Kolmogorov-Chaitin complexity of digital controller implementations. - Whidborne, James F.; McKernan, John; Gu, Da-Wei (Springer Science Business Media, 2006)
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 statespace realizations, parallel and cascade realizations, and for a newly proposed generalized implicit state-space realization. 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 lower complexity and better performance, than lower-order controllers with longer word-length.
Keywords: Controller complexity; finite-precision arithmetic; finite word length; digital controller; Kolmogorov-Chaitin complexity