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Algorithm for constructing an optimal control strategy in a nonlinear differential game with Lipschitz compactly supported payoff

Algorithm for constructing an optimal control strategy in a nonlinear differential game with... For a zero-sum differential game, we consider an algorithm for constructing optimal control strategies with the use of backward minimax constructions. The dynamics of the game is not necessarily linear, the players’ controls satisfy geometric constraints, and the terminal payoff function satisfies the Lipschitz condition and is compactly supported. The game value function is computed by multilinear interpolation of grid functions. We show that the algorithm error can be arbitrarily small if the discretization step in time is sufficiently small and the discretization step in the state space has a higher smallness order than the time discretization step. We show that the algorithm can be used for differential games with a terminal set. We present the results of computations for a problem of conflict control of a nonlinear pendulum. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Algorithm for constructing an optimal control strategy in a nonlinear differential game with Lipschitz compactly supported payoff

Ivanov, G.
Differential Equations , Volume 48 (4) – May 28, 2012
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References (18)

Publisher
Springer Journals
Copyright
Copyright © 2012 by Pleiades Publishing, Ltd.
Subject
Mathematics; Partial Differential Equations; Difference and Functional Equations; Ordinary Differential Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1134/S0012266112040106
Publisher site
See Article on Publisher Site

Abstract

For a zero-sum differential game, we consider an algorithm for constructing optimal control strategies with the use of backward minimax constructions. The dynamics of the game is not necessarily linear, the players’ controls satisfy geometric constraints, and the terminal payoff function satisfies the Lipschitz condition and is compactly supported. The game value function is computed by multilinear interpolation of grid functions. We show that the algorithm error can be arbitrarily small if the discretization step in time is sufficiently small and the discretization step in the state space has a higher smallness order than the time discretization step. We show that the algorithm can be used for differential games with a terminal set. We present the results of computations for a problem of conflict control of a nonlinear pendulum.

Journal

Differential Equations – Springer Journals

Published: May 28, 2012

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