caa a22 4500 606217142 CHVBK 20210128101106.0 cr unu---uuuuu 210128e20150701xx s 000 0 eng 10.1007/s10598-015-9274-1 doi (NATIONALLICENCE)springer-10.1007/s10598-015-9274-1 Generalized Chaplygin Problem: Theoretical Analysis and Numerical Experiments [Elektronische Daten] [Yu. Kiselev, S. Avvakumov] We investigate a modified Chaplygin problem with flight path enclosing the maximum area. A twodimensional controlled plant with simple motion and control region in the form of a smooth planar convex compactum with interior point O should describe, in a given time, a closed curve enclosing a plane region of maxi-mum area. The initial and the final points of the trajectory coincide. The direction of the velocity vector at the initial time is given. The problem is solved by the Pontryagin maximum principle. A procedure to construct a programmed optimal control is described. An optimal control law is described in synthesis form (feedback form). The theoretical analysis relies on the apparatus of support and distance functions. The optimal trajectory can be derived from the polar of the control region by simple linear transformations: multiplication by a positive number, rotation through a right angle, and parallel translation. Numerical experiments have been carried out. The discussion is illustrated with graphs. Springer Science+Business Media New York, 2015 optimal control nationallicence Pontryagin maximum principle nationallicence maximum-principle boundary-value problem nationallicence programmed control nationallicence feedback nationallicence support and distance functions nationallicence numerical experiments nationallicence Kiselev Yu Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, Russia aut Avvakumov S. Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, Russia aut Computational Mathematics and Modeling Springer US; http://www.springer-ny.com 26/3(2015-07-01), 299-335 1046-283X 26:3<299 2015 26 10598 https://doi.org/10.1007/s10598-015-9274-1 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10598-015-9274-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Kiselev Yu Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, Russia aut NATIONALLICENCE 700 1- Avvakumov S. Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, Russia aut NATIONALLICENCE 773 0- Computational Mathematics and Modeling Springer US; http://www.springer-ny.com 26/3(2015-07-01), 299-335 1046-283X 26:3<299 2015 26 10598