An optimal filter for updated input of iterative learning controllers with multiplicative and additive noises

Multiplicative and additive noises, arising from both sensor-to-controller and controller-to-actuator channels, affect the convergence performance of wireless networked iterative learning control (ILC) systems. In order to guarantee the convergence performance of such ILC systems, this paper designs an input filter at the actuator side for estimating the controller updated input. Specifically, a P-type learning controller is considered firstly, and then a mathematical model is developed to describe the transmission processes of both measured output data and updated input data with the effect of those noises. On the basis of state augmentation, these two data transmission processes are further combined with the controller learning process to build a filtering model. Finally, according to this filtering model and the orthogonality projection theory, the optimal input filter in the sense of linear minimum variance is designed in front of actuators. The convergence performance of the filtering error covariance matrix is analysed theoretically. Furthermore, because the input filter is designed only with the controller learning process and the two data transmission processes, the convergence performance of any system with the considered controller can be improved by driving with the filtered input. Finally, numerical results are given to illustrate the effectiveness of the proposed method.