N人线性-非二次微分对策

N-Person Linear-Nonquadratic Differential Game

研究受多个局中人(人数可任意)影响的线性时变常微分系统和非二次目标泛函组构成的非零和微分对策问题.给出了两个拟Riccati偏微分方程组——(80)和(23),以及相应于方程组(23)的非线性积分方程组族(43).运用方程组(80)的regular解推导出了闭环Nash均衡策略;利用Pontryagin最大值原理和方程组(23)的normal解得出了开环Nash均衡策略的闭环表示;还揭示了(43)之解族与(23)之解两者的双向联系.

The nonzero-sum differential game problem consisting of linear time-variant ordinary differential system driven by n-person and nonquadratie objective functionals is studied. Two quasi-Riecati equations--（80） and （23）, and a nonlinear integral equations family--（43） are given. Taking advantage of a regular solution of （80）, a closed-loop Nash equilibrium strategy is derived; A closed-loop representation of the open-loop Nash equilibrium strategy is obtained by making use of Pontryagin＇s maximum principle and the normal solution of （23）. Besides, the two-way relationships between the solutions family of （43） and the solution of （23） are revealed.