Learning Gain Self-Regulation Iterative Learning Control for Suppressing Singular System Measurement Noise

In this paper, in order to improve the tracking precision and convergence speed of singular systems with measurement noise in the limited interval, an iterative learning control algorithm with learning gain self-regulation is proposed under the condition of incompletely known model information of the singular systems. The proposed self-regulation learning gain is constructed by using the left multiplication of a diagonal matrix by constant learning gain. The diagonal matrix has consisted of nonlinear functions with self-regulation characteristic according to error amplitude. And, the contraction mapping method is used to prove that the proposed algorithm can make the tracking error converge to a bound as the iterations increase in the limited time interval. The bound is only related to both system parameter and external disturbance. When the external disturbance is completely eliminated and iterations converge to infinite, system output can track precisely the desired trajectory. At the same time, the sufficient condition of the algorithm is derived. Furthermore, the simulation results show the effectiveness of the proposed algorithm.