N Linear - Non-quadratic Differential Game

This paper studies the nonzero-sum differential game problem consisting of a linear time-variant system driven by N-person and corresponding objective functionals.Two quasi-Riccati equations—(4.1)and(6.1),and a nonlinear integral equations family—(5.1) are given.Taking ad-vantage of the regular solution of (6.1),a closed-loop Nash equilibrium strategy is derived;The 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 (4.1). Besides,the two-way relationships between the normal solution of (4.1) and the continuously differentiable solutions family of (5.1) are revealed.