Model-Free Adaptive Iterative Learning Control of High-Order Pseudo Partial Derivatives for Nonlinear Systems

In this work, a model-free adaptive iterative learning control of high-order pseudo partial derivatives is presented for a category of nonlinear discrete-time systems that have features defined by non-repetitive disturbances. Firstly, the nonlinear system is initially transformed into a dynamic linearized data model, taking into account external non-repetitive disturbances by the iterative dynamic linearized method. Simultaneously, a high-order estimation method is developed utilizing historical batch input and output data, and an iterative extended state observer is constructed for estimating non-repetitive disturbances in the linearized data model to compensate for actual disturbances; Secondly, a model-free adaptive iterative learning control approach was devised, this approach employs estimated values of high-order pseudo partial derivatives and non-repetitive disturbances. The idea of compressive mapping was used to illustrate the provided algorithm’s convergence, and the conditions required for its convergence were given. The study’s findings show that, within a limited period of time, the suggested method may lower the tracking error to the expected trajectory’s neighborhood, independent of explicit mathematical model information, and the proposed technique enhances tracking precision compared with low-order control algorithms. Finally, It has been shown through simulation results that the suggested strategy is effective in improving tracking accuracy.