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Linear-quadratic zero-sum differential games for generalized statespace systems

机译：广义状态空间系统的线性二次零和微分对策

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摘要

In this note, we consider linear-quadratic zero-sum differential games for generalized state space systems. It is well known that a unique linear feedback saddle-point solution can exist in the game of state space systems. However, for the generalized state space system, we show that the game admits uncountably many linear feedback saddle-point solutions. Sufficient conditions for the existence of Linear feedback saddlepoint solutions are found. A constructive method is given to find these linear feedback saddle-point solutions. A simple example is included to illustrate the nonuniqueness of the linear feedback saddle-point solutions
机译：在本文中，我们考虑了广义状态空间系统的线性二次零和微分博弈。众所周知，状态空间系统的游戏中可能存在独特的线性反馈鞍点解。但是，对于广义状态空间系统，我们证明了该游戏承认了无数个线性反馈鞍点解。找到存在线性反馈鞍点解的充分条件。给出了一种构造方法来找到这些线性反馈鞍点解。包含一个简单的示例来说明线性反馈鞍点解的非唯一性

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