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Izv. IMI UdGU, 2016, Issue 2(48), Pages 82–151 (Mi iimi336)  

Numerical methods for solving differential games with nonterminal payoff

D. V. Kornev

N.N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi, 16, Yekaterinburg, 620219, Russia

Abstract: Linear convex positional differential games with geometric constraints on control actions and nonterminal payoff which evaluates a norm of a set of motion deviations at given instants of time from given target points are considered. Cases when the saddle point in a small game is either present or absent together with possible presence of additional integral constraints on control actions are studied. In each of these cases numerical methods for calculating the game value in appropriate classes of strategies and for constructing corresponding optimal control laws are elaborated. Numerical methods are based on backward constructions of upper convex hulls of auxiliary program functions. Domains of these functions are approximated by a pixel method, functions are stored as tables, upper convex hull is computed approximately as a lower envelope of a finite family of supporting hyperplanes to subgraphs of these functions. Details of software implementation for modern computational systems are discussed. Results of simulations in model examples are given.

Keywords: control theory, differential games, feedback strategies, resource constraints.

Funding Agency Grant Number
Russian Academy of Sciences - Federal Agency for Scientific Organizations 09-П-1-1015
12-П-1-1002
Russian Foundation for Basic Research 11-01-12088_офи_м
14-01-31319_мол_а
12-01-31247_мол_а
Ministry of Education and Science of the Russian Federation НШ-5927.2012.1


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Document Type: Article
UDC: 517.977.1/8
MSC: 49N35, 49N70, 49L20
Received: 01.10.2016

Citation: D. V. Kornev, “Numerical methods for solving differential games with nonterminal payoff”, Izv. IMI UdGU, 2016, no. 2(48), 82–151

Citation in format AMSBIB
\Bibitem{Kor16}
\by D.~V.~Kornev
\paper Numerical methods for solving differential games with nonterminal payoff
\jour Izv. IMI UdGU
\yr 2016
\issue 2(48)
\pages 82--151
\mathnet{http://mi.mathnet.ru/iimi336}
\elib{http://elibrary.ru/item.asp?id=27507186}


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  • Известия Института математики и информатики Удмуртского государственного университета Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta
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