Evaluation of initial input effects on discrete-time stochastic iterative learning control

This paper is devoted to the performance evaluation of initial input effects on discrete-time iterative learning control (ILC) when the plants are subject to random iteration-varying disturbances. The optimal selection of initial input is provided from the viewpoints of both expectation and variance by investigating the derivative of the error function with respect to the initial input. It is shown that the nonrandom initial input minimizing the initial expected tracking error can enable the tracking error to possess the minimal expectation and variance at all iterations. Simulation tests are included to verify the theoretical study.