BILINEARIZED MODEL-BASED DISCRETE-TIME ITERATIVE LEARNING CONTROL FOR NONLINEAR SYSTEMS

Iterative learning control (ILC) learns to track a pre-defined maneuver with high accuracy through practice. It aims to approach the hardware reproducibility error level, beyond the accuracy of the system model used in the learning process. ILC can be used in spacecraft fine pointing sensors doing repeated scanning maneuvers. This paper improves upon linearized model-based ILC for nonlinear systems by using a Carleman bilinearized model instead. By capturing more nonlinear dynamics, a bilinearized model is a considerable improvement over the linearized model. This results in a faster convergence. To limit the learning inside of the neighborhood along the reference for linearization/bilinearization, a homotopy of the desired trajectory is used. Numerical examples show this bilinearized model based ILC algorithm converges substantially faster and does so in a manner closer to monotonic by comparison to ILC through linearization.