The linear quadratic differential game plays an important role in many fields. It is well known that the saddle point of linear quadratic differential game is given in a feedback form with a solution of Riccati differential equation. However, the control-related Riccati differential equation cannot be solved analytically in many cases. Then the optimal controls may be difficult to be implemented in practice. In order to simplify the forms of optimal controls, in this paper, we investigate a parametric approximate optimal control problem of linear quadratic differential game under uncertain environment. First, we introduce an uncertain linear quadratic differential game model and its analytic optimal controls. Then, an uncertain linear quadratic differential game model with constrained parametric control domain is formulated. Moreover, a parametric approximate optimization method is presented for solving the optimal control parameters. Finally, a counter terror problem is analyzed to show the efficiency of our presented method.

线性二次微分博弈在许多领域都发挥着重要作用。众所周知，线性二次微分对策的鞍点以具有Riccati微分方程解的反馈形式给出。但是，在许多情况下，无法解析地求解与控制相关的Riccati微分方程。然后，最佳控制可能难以在实践中实施。为了简化最优控制形式，本文研究了不确定环境下线性二次微分对策的参数近似最优控制问题。首先，我们介绍了一个不确定的线性二次微分博弈模型及其解析最优控制。然后，建立了具有约束参数控制域的不确定线性二次差分博弈模型。而且，提出了一种用于求解最优控制参数的参数近似优化方法。最后，对反恐问题进行了分析，以表明我们提出的方法的有效性。