Algorithms for computing Minkowski operators and their application in differential games

Autor:	Pavel Dvurechensky, G. E. Ivanov
Rok vydání:	2014
Předmět:	Algebra Set (abstract data type) Computational Mathematics Nonlinear system TheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITY Differential game Minkowski space Element (category theory) Algorithm Minkowski addition Differential (mathematics) Convolution Mathematics
Zdroj:	Computational Mathematics and Mathematical Physics. 54:235-264
ISSN:	1555-6662 0965-5425
DOI:	10.1134/s0965542514020055
Popis:	The Minkowski operators are considered, which extend the concepts of the Minkowski sum and difference to the case where one of the summands depends on an element of the other term. The properties of these operators are examined. Convolution methods of computer geometry and algorithms for computing the values of the Minkowski operators are developed. These algorithms are used to construct epsilon-optimal control strategies in a nonlinear differential game with a nonconvex target set. The errors of the proposed algorithms are estimated in detail. Numerical results for the conflicting control of a nonlinear pendulum are presented.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::f38ec64f9edb668b0ec9de4745fd82cc https://doi.org/10.1134/s0965542514020055 Zobrazit plný text záznamu Full text from SpringerLink