中文摘要：

苏(1， 1 ) 动态对称具有在在理论、适用的物理分析无界的量系统的基本重要性。在这份报纸，我们学习与苏一起与量系统联系的概括协调状态的控制(1， 1 ) 动态对称。在苏上基于一个假 Riemannian 度量标准(1， 1 ) 组，我们为最小化驾驶系统到需要的最后的状态的控制的领域 fluence 获得必要条件。进一步的分析证明候选人最佳的控制答案能被分类进正常、反常的 extremals。当控制 Hamiltonian 是非寓言的时，反常 extremals 能仅仅是经常的函数，当正常 extremals 能被 Weierstrass 椭圆形的函数根据控制 Hamiltonian 的 parabolicity 表示时。作为一种特殊情况，最大地挤压一个概括协调状态的最佳的控制解决方案是一个正弦曲线领域，它与在实验室被使用的一致。

英文摘要：

SU（1,1） dynamical symmetry is of fundamental importance in analyzing unbounded quantum systems in theoretical and applied physics. In this paper, we study the control of generalized coherent states associated with quantum systems with SU（1,1） dynamical symmetry. Based on a pseudo Riemannian metric on the SU（1,1） group, we obtain necessary conditions for minimizing the field fluence of controls that steer the system to the desired final state. Further analyses show that the candidate optimal control solutions can be classified into normal and abnormal extremals. The abnormal extremals can only be constant functions when the control Hamiltonian is non-parabolic, while the normal extremals can be expressed by Weierstrass elliptic functions according to the parabolicity of the control Hamiltonian. As a special case, the optimal control solution that maximally squeezes a generalized coherent state is a sinusoidal field, which is consistent with what is used in the laboratory.