Algorithms for computing Minkowski operators and their application in differential games
Pavel DvurechenskyMoscow Institute of Physics and Technology (State University), Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141700, RussiaG. E. IvanovMoscow Institute of Physics and Technology (State University), Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141700, Russia
2014en
ABI
Abstract
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.
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