The authors regret the implementation order of data augmentation and data splitting was incorrectly stated. Data augmentation should be implemented after data splitting. While the correct implementation order and its impacts on leakage detection performance were accurately discussed in Section 3.2 “Biased results caused by data leakage”, there were errors in the highlights, abstract, and conclusions sections. The corrections are as follows: 1. The second highlight should be corrected to “Data augmentation after splitting prevents biased results due to data leakage.”2. In the abstract, the corresponding sentence should be corrected to “Results indicate the importance of implementing data augmentation after data splitting to prevent data leakage and overly optimistic outcomes.”3. In the second paragraph of the conclusions, the first sentence should be corrected to “It is recommended to implement data augmentation after data splitting to avoid data leakage, which could lead to biased and overly optimistic results.”The authors would like to apologise for any inconvenience caused.

An optimal adaptive compensation control scheme is proposed for a class of multi-input multi-output (MIMO) affine nonlinear systems with actuator failures. Considering stuck actuators and partial effectiveness failures, an adaptive dynamic programming method is adopted by using neural network to approximate the cost function. It adjust the weights of the neural network by using an online adaptive algorithm. An adaptive parameter adjustment law is designed to estimate the actuator failure coefficients. The proposed optimal adaptive compensation law can guarantee that the closed-loop system with actuator failures is stable and that the given reference signals are effectively tracked. Simulation results demonstrate the effectiveness of the proposed method.