Calculation of elements of a guiding program package for singular clusters of the set of initial states in the package guidance problem (Q2185795)

The paper deals with a problem of package guidance at a given time moment for a linear controlled dynamical system with a finite set of initial states. The considered control set is convex whereas the target set is convex and closed. The authors address the case where the set of initial states has singular clusters for which the available algorithm for computing the elements of a guiding program package is not applicable. For this case, they suggest a new solving method based on passing to perturbed extended problem of program guidance and on the procedure of approximation of a weakly convex (in general case) set of control of a smooth convex compact. The final section of the paper gives a model numerical example illustrating the presented technique.