Numerical Method Based on Hamilton System and Symplectic Algorithm to Differential Games

XU Zi-xiang; ZHOU De-yun; DENG Zi-chen

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Article Navigation > Applied Mathematics and Mechanics > 2006 > 27(3): 305-310

XU Zi-xiang, ZHOU De-yun, DENG Zi-chen. Numerical Method Based on Hamilton System and Symplectic Algorithm to Differential Games[J]. Applied Mathematics and Mechanics, 2006, 27(3): 305-310.

Citation:

XU Zi-xiang, ZHOU De-yun, DENG Zi-chen. Numerical Method Based on Hamilton System and Symplectic Algorithm to Differential Games[J]. Applied Mathematics and Mechanics, 2006, 27(3): 305-310.

Citation:

XU Zi-xiang, ZHOU De-yun, DENG Zi-chen. Numerical Method Based on Hamilton System and Symplectic Algorithm to Differential Games[J]. Applied Mathematics and Mechanics, 2006, 27(3): 305-310.

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Numerical Method Based on Hamilton System and Symplectic Algorithm to Differential Games

1.
School of Electron and Information, North-western Politechnical University, Xi'an 710072, P. R. China;

Received Date: 2004-11-23
Rev Recd Date: 2005-11-15
Publish Date: 2006-03-15

Abstract

Abstract

The resolution of differential games often concerns the difficult problem of Two Point Border Value(TPBV),then ascribe linear quadratic differential game to Hamilton system.To Hamilton system,the algorithm of symplectic geometry has the merits of being able to copy the dynamic structure of Hamilton system and to keep the measure of phase plane.From the point of view of Hamilton system,the symplectic characters of linear quadratic differential game were probed;And as a try,Symplectic-Runge-Kutta algorithm was inducted to the resolution of infinite horizon linear quadratic differential game.An example of numerical calculation was presented,and the result can illuminate the feasiblity of this method.At the same time,it embodies the fine conservation characteristics of symplectic algorithm to system energy.
- differential game,
- Hamilton system,
- algorithm of symplectic geometry,
- linear quadratic

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References(7)

References

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