Abstract
The resolution of differential games often concerns the difficult problem of two points 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 keep the measure of phase plane. From the viewpoint of Hamilton system, the symplectic characters of linear quadratic differential game were probed; as a try, Symplectic-Runge-Kutta algorithm was presented for the resolution of infinite horizon linear quadratic differential game. An example of numerical calculation was given, and the result can illuminate the feasibility of this method. At the same time, it embodies the fine conservation characteristics of symplectic algorithm to system energy.
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Communicated by ZHONG Wan-xie
Project supported by the National Aeronautics Base Science Foundation of China (No.2000CB080601) and the National Defence Key Pre-research Program of China during the 10th Five-Year Plan Period (No.2002BK080602)
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Xu, Zx., Zhou, Dy. & Deng, Zc. Numerical method based on Hamilton system and symplectic algorithm to differential games. Appl Math Mech 27, 341–346 (2006). https://doi.org/10.1007/s10483-006-0309-y
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DOI: https://doi.org/10.1007/s10483-006-0309-y