Kolmogorov-Chaitin complexity of linear digital controllers implemented using fixed-point arithmetic

Abstract

The complexity of linear, fixed-point arithmetic, digital controllers is investigated from a Kolmogorov-Chaitin perspective. Based on the idea of Kolmogorov-Chaitin complexity, practical measures of complexity are developed for both state-space realizations, and for parallel and cascade realizations. The complexity of solutions to a restricted complexity controller benchmark problem is investigated using this measure. The results show that, from a Kolmogorov-Chaitin viewpoint, higher-order controllers with a shorter word-length may have a lower complexity but a better performance than lower-order controllers with longer word-length.