Adaptive Gain Design

In practical applications, stochastic noises are introduced into the system dynamics due to various factors such as mechanical vibration and measurement error. These noises need to be effectively addressed through novel frameworks and techniques. In this regard, ILC for stochastic systems has garnered significant attention Shen and Wang (2014). One common approach is the application of zero-phase low-pass and linear-phase filters. The Kalman filtering (KF) technique Saab (2001a, 2003); Cao et al. (2016a, b), which obtains the direction regulation matrix by minimizing the error covariance matrix, has been observed to be highly effective in handling random noises. However, obtaining an optimal gain matrix requires specific knowledge about system matrices and statistical properties of random noises such as covariance matrices.