Adaptive iterative learning control for 2-D nonlinear discrete systems with iteration-dependent uncertainties

In the existing high-order internal model (HOIM)-based iterative learning control (ILC) results, they are primarily concerned with 1-D systems with fixed orders and coefficients. This paper first investigates the iteration-dependent HOIM-based adaptive ILC problem for 2-D nonlinear discrete systems with unknown input gain and multiple unknown iteration-dependent parameters, which can be generated by multiple HOIMs with iteration-dependent orders and coefficients. The adaptive control law with parameter learning law is designed by using the recursive least squares algorithm. Under iteration-dependent boundary states and reference trajectory, the proposed adaptive ILC algorithm is capable to drive the ILC tracking error to be zero asymptotically. In addition, the established adaptive ILC results can be extended to 2-D nonlinear discrete systems with multiple iteration-dependent HOIM-based boundary states, reference trajectory, and external disturbances. Finally, an illustrative example on practical dynamical processes is provided to demonstrate the validity and feasibility of the designed method.