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On Grid Optimal Feedbacks to Control Problems of Prescribed Duration on the Plane

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Advances in Dynamic Games

Part of the book series: Annals of the International Society of Dynamic Games ((AISDG,volume 11))

Abstract

We consider optimal control problems of prescribed duration. A new numerical method is suggested to solve the problems of controlling until a given instant. The solution is based on a generalization of the method of characteristics for Hamilton–Jacobi–Bellman equations. Constructions of optimal grid synthesis are suggested and numerical algorithms solving the problems on the plane are created. Efficiency of the grid feedback is estimated. Results of simulations using the numerical algorithms are exposed.

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Authors and Affiliations

  1. Institute of Mathematics and Mechanics UrB RAS, S. Kovalevskaja str., 16, Ekaterinburg, 620990, Russia

    Nina N. Subbotina & Timofey B. Tokmantsev

Authors
  1. Nina N. Subbotina
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  2. Timofey B. Tokmantsev
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Corresponding author

Correspondence to Nina N. Subbotina .

Editor information

Editors and Affiliations

  1. , HEC Montréal, Department of Management Science, 3000 Chemin de la Côte-Sainte-Catherine, Montreal, H3T2A7, Canada

    Michèle Breton

  2. Wrocław University of Technology, Institute of Mathematics and Computer Sc, Wybrzeże Wyspiańskiego 27, Wrocław, PL-50-370, Poland

    Krzysztof Szajowski

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Subbotina, N.N., Tokmantsev, T.B. (2011). On Grid Optimal Feedbacks to Control Problems of Prescribed Duration on the Plane. In: Breton, M., Szajowski, K. (eds) Advances in Dynamic Games. Annals of the International Society of Dynamic Games, vol 11. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-8089-3_7

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