Accelerated Iterative Learning Control for Linear Discrete Systems with Parametric Perturbation and Measurement Noise

Abstract

An iterative learning control algorithm based on error backward association and control parameter correction has been proposed for a class of linear discrete time-invariant systems with repeated operation characteristics, parameter disturbance, and measurement noise taking PD type example. Firstly, the concrete form of the accelerated learning law is presented, based on the detailed description of how the control factor is obtained in the algorithm. Secondly, with the help of the vector method, the convergence of the algorithm for the strict mathematical proof, combined with the theory of spectral radius, sucient conditions for the convergence of the algorithm is presented for parameter determination and no noise, parameter uncertainty but excluding measurement noise, parameters uncertainty and with measurement noise, and the measurement noise of four types of scenarios respectively. Finally, the theoretical results show that the convergence rate mainly depends on the size of the controlled object, the learning parameters of the control law, the correction coecient, the association factor and the learning interval. Simulation results show that the proposed algorithm has a faster convergence rate than the traditional PD algorithm under the same conditions.