Abstract
Abstract 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.
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