Accelerated Iterative Learning Control Algorithms for Discrete Systems under Random Disturbances

Iterative learning control (ILC) algorithms emerged in connection with the tasks of increasing the accuracy of repetitive operations performed by robots. They use information from past repetitions to adjust the control signal for the current repetition. In the ILC literature, these repetitions are called trial steps, trials, or passes. A critical efficiency index of such algorithms is the convergence rate of the learning error to a given value, ideally to zero. To increase the convergence rate of ILC algorithms, the authors have recently proposed a combination of the heavy ball method and the vector Lyapunov function method for repetitive processes. As it turns out, this approach allows implicitly predicting the gradient direction of the cost function and, thereby, significantly increasing the convergence rate. In the examples, convergence to computer zero was achieved in just a few trials; however, the inevitable random disturbances affecting the system and measurement noise reducing the achievable accuracy were both neglected. In this paper, the specified approach is extended to the case of discrete systems, taking into account the aforementioned random factors. Modeling results, confirming the theoretical results, are presented using the example of a laboratory portal robot.