中文摘要：

为了实现统一混沌系统的镇定控制，根据最小值原理为统一混沌系统设计了最优控制器，该控制器能将统一混沌系统的两个不稳定的平衡点镇定；针对控制作用施加的三个不同位置，推导了最优控制的三种不同的切换控制曲线；特别是针对控制作用施加在第三个方程时因混沌系统对初始条件的极端敏感性而造成的其中一个不稳定平衡点无法镇定的情形而引入逻辑判断环节以保证控制作用的正确加入时刻进行了说明。所得到的控制规律是bang-bang控制，通过施加闭环控制后对系统状态变化和系统相轨迹投影的仿真结果证明了所建议方法的正确性。

英文摘要：

In order to realize the stabilizing control of the unified chaos system, optimal control was designed for the unified chaos system based on the Minimum Principle. The two equilibria of the unified chaos system, which are essentially unstable, can be stabilized by the optimal controller. In case of clarity and completeness, all the three different switching surfaces or curves which are depend on the imposed positions of the control signal are derived and the resulted control law is proved to be a bang-bang one. Logic decision part is employed to guarantee the right action of the control when it is added to the third equation so as to overcome the drawback of the single switching control. Simulation results of the transient process of the states and the projections of the phase locus of the closed control system are provided to demonstrate the effectiveness of the suggested scheme.