Kolmogorov-Chaitin Complexity of Digital Controller Implementations

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 state-space 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.