will be shorten as the number of iteration increases; and then, system output tracks the desired output trajectory in the second section. Meanwhile, exponential variable gain with respect to time and iteration make the system output error converge quickly and reduce fluctuations. Theoretical proof and numerical simulation show the effectiveness of the algorithm.