This work presents a novel adaptive iterative learning control (AILC) approach for a class of nonlinear nonsquare systems with unknown control gain matrices. The proposed strategy avoids explicitly incorporating the control gain matrices into the control algorithms and does not require them to be invertible, thereby significantly broadening the applicability of AILC. In the proposed AILC method, a newly designed virtual control gain matrix is introduced, enabling the transformation of the unknown control gain matrix into a form of norm-bounded system uncertainty while accounting for input saturation. Building on this reformulation, a structurally simple AILC scheme is developed, incorporating an input-dependent auxiliary system to mitigate the effects of input constraints. Moreover, the proposed method is extended to nonaffine nonlinear systems by integrating neural network techniques. The convergence of the proposed AILC laws is rigorously analyzed within the composite energy function (CEF) framework, and its effectiveness is demonstrated through implementation on a permanent magnet synchronous motor (PMSM) and a numerical example of a nonaffine system.

The discrete algebraic reconstruction technique has many advantages in computed tomography and electron tomography. However, the number of gray levels and the absolute gray values that should be known in advance are typically not available in experiments especially when there are many gray levels in the image. In this paper, we report an automatic discrete tomography reconstruction algorithm to improve its feasibility in practice, without needing to know these two parameters. In our algorithm, the number of gray levels is estimated by labeling the connected components in the tomogram and the absolute values of them are determined by the modal value of each domain. The proposed algorithm was extensively validated on both simulated and experimental datasets. The results show that our algorithm can accurately recover not only the morphology but also the gray levels of the interested objects, even in the images with multiple gray levels. It is demonstrated that the presented algorithm is robust for eliminating missing wedge artifacts and tolerable for noisy data.