Vol. 25, no. 1, 2019
A fixed-time package guidance problem is considered for a linear controlled dynamical system with a finite set of initial states. The control set is convex and compact and the target set is convex and closed. The paper focuses on the case where the set of initial states has singular clusters for which the existing algorithm for estimating the elements of a guiding program package is not applicable. It is suggested to consider a perturbed problem of augmented program guidance with a smoothed control set. It is proved that the motions of the original and perturbed problems are close to each other at the terminal time; the corresponding estimates are provided. In the case of an augmented target set with nonempty interior, it is also shown that a solution of the augmented program guidance problem that is precisely guiding to the target set can be obtained by applying the existing algorithm for the perturbed problem with compressed target set. The suggested theoretical constructions are illustrated with a model example.
Keywords: incomplete information, linear dynamical system, guidance problem, program package, singular cluster, smooth approximation
Received November 23, 2018;
Revised December 27, 2018;
Accepted January 14, 2018
Funding Agency: This work was supported by the Russian Science Foundation (project no. 14-11-00539).
Sergei Mikhailovich Orlov, Cand. Sci. (Phys.-Math.), Lomonosov Moscow State University, Moscow, 119991 Russia; Research Scholar, International Institute for Applied Systems Analysis, Laxenburg, 2361 Austria, e-mail: sergey.orlov@cs.msu.ru
Nikita Vital’evich Strelkovskii. Cand. Sci. (Phys.-Math.), International Institute for Applied Systems Analysis, Laxenburg, 2361 Austria; Lomonosov Moscow State University, Moscow, 119991 Russia, e-mail: strelkon@iiasa.ac.at
Cite this article as: S.M. Orlov, N.V. Strelkovskii. Calculation of elements of a guiding program package for singular clusters of the set of initial states in the package guidance problem, Trudy Instituta Matematiki i Mekhaniki URO RAN, 2019, vol. 25, no. 1, pp. 150-165.
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