Probability-based adaptive iterative learning control algorithm for suppressing the morphologically similar and varying-scale interferences

Abstract

Conventional iterative learning control (ILC) algorithm is designed for tasks with strictly repetitive characteristics, which is difficult to be satisfied in industrial applications. Thus, the applicational range of ILC is limited. Aiming at solving the problem of controlling the output to a certain range under the morphologically-similar but varying-scale interferences, finitely historical conditions are selected, of which a measurable and time-scale-concerned parameter is selected. Then, some clusters of the conditions are formulated, in which the probability distributions are initialised by the known conditions while the corresponding control inputs are initialised based on the conventional ILC algorithm. Next, based on the ideology of expectation maximization (EM) algorithm, the control inputs and the probability distributions are iteratively updated to make the ILC for suppressing the morphologically-similar and varying-scale interferences possible: (1) the control input is calculated by the prior-probability that current conditions belong to a cluster and the corresponding control inputs for the cluster; (2) the control input will be updated by the prior-probability and the control error; (3) the posterior-probability will be calculated and the cluster will be refreshed. Finally, probability distribution and corresponding control inputs will be gained for the novel ILC algorithm after enough iterations to make the error of the control smaller. By convergence analysis and an applicational simulation, the adaptivity and feasibility of the novel ILC algorithm have been proved.