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Generalized Chaplygin Problem: Theoretical Analysis and Numerical Experiments

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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.

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Authors and Affiliations

  1. Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, Russia

    Yu. N. Kiselev & S. N. Avvakumov

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  1. Yu. N. Kiselev
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  2. S. N. Avvakumov
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Correspondence to Yu. N. Kiselev or S. N. Avvakumov.

Additional information

Translated from Prikladnaya Matematika i Informatika, No. 46, 2014, pp. 5–45.

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Kiselev, Y.N., Avvakumov, S.N. Generalized Chaplygin Problem: Theoretical Analysis and Numerical Experiments. Comput Math Model 26, 299–335 (2015). https://doi.org/10.1007/s10598-015-9274-1

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  • DOI: https://doi.org/10.1007/s10598-015-9274-1

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