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中文摘要：
这份报纸在有限时间的最佳的控制在二次的最佳的性能索引上涉及冗余的控制输入的效果。实际上，二次的性能上的冗余的控制输入的效果索引是相等的在 Riccati 微分方程(RDE ) 的解决方案上学习冗余的控制输入的效果。因此，一些足够的条件被介绍严格地减少有输入矩阵的列的 RDE 的答案增加了。特别，一个必要、足够的条件被导出严格地减少在控制输入扩展以后的同类的 RDE 的解决方案。而且，一个足够的条件被获得，它保证最小的控制精力索引严格地与输入扩展减少。冗余的控制输入能基于这些结果改进系统性能，这被显示出。一些例子被举说明相关问题的有效性。
英文摘要：
This paper is concerned with the effects of redundant control inputs on the quadratic optimal performance index in finite-time optimal control. Actually, the effects of redundant control input on quadratic performance index is equal to study the effects of the redundant control input on the solution of Riccati differential equation （RDE）. Hence, some sufficient conditions are presented to strictly decrease the solution of RDE with the column of input matrix increased. Especially, a necessary and sufficient condition is derived to strictly decrease the solution of the homogeneous RDE after control input extensions. Moreover, one sufficient condition is obtained, which guarantees that the minimum control energy index strictly decreases with input extension. It is shown that redundant control inputs can improve the system performance based on these results. Some examples are taken to illustrate the effectiveness of related problems.
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