Parallel algorithm for calculating the invariant sets of high-dimensional linear systems under uncertainty

Abstract

The development of efficient computational methods for synthesizing controls of high-dimensional linear systems is an important problem in theoretical mathematics and its applications. This is especially true for systems with geometrical constraints imposed on the controls and uncertain disturbances. It is well known that the synthesis of target controls under the indicated conditions is based on the construction of weakly invariant sets (reverse reachable sets) generated by the solving equations of the process under study. Methods for constructing such equations and corresponding invariant sets are described, and the computational features for high-dimensional systems are discussed. The approaches proposed are based on the previously developed theory and methods of ellipsoidal approximations of multivalued functions.