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 indicator of the efficiency of such algorithms is the rate of convergence of the learning error to a given value, ideally to zero. To increase the convergence rate of ILC algorithms, the authors in their recent works proposed a combination of the heavy ball method and the vector Lyapunov function method for repetitive processes that they had developed earlier. It turns out that this approach allows one to implicitly predict the gradient direction of the cost function, which allows one to significantly increase the convergence rate. In the examples, convergence to computer zero was achieved in just a few trial steps. However, this did not take into account the inevitably present random disturbances affecting the system and measurement noise, which reduce the achievable accuracy. In this paper, the specified approach is extended to the case of discrete systems, taking into account the aforementioned random factors. The results of modeling, confirming the theoretical results, are presented using the example of a laboratory portal robot.

Iterative learning control, repetitive processes, learning error, convergence rate, optimization methods, vector Lyapunov function, random disturbances, linear matrix inequality (LMI)