Estimation of reachability sets for large-scale uncertain systems: From theory to computation

The estimation of reachability sets for systems of high dimensions is a challenging issue due to its high computational complexity. For linear systems, an efficient way of calculating such estimates is to find their set-valued approximations provided by ellipsoidal calculus. The present paper deals with various aspects of such approach as applied to systems of high dimensions with unknown but bounded input disturbances. We present an innovative technique based on parallel computation that involves on-line mixing of ellipsoidal tubes found in parallel. This improves robustness of the ellipsoidal estimates. Finally discussed is an implementation of the algorithm intended for supercomputer clusters.